diff --git a/demo/browser/astronomy.browser.js b/demo/browser/astronomy.browser.js
index ecc78b6a..5f2f68de 100644
--- a/demo/browser/astronomy.browser.js
+++ b/demo/browser/astronomy.browser.js
@@ -1565,7 +1565,7 @@ function sidereal_time(time) {
     if (gst < 0) {
         gst += 24;
     }
-    return gst;
+    return gst; // return sidereal hours in the half-open range [0, 24).
 }
 function terra(observer, st) {
     const df = 1 - 0.003352819697896; // flattening of the Earth
@@ -1927,26 +1927,61 @@ function Horizon(date, observer, ra, dec, refraction) {
     const cosdc = Math.cos(dec * DEG2RAD);
     const sinra = Math.sin(ra * 15 * DEG2RAD);
     const cosra = Math.cos(ra * 15 * DEG2RAD);
+    // Calculate three mutually perpendicular unit vectors
+    // in equatorial coordinates: uze, une, uwe.
+    //
+    // uze = The direction of the observer's local zenith (straight up).
+    // une = The direction toward due north on the observer's horizon.
+    // uwe = The direction toward due west on the observer's horizon.
+    //
+    // HOWEVER, these are uncorrected for the Earth's rotation due to the time of day.
+    //
+    // The components of these 3 vectors are as follows:
+    // x = direction from center of Earth toward 0 degrees longitude (the prime meridian) on equator.
+    // y = direction from center of Earth toward 90 degrees west longitude on equator.
+    // z = direction from center of Earth toward the north pole.
     let uze = [coslat * coslon, coslat * sinlon, sinlat];
     let une = [-sinlat * coslon, -sinlat * sinlon, coslat];
     let uwe = [sinlon, -coslon, 0];
+    // Correct the vectors uze, une, uwe for the Earth's rotation by calculating
+    // sideral time. Call spin() for each uncorrected vector to rotate about
+    // the Earth's axis to yield corrected unit vectors uz, un, uw.
+    // Multiply sidereal hours by -15 to convert to degrees and flip eastward
+    // rotation of the Earth to westward apparent movement of objects with time.
     const spin_angle = -15 * sidereal_time(time);
     let uz = spin(spin_angle, uze);
     let un = spin(spin_angle, une);
     let uw = spin(spin_angle, uwe);
+    // Convert angular equatorial coordinates (RA, DEC) to
+    // cartesian equatorial coordinates in 'p', using the
+    // same orientation system as uze, une, uwe.
     let p = [cosdc * cosra, cosdc * sinra, sindc];
+    // Use dot products of p with the zenith, north, and west
+    // vectors to obtain the cartesian coordinates of the body in
+    // the observer's horizontal orientation system.
+    // pz = zenith component [-1, +1]
+    // pn = north  component [-1, +1]
+    // pw = west   component [-1, +1]
     const pz = p[0] * uz[0] + p[1] * uz[1] + p[2] * uz[2];
     const pn = p[0] * un[0] + p[1] * un[1] + p[2] * un[2];
     const pw = p[0] * uw[0] + p[1] * uw[1] + p[2] * uw[2];
+    // proj is the "shadow" of the body vector along the observer's flat ground.
     let proj = Math.sqrt(pn * pn + pw * pw);
-    let az = 0;
+    // Calculate az = azimuth (compass direction clockwise from East.)
+    let az;
     if (proj > 0) {
+        // If the body is not exactly straight up/down, it has an azimuth.
+        // Invert the angle to produce degrees eastward from north.
         az = -Math.atan2(pw, pn) * RAD2DEG;
         if (az < 0)
             az += 360;
-        if (az >= 360)
-            az -= 360;
     }
+    else {
+        // The body is straight up/down, so it does not have an azimuth.
+        // Report an arbitrary but reasonable value.
+        az = 0;
+    }
+    // zd = the angle of the body away from the observer's zenith, in degrees.
     let zd = Math.atan2(proj, pz) * RAD2DEG;
     let out_ra = ra;
     let out_dec = dec;
@@ -1969,9 +2004,6 @@ function Horizon(date, observer, ra, dec, refraction) {
                 if (out_ra < 0) {
                     out_ra += 24;
                 }
-                if (out_ra >= 24) {
-                    out_ra -= 24;
-                }
             }
             else {
                 out_ra = 0;
diff --git a/demo/nodejs/astronomy.js b/demo/nodejs/astronomy.js
index 690534ee..cc5d843d 100644
--- a/demo/nodejs/astronomy.js
+++ b/demo/nodejs/astronomy.js
@@ -1564,7 +1564,7 @@ function sidereal_time(time) {
     if (gst < 0) {
         gst += 24;
     }
-    return gst;
+    return gst; // return sidereal hours in the half-open range [0, 24).
 }
 function terra(observer, st) {
     const df = 1 - 0.003352819697896; // flattening of the Earth
@@ -1926,26 +1926,61 @@ function Horizon(date, observer, ra, dec, refraction) {
     const cosdc = Math.cos(dec * DEG2RAD);
     const sinra = Math.sin(ra * 15 * DEG2RAD);
     const cosra = Math.cos(ra * 15 * DEG2RAD);
+    // Calculate three mutually perpendicular unit vectors
+    // in equatorial coordinates: uze, une, uwe.
+    //
+    // uze = The direction of the observer's local zenith (straight up).
+    // une = The direction toward due north on the observer's horizon.
+    // uwe = The direction toward due west on the observer's horizon.
+    //
+    // HOWEVER, these are uncorrected for the Earth's rotation due to the time of day.
+    //
+    // The components of these 3 vectors are as follows:
+    // x = direction from center of Earth toward 0 degrees longitude (the prime meridian) on equator.
+    // y = direction from center of Earth toward 90 degrees west longitude on equator.
+    // z = direction from center of Earth toward the north pole.
     let uze = [coslat * coslon, coslat * sinlon, sinlat];
     let une = [-sinlat * coslon, -sinlat * sinlon, coslat];
     let uwe = [sinlon, -coslon, 0];
+    // Correct the vectors uze, une, uwe for the Earth's rotation by calculating
+    // sideral time. Call spin() for each uncorrected vector to rotate about
+    // the Earth's axis to yield corrected unit vectors uz, un, uw.
+    // Multiply sidereal hours by -15 to convert to degrees and flip eastward
+    // rotation of the Earth to westward apparent movement of objects with time.
     const spin_angle = -15 * sidereal_time(time);
     let uz = spin(spin_angle, uze);
     let un = spin(spin_angle, une);
     let uw = spin(spin_angle, uwe);
+    // Convert angular equatorial coordinates (RA, DEC) to
+    // cartesian equatorial coordinates in 'p', using the
+    // same orientation system as uze, une, uwe.
     let p = [cosdc * cosra, cosdc * sinra, sindc];
+    // Use dot products of p with the zenith, north, and west
+    // vectors to obtain the cartesian coordinates of the body in
+    // the observer's horizontal orientation system.
+    // pz = zenith component [-1, +1]
+    // pn = north  component [-1, +1]
+    // pw = west   component [-1, +1]
     const pz = p[0] * uz[0] + p[1] * uz[1] + p[2] * uz[2];
     const pn = p[0] * un[0] + p[1] * un[1] + p[2] * un[2];
     const pw = p[0] * uw[0] + p[1] * uw[1] + p[2] * uw[2];
+    // proj is the "shadow" of the body vector along the observer's flat ground.
     let proj = Math.sqrt(pn * pn + pw * pw);
-    let az = 0;
+    // Calculate az = azimuth (compass direction clockwise from East.)
+    let az;
     if (proj > 0) {
+        // If the body is not exactly straight up/down, it has an azimuth.
+        // Invert the angle to produce degrees eastward from north.
         az = -Math.atan2(pw, pn) * RAD2DEG;
         if (az < 0)
             az += 360;
-        if (az >= 360)
-            az -= 360;
     }
+    else {
+        // The body is straight up/down, so it does not have an azimuth.
+        // Report an arbitrary but reasonable value.
+        az = 0;
+    }
+    // zd = the angle of the body away from the observer's zenith, in degrees.
     let zd = Math.atan2(proj, pz) * RAD2DEG;
     let out_ra = ra;
     let out_dec = dec;
@@ -1968,9 +2003,6 @@ function Horizon(date, observer, ra, dec, refraction) {
                 if (out_ra < 0) {
                     out_ra += 24;
                 }
-                if (out_ra >= 24) {
-                    out_ra -= 24;
-                }
             }
             else {
                 out_ra = 0;
diff --git a/demo/python/astronomy.py b/demo/python/astronomy.py
index b9df9b9b..fc7c6679 100644
--- a/demo/python/astronomy.py
+++ b/demo/python/astronomy.py
@@ -1416,6 +1416,7 @@ def _sidereal_time(time):
     gst = math.fmod((st/3600.0 + theta), 360.0) / 15.0
     if gst < 0.0:
         gst += 24.0
+    # return sidereal hours in the half-open range [0, 24).
     return gst
 
 
@@ -3885,29 +3886,69 @@ def Horizon(time, observer, ra, dec, refraction):
     sinra = math.sin(rarad)
     cosra = math.cos(rarad)
 
+    # Calculate three mutually perpendicular unit vectors
+    # in equatorial coordinates: uze, une, uwe.
+    #
+    # uze = The direction of the observer's local zenith (straight up).
+    # une = The direction toward due north on the observer's horizon.
+    # uwe = The direction toward due west on the observer's horizon.
+    #
+    # HOWEVER, these are uncorrected for the Earth's rotation due to the time of day.
+    #
+    # The components of these 3 vectors are as follows:
+    # [0] = x = direction from center of Earth toward 0 degrees longitude (the prime meridian) on equator.
+    # [1] = y = direction from center of Earth toward 90 degrees west longitude on equator.
+    # [2] = z = direction from center of Earth toward the north pole.
+
     uze = [coslat*coslon, coslat*sinlon, sinlat]
     une = [-sinlat*coslon, -sinlat*sinlon, coslat]
     uwe = [sinlon, -coslon, 0.0]
 
+    # Correct the vectors uze, une, uwe for the Earth's rotation by calculating
+    # sideral time. Call spin() for each uncorrected vector to rotate about
+    # the Earth's axis to yield corrected unit vectors uz, un, uw.
+    # Multiply sidereal hours by -15 to convert to degrees and flip eastward
+    # rotation of the Earth to westward apparent movement of objects with time.
+
     angle = -15.0 * _sidereal_time(time)
     uz = _spin(angle, uze)
     un = _spin(angle, une)
     uw = _spin(angle, uwe)
 
+    # Convert angular equatorial coordinates (RA, DEC) to
+    # cartesian equatorial coordinates in 'p', using the
+    # same orientation system as uze, une, uwe.
+
     p = [cosdc*cosra, cosdc*sinra, sindc]
 
+    # Use dot products of p with the zenith, north, and west
+    # vectors to obtain the cartesian coordinates of the body in
+    # the observer's horizontal orientation system.
+    #
+    # pz = zenith component [-1, +1]
+    # pn = north  component [-1, +1]
+    # pw = west   component [-1, +1]
+
     pz = p[0]*uz[0] + p[1]*uz[1] + p[2]*uz[2]
     pn = p[0]*un[0] + p[1]*un[1] + p[2]*un[2]
     pw = p[0]*uw[0] + p[1]*uw[1] + p[2]*uw[2]
 
+    # proj is the "shadow" of the body vector along the observer's flat ground.
     proj = math.sqrt(pn*pn + pw*pw)
-    az = 0.0
+
+    # Calculate az = azimuth (compass direction clockwise from East.)
     if proj > 0.0:
+        # If the body is not exactly straight up/down, it has an azimuth.
+        # Invert the angle to produce degrees eastward from north.
         az = math.degrees(-math.atan2(pw, pn))
         if az < 0:
             az += 360
-        if az >= 360:
-            az -= 360
+    else:
+        # The body is straight up/down, so it does not have an azimuth.
+        # Report an arbitrary but reasonable value.
+        az = 0.0
+
+    # zd = the angle of the body away from the observer's zenith.
     zd = math.degrees(math.atan2(proj, pz))
     hor_ra = ra
     hor_dec = dec
@@ -3930,8 +3971,6 @@ def Horizon(time, observer, ra, dec, refraction):
                 hor_ra = math.degrees(math.atan2(pr[1], pr[0])) / 15
                 if hor_ra < 0:
                     hor_ra += 24
-                if hor_ra >= 24:
-                    hor_ra -= 24
             else:
                 hor_ra = 0
             hor_dec = math.degrees(math.atan2(pr[2], proj))
diff --git a/generate/template/astronomy.c b/generate/template/astronomy.c
index 9f8af335..c1663ada 100644
--- a/generate/template/astronomy.c
+++ b/generate/template/astronomy.c
@@ -1375,7 +1375,7 @@ static double sidereal_time(astro_time_t *time)
     if (gst < 0.0)
         gst += 24.0;
 
-    return gst;
+    return gst;     /* return sidereal hours in the half-open range [0, 24). */
 }
 
 static void terra(astro_observer_t observer, double st, double pos[3])
@@ -2678,6 +2678,22 @@ astro_horizon_t Astronomy_Horizon(
     double sinra = sin(ra * 15 * DEG2RAD);
     double cosra = cos(ra * 15 * DEG2RAD);
 
+    /*
+        Calculate three mutually perpendicular unit vectors
+        in equatorial coordinates: uze, une, uwe.
+
+        uze = The direction of the observer's local zenith (straight up).
+        une = The direction toward due north on the observer's horizon.
+        uwe = The direction toward due west on the observer's horizon.
+
+        HOWEVER, these are uncorrected for the Earth's rotation due to the time of day.
+
+        The components of these 3 vectors are as follows:
+        [0] = x = direction from center of Earth toward 0 degrees longitude (the prime meridian) on equator.
+        [1] = y = direction from center of Earth toward 90 degrees west longitude on equator.
+        [2] = z = direction from center of Earth toward the north pole.
+    */
+
     uze[0] = coslat * coslon;
     uze[1] = coslat * sinlon;
     uze[2] = sinlat;
@@ -2690,29 +2706,61 @@ astro_horizon_t Astronomy_Horizon(
     uwe[1] = -coslon;
     uwe[2] = 0.0;
 
+    /*
+        Correct the vectors uze, une, uwe for the Earth's rotation by calculating
+        sideral time. Call spin() for each uncorrected vector to rotate about
+        the Earth's axis to yield corrected unit vectors uz, un, uw.
+        Multiply sidereal hours by -15 to convert to degrees and flip eastward
+        rotation of the Earth to westward apparent movement of objects with time.
+    */
+
     spin_angle = -15.0 * sidereal_time(time);
     spin(spin_angle, uze, uz);
     spin(spin_angle, une, un);
     spin(spin_angle, uwe, uw);
 
+    /*
+        Convert angular equatorial coordinates (RA, DEC) to
+        cartesian equatorial coordinates in 'p', using the
+        same orientation system as uze, une, uwe.
+    */
+
     p[0] = cosdc * cosra;
     p[1] = cosdc * sinra;
     p[2] = sindc;
 
+    /*
+        Use dot products of p with the zenith, north, and west
+        vectors to obtain the cartesian coordinates of the body in
+        the observer's horizontal orientation system.
+
+        pz = zenith component [-1, +1]
+        pn = north  component [-1, +1]
+        pw = west   component [-1, +1]
+    */
+
     pz = p[0]*uz[0] + p[1]*uz[1] + p[2]*uz[2];
     pn = p[0]*un[0] + p[1]*un[1] + p[2]*un[2];
     pw = p[0]*uw[0] + p[1]*uw[1] + p[2]*uw[2];
 
+    /* proj is the "shadow" of the body vector along the observer's flat ground. */
     proj = sqrt(pn*pn + pw*pw);
-    az = 0.0;
     if (proj > 0.0)
     {
+        /* If the body is not exactly straight up/down, it has an azimuth. */
+        /* Invert the angle to produce degrees eastward from north. */
         az = -atan2(pw, pn) * RAD2DEG;
-        if (az < 0)
+        if (az < 0.0)
             az += 360;
-        else if (az >= 360)
-            az -= 360;
     }
+    else
+    {
+        /* The body is straight up/down, so it does not have an azimuth. */
+        /* Report an arbitrary but reasonable value. */
+        az = 0.0;
+    }
+
+    /* zd = the angle of the body away from the observer's zenith, in degrees. */
     zd = atan2(proj, pz) * RAD2DEG;
     hor.ra = ra;
     hor.dec = dec;
@@ -2743,8 +2791,6 @@ astro_horizon_t Astronomy_Horizon(
                 hor.ra = atan2(pr[1], pr[0]) * (RAD2DEG / 15.0);
                 if (hor.ra < 0.0)
                     hor.ra += 24.0;
-                else if (hor.ra >= 24.0)
-                    hor.ra -= 24.0;
             }
             else
             {
diff --git a/generate/template/astronomy.cs b/generate/template/astronomy.cs
index 39941ff0..41c9dc0b 100644
--- a/generate/template/astronomy.cs
+++ b/generate/template/astronomy.cs
@@ -2612,7 +2612,7 @@ $ASTRO_IAU_DATA()
             if (gst < 0.0)
                 gst += 24.0;
 
-            return gst;
+            return gst;     // return sidereal hours in the half-open range [0, 24).
         }
 
         private static AstroVector terra(Observer observer, double st)
@@ -3144,30 +3144,69 @@ $ASTRO_IAU_DATA()
             double sinra = Math.Sin(ra * 15 * DEG2RAD);
             double cosra = Math.Cos(ra * 15 * DEG2RAD);
 
+            // Calculate three mutually perpendicular unit vectors
+            // in equatorial coordinates: uze, une, uwe.
+            //
+            // uze = The direction of the observer's local zenith (straight up).
+            // une = The direction toward due north on the observer's horizon.
+            // uwe = The direction toward due west on the observer's horizon.
+            //
+            // HOWEVER, these are uncorrected for the Earth's rotation due to the time of day.
+            //
+            // The components of these 3 vectors are as follows:
+            // x = direction from center of Earth toward 0 degrees longitude (the prime meridian) on equator.
+            // y = direction from center of Earth toward 90 degrees west longitude on equator.
+            // z = direction from center of Earth toward the north pole.
             var uze = new AstroVector(coslat * coslon, coslat * sinlon, sinlat, null);
             var une = new AstroVector(-sinlat * coslon, -sinlat * sinlon, coslat, null);
             var uwe = new AstroVector(sinlon, -coslon, 0.0, null);
 
+            // Correct the vectors uze, une, uwe for the Earth's rotation by calculating
+            // sideral time. Call spin() for each uncorrected vector to rotate about
+            // the Earth's axis to yield corrected unit vectors uz, un, uw.
+            // Multiply sidereal hours by -15 to convert to degrees and flip eastward
+            // rotation of the Earth to westward apparent movement of objects with time.
             double spin_angle = -15.0 * sidereal_time(time);
             AstroVector uz = spin(spin_angle, uze);
             AstroVector un = spin(spin_angle, une);
             AstroVector uw = spin(spin_angle, uwe);
 
+            // Convert angular equatorial coordinates (RA, DEC) to
+            // cartesian equatorial coordinates in 'p', using the
+            // same orientation system as uze, une, uwe.
             var p = new AstroVector(cosdc * cosra, cosdc * sinra, sindc, null);
+
+            // Use dot products of p with the zenith, north, and west
+            // vectors to obtain the cartesian coordinates of the body in
+            // the observer's horizontal orientation system.
+            // pz = zenith component [-1, +1]
+            // pn = north  component [-1, +1]
+            // pw = west   component [-1, +1]
             double pz = p.x*uz.x + p.y*uz.y + p.z*uz.z;
             double pn = p.x*un.x + p.y*un.y + p.z*un.z;
             double pw = p.x*uw.x + p.y*uw.y + p.z*uw.z;
 
+            // proj is the "shadow" of the body vector along the observer's flat ground.
             double proj = Math.Sqrt(pn*pn + pw*pw);
-            double az = 0.0;
+
+            // Calculate az = azimuth (compass direction clockwise from East.)
+            double az;
             if (proj > 0.0)
             {
+                // If the body is not exactly straight up/down, it has an azimuth.
+                // Invert the angle to produce degrees eastward from north.
                 az = -Math.Atan2(pw, pn) * RAD2DEG;
                 if (az < 0.0)
                     az += 360.0;
-                else if (az >= 360.0)
-                    az -= 360.0;
             }
+            else
+            {
+                // The body is straight up/down, so it does not have an azimuth.
+                // Report an arbitrary but reasonable value.
+                az = 0.0;
+            }
+
+            // zd = the angle of the body away from the observer's zenith, in degrees.
             double zd = Math.Atan2(proj, pz) * RAD2DEG;
             double hor_ra = ra;
             double hor_dec = dec;
@@ -3195,8 +3234,6 @@ $ASTRO_IAU_DATA()
                         hor_ra = Math.Atan2(pry, prx) * (RAD2DEG / 15.0);
                         if (hor_ra < 0.0)
                             hor_ra += 24.0;
-                        else if (hor_ra >= 24.0)
-                            hor_ra -= 24.0;
                     }
                     else
                     {
diff --git a/generate/template/astronomy.py b/generate/template/astronomy.py
index 0b464913..d7650d83 100644
--- a/generate/template/astronomy.py
+++ b/generate/template/astronomy.py
@@ -880,6 +880,7 @@ def _sidereal_time(time):
     gst = math.fmod((st/3600.0 + theta), 360.0) / 15.0
     if gst < 0.0:
         gst += 24.0
+    # return sidereal hours in the half-open range [0, 24).
     return gst
 
 
@@ -1988,29 +1989,69 @@ def Horizon(time, observer, ra, dec, refraction):
     sinra = math.sin(rarad)
     cosra = math.cos(rarad)
 
+    # Calculate three mutually perpendicular unit vectors
+    # in equatorial coordinates: uze, une, uwe.
+    #
+    # uze = The direction of the observer's local zenith (straight up).
+    # une = The direction toward due north on the observer's horizon.
+    # uwe = The direction toward due west on the observer's horizon.
+    #
+    # HOWEVER, these are uncorrected for the Earth's rotation due to the time of day.
+    #
+    # The components of these 3 vectors are as follows:
+    # [0] = x = direction from center of Earth toward 0 degrees longitude (the prime meridian) on equator.
+    # [1] = y = direction from center of Earth toward 90 degrees west longitude on equator.
+    # [2] = z = direction from center of Earth toward the north pole.
+
     uze = [coslat*coslon, coslat*sinlon, sinlat]
     une = [-sinlat*coslon, -sinlat*sinlon, coslat]
     uwe = [sinlon, -coslon, 0.0]
 
+    # Correct the vectors uze, une, uwe for the Earth's rotation by calculating
+    # sideral time. Call spin() for each uncorrected vector to rotate about
+    # the Earth's axis to yield corrected unit vectors uz, un, uw.
+    # Multiply sidereal hours by -15 to convert to degrees and flip eastward
+    # rotation of the Earth to westward apparent movement of objects with time.
+
     angle = -15.0 * _sidereal_time(time)
     uz = _spin(angle, uze)
     un = _spin(angle, une)
     uw = _spin(angle, uwe)
 
+    # Convert angular equatorial coordinates (RA, DEC) to
+    # cartesian equatorial coordinates in 'p', using the
+    # same orientation system as uze, une, uwe.
+
     p = [cosdc*cosra, cosdc*sinra, sindc]
 
+    # Use dot products of p with the zenith, north, and west
+    # vectors to obtain the cartesian coordinates of the body in
+    # the observer's horizontal orientation system.
+    #
+    # pz = zenith component [-1, +1]
+    # pn = north  component [-1, +1]
+    # pw = west   component [-1, +1]
+
     pz = p[0]*uz[0] + p[1]*uz[1] + p[2]*uz[2]
     pn = p[0]*un[0] + p[1]*un[1] + p[2]*un[2]
     pw = p[0]*uw[0] + p[1]*uw[1] + p[2]*uw[2]
 
+    # proj is the "shadow" of the body vector along the observer's flat ground.
     proj = math.sqrt(pn*pn + pw*pw)
-    az = 0.0
+
+    # Calculate az = azimuth (compass direction clockwise from East.)
     if proj > 0.0:
+        # If the body is not exactly straight up/down, it has an azimuth.
+        # Invert the angle to produce degrees eastward from north.
         az = math.degrees(-math.atan2(pw, pn))
         if az < 0:
             az += 360
-        if az >= 360:
-            az -= 360
+    else:
+        # The body is straight up/down, so it does not have an azimuth.
+        # Report an arbitrary but reasonable value.
+        az = 0.0
+
+    # zd = the angle of the body away from the observer's zenith.
     zd = math.degrees(math.atan2(proj, pz))
     hor_ra = ra
     hor_dec = dec
@@ -2033,8 +2074,6 @@ def Horizon(time, observer, ra, dec, refraction):
                 hor_ra = math.degrees(math.atan2(pr[1], pr[0])) / 15
                 if hor_ra < 0:
                     hor_ra += 24
-                if hor_ra >= 24:
-                    hor_ra -= 24
             else:
                 hor_ra = 0
             hor_dec = math.degrees(math.atan2(pr[2], proj))
diff --git a/generate/template/astronomy.ts b/generate/template/astronomy.ts
index eeca45fd..b6d84b26 100644
--- a/generate/template/astronomy.ts
+++ b/generate/template/astronomy.ts
@@ -849,7 +849,7 @@ function sidereal_time(time: AstroTime): number {          // calculates Greenwi
     if (gst < 0) {
         gst += 24;
     }
-    return gst;
+    return gst;     // return sidereal hours in the half-open range [0, 24).
 }
 
 function terra(observer: Observer, st: number): TerraInfo {
@@ -1257,28 +1257,70 @@ export function Horizon(date: FlexibleDateTime, observer: Observer, ra: number,
     const cosdc = Math.cos(dec * DEG2RAD);
     const sinra = Math.sin(ra * 15 * DEG2RAD);
     const cosra = Math.cos(ra * 15 * DEG2RAD);
+
+    // Calculate three mutually perpendicular unit vectors
+    // in equatorial coordinates: uze, une, uwe.
+    //
+    // uze = The direction of the observer's local zenith (straight up).
+    // une = The direction toward due north on the observer's horizon.
+    // uwe = The direction toward due west on the observer's horizon.
+    //
+    // HOWEVER, these are uncorrected for the Earth's rotation due to the time of day.
+    //
+    // The components of these 3 vectors are as follows:
+    // x = direction from center of Earth toward 0 degrees longitude (the prime meridian) on equator.
+    // y = direction from center of Earth toward 90 degrees west longitude on equator.
+    // z = direction from center of Earth toward the north pole.
+
     let uze: ArrayVector = [coslat*coslon, coslat*sinlon, sinlat];
     let une: ArrayVector = [-sinlat*coslon, -sinlat*sinlon, coslat];
     let uwe: ArrayVector = [sinlon, -coslon, 0];
 
+    // Correct the vectors uze, une, uwe for the Earth's rotation by calculating
+    // sideral time. Call spin() for each uncorrected vector to rotate about
+    // the Earth's axis to yield corrected unit vectors uz, un, uw.
+    // Multiply sidereal hours by -15 to convert to degrees and flip eastward
+    // rotation of the Earth to westward apparent movement of objects with time.
+
     const spin_angle = -15 * sidereal_time(time);
     let uz = spin(spin_angle, uze);
     let un = spin(spin_angle, une);
     let uw = spin(spin_angle, uwe);
 
+    // Convert angular equatorial coordinates (RA, DEC) to
+    // cartesian equatorial coordinates in 'p', using the
+    // same orientation system as uze, une, uwe.
+
     let p = [cosdc*cosra, cosdc*sinra, sindc];
 
+    // Use dot products of p with the zenith, north, and west
+    // vectors to obtain the cartesian coordinates of the body in
+    // the observer's horizontal orientation system.
+    // pz = zenith component [-1, +1]
+    // pn = north  component [-1, +1]
+    // pw = west   component [-1, +1]
+
     const pz = p[0]*uz[0] + p[1]*uz[1] + p[2]*uz[2];
     const pn = p[0]*un[0] + p[1]*un[1] + p[2]*un[2];
     const pw = p[0]*uw[0] + p[1]*uw[1] + p[2]*uw[2];
 
+    // proj is the "shadow" of the body vector along the observer's flat ground.
     let proj = Math.sqrt(pn*pn + pw*pw);
-    let az = 0;
+
+    // Calculate az = azimuth (compass direction clockwise from East.)
+    let az: number;
     if (proj > 0) {
+        // If the body is not exactly straight up/down, it has an azimuth.
+        // Invert the angle to produce degrees eastward from north.
         az = -Math.atan2(pw, pn) * RAD2DEG;
         if (az < 0) az += 360;
-        if (az >= 360) az -= 360;
+    } else {
+        // The body is straight up/down, so it does not have an azimuth.
+        // Report an arbitrary but reasonable value.
+        az = 0;
     }
+
+    // zd = the angle of the body away from the observer's zenith, in degrees.
     let zd = Math.atan2(proj, pz) * RAD2DEG;
     let out_ra = ra;
     let out_dec = dec;
@@ -1302,9 +1344,6 @@ export function Horizon(date: FlexibleDateTime, observer: Observer, ra: number,
                 if (out_ra < 0) {
                     out_ra += 24;
                 }
-                if (out_ra >= 24) {
-                    out_ra -= 24;
-                }
             } else {
                 out_ra = 0;
             }
diff --git a/source/c/astronomy.c b/source/c/astronomy.c
index eefe2a84..17d0a4c1 100644
--- a/source/c/astronomy.c
+++ b/source/c/astronomy.c
@@ -1453,7 +1453,7 @@ static double sidereal_time(astro_time_t *time)
     if (gst < 0.0)
         gst += 24.0;
 
-    return gst;
+    return gst;     /* return sidereal hours in the half-open range [0, 24). */
 }
 
 static void terra(astro_observer_t observer, double st, double pos[3])
@@ -3730,6 +3730,22 @@ astro_horizon_t Astronomy_Horizon(
     double sinra = sin(ra * 15 * DEG2RAD);
     double cosra = cos(ra * 15 * DEG2RAD);
 
+    /*
+        Calculate three mutually perpendicular unit vectors
+        in equatorial coordinates: uze, une, uwe.
+
+        uze = The direction of the observer's local zenith (straight up).
+        une = The direction toward due north on the observer's horizon.
+        uwe = The direction toward due west on the observer's horizon.
+
+        HOWEVER, these are uncorrected for the Earth's rotation due to the time of day.
+
+        The components of these 3 vectors are as follows:
+        [0] = x = direction from center of Earth toward 0 degrees longitude (the prime meridian) on equator.
+        [1] = y = direction from center of Earth toward 90 degrees west longitude on equator.
+        [2] = z = direction from center of Earth toward the north pole.
+    */
+
     uze[0] = coslat * coslon;
     uze[1] = coslat * sinlon;
     uze[2] = sinlat;
@@ -3742,29 +3758,61 @@ astro_horizon_t Astronomy_Horizon(
     uwe[1] = -coslon;
     uwe[2] = 0.0;
 
+    /*
+        Correct the vectors uze, une, uwe for the Earth's rotation by calculating
+        sideral time. Call spin() for each uncorrected vector to rotate about
+        the Earth's axis to yield corrected unit vectors uz, un, uw.
+        Multiply sidereal hours by -15 to convert to degrees and flip eastward
+        rotation of the Earth to westward apparent movement of objects with time.
+    */
+
     spin_angle = -15.0 * sidereal_time(time);
     spin(spin_angle, uze, uz);
     spin(spin_angle, une, un);
     spin(spin_angle, uwe, uw);
 
+    /*
+        Convert angular equatorial coordinates (RA, DEC) to
+        cartesian equatorial coordinates in 'p', using the
+        same orientation system as uze, une, uwe.
+    */
+
     p[0] = cosdc * cosra;
     p[1] = cosdc * sinra;
     p[2] = sindc;
 
+    /*
+        Use dot products of p with the zenith, north, and west
+        vectors to obtain the cartesian coordinates of the body in
+        the observer's horizontal orientation system.
+
+        pz = zenith component [-1, +1]
+        pn = north  component [-1, +1]
+        pw = west   component [-1, +1]
+    */
+
     pz = p[0]*uz[0] + p[1]*uz[1] + p[2]*uz[2];
     pn = p[0]*un[0] + p[1]*un[1] + p[2]*un[2];
     pw = p[0]*uw[0] + p[1]*uw[1] + p[2]*uw[2];
 
+    /* proj is the "shadow" of the body vector along the observer's flat ground. */
     proj = sqrt(pn*pn + pw*pw);
-    az = 0.0;
     if (proj > 0.0)
     {
+        /* If the body is not exactly straight up/down, it has an azimuth. */
+        /* Invert the angle to produce degrees eastward from north. */
         az = -atan2(pw, pn) * RAD2DEG;
-        if (az < 0)
+        if (az < 0.0)
             az += 360;
-        else if (az >= 360)
-            az -= 360;
     }
+    else
+    {
+        /* The body is straight up/down, so it does not have an azimuth. */
+        /* Report an arbitrary but reasonable value. */
+        az = 0.0;
+    }
+
+    /* zd = the angle of the body away from the observer's zenith, in degrees. */
     zd = atan2(proj, pz) * RAD2DEG;
     hor.ra = ra;
     hor.dec = dec;
@@ -3795,8 +3843,6 @@ astro_horizon_t Astronomy_Horizon(
                 hor.ra = atan2(pr[1], pr[0]) * (RAD2DEG / 15.0);
                 if (hor.ra < 0.0)
                     hor.ra += 24.0;
-                else if (hor.ra >= 24.0)
-                    hor.ra -= 24.0;
             }
             else
             {
diff --git a/source/csharp/astronomy.cs b/source/csharp/astronomy.cs
index 0d71f4a9..ddae6bdc 100644
--- a/source/csharp/astronomy.cs
+++ b/source/csharp/astronomy.cs
@@ -3668,7 +3668,7 @@ namespace CosineKitty
             if (gst < 0.0)
                 gst += 24.0;
 
-            return gst;
+            return gst;     // return sidereal hours in the half-open range [0, 24).
         }
 
         private static AstroVector terra(Observer observer, double st)
@@ -4200,30 +4200,69 @@ namespace CosineKitty
             double sinra = Math.Sin(ra * 15 * DEG2RAD);
             double cosra = Math.Cos(ra * 15 * DEG2RAD);
 
+            // Calculate three mutually perpendicular unit vectors
+            // in equatorial coordinates: uze, une, uwe.
+            //
+            // uze = The direction of the observer's local zenith (straight up).
+            // une = The direction toward due north on the observer's horizon.
+            // uwe = The direction toward due west on the observer's horizon.
+            //
+            // HOWEVER, these are uncorrected for the Earth's rotation due to the time of day.
+            //
+            // The components of these 3 vectors are as follows:
+            // x = direction from center of Earth toward 0 degrees longitude (the prime meridian) on equator.
+            // y = direction from center of Earth toward 90 degrees west longitude on equator.
+            // z = direction from center of Earth toward the north pole.
             var uze = new AstroVector(coslat * coslon, coslat * sinlon, sinlat, null);
             var une = new AstroVector(-sinlat * coslon, -sinlat * sinlon, coslat, null);
             var uwe = new AstroVector(sinlon, -coslon, 0.0, null);
 
+            // Correct the vectors uze, une, uwe for the Earth's rotation by calculating
+            // sideral time. Call spin() for each uncorrected vector to rotate about
+            // the Earth's axis to yield corrected unit vectors uz, un, uw.
+            // Multiply sidereal hours by -15 to convert to degrees and flip eastward
+            // rotation of the Earth to westward apparent movement of objects with time.
             double spin_angle = -15.0 * sidereal_time(time);
             AstroVector uz = spin(spin_angle, uze);
             AstroVector un = spin(spin_angle, une);
             AstroVector uw = spin(spin_angle, uwe);
 
+            // Convert angular equatorial coordinates (RA, DEC) to
+            // cartesian equatorial coordinates in 'p', using the
+            // same orientation system as uze, une, uwe.
             var p = new AstroVector(cosdc * cosra, cosdc * sinra, sindc, null);
+
+            // Use dot products of p with the zenith, north, and west
+            // vectors to obtain the cartesian coordinates of the body in
+            // the observer's horizontal orientation system.
+            // pz = zenith component [-1, +1]
+            // pn = north  component [-1, +1]
+            // pw = west   component [-1, +1]
             double pz = p.x*uz.x + p.y*uz.y + p.z*uz.z;
             double pn = p.x*un.x + p.y*un.y + p.z*un.z;
             double pw = p.x*uw.x + p.y*uw.y + p.z*uw.z;
 
+            // proj is the "shadow" of the body vector along the observer's flat ground.
             double proj = Math.Sqrt(pn*pn + pw*pw);
-            double az = 0.0;
+
+            // Calculate az = azimuth (compass direction clockwise from East.)
+            double az;
             if (proj > 0.0)
             {
+                // If the body is not exactly straight up/down, it has an azimuth.
+                // Invert the angle to produce degrees eastward from north.
                 az = -Math.Atan2(pw, pn) * RAD2DEG;
                 if (az < 0.0)
                     az += 360.0;
-                else if (az >= 360.0)
-                    az -= 360.0;
             }
+            else
+            {
+                // The body is straight up/down, so it does not have an azimuth.
+                // Report an arbitrary but reasonable value.
+                az = 0.0;
+            }
+
+            // zd = the angle of the body away from the observer's zenith, in degrees.
             double zd = Math.Atan2(proj, pz) * RAD2DEG;
             double hor_ra = ra;
             double hor_dec = dec;
@@ -4251,8 +4290,6 @@ namespace CosineKitty
                         hor_ra = Math.Atan2(pry, prx) * (RAD2DEG / 15.0);
                         if (hor_ra < 0.0)
                             hor_ra += 24.0;
-                        else if (hor_ra >= 24.0)
-                            hor_ra -= 24.0;
                     }
                     else
                     {
diff --git a/source/js/astronomy.browser.js b/source/js/astronomy.browser.js
index ecc78b6a..5f2f68de 100644
--- a/source/js/astronomy.browser.js
+++ b/source/js/astronomy.browser.js
@@ -1565,7 +1565,7 @@ function sidereal_time(time) {
     if (gst < 0) {
         gst += 24;
     }
-    return gst;
+    return gst; // return sidereal hours in the half-open range [0, 24).
 }
 function terra(observer, st) {
     const df = 1 - 0.003352819697896; // flattening of the Earth
@@ -1927,26 +1927,61 @@ function Horizon(date, observer, ra, dec, refraction) {
     const cosdc = Math.cos(dec * DEG2RAD);
     const sinra = Math.sin(ra * 15 * DEG2RAD);
     const cosra = Math.cos(ra * 15 * DEG2RAD);
+    // Calculate three mutually perpendicular unit vectors
+    // in equatorial coordinates: uze, une, uwe.
+    //
+    // uze = The direction of the observer's local zenith (straight up).
+    // une = The direction toward due north on the observer's horizon.
+    // uwe = The direction toward due west on the observer's horizon.
+    //
+    // HOWEVER, these are uncorrected for the Earth's rotation due to the time of day.
+    //
+    // The components of these 3 vectors are as follows:
+    // x = direction from center of Earth toward 0 degrees longitude (the prime meridian) on equator.
+    // y = direction from center of Earth toward 90 degrees west longitude on equator.
+    // z = direction from center of Earth toward the north pole.
     let uze = [coslat * coslon, coslat * sinlon, sinlat];
     let une = [-sinlat * coslon, -sinlat * sinlon, coslat];
     let uwe = [sinlon, -coslon, 0];
+    // Correct the vectors uze, une, uwe for the Earth's rotation by calculating
+    // sideral time. Call spin() for each uncorrected vector to rotate about
+    // the Earth's axis to yield corrected unit vectors uz, un, uw.
+    // Multiply sidereal hours by -15 to convert to degrees and flip eastward
+    // rotation of the Earth to westward apparent movement of objects with time.
     const spin_angle = -15 * sidereal_time(time);
     let uz = spin(spin_angle, uze);
     let un = spin(spin_angle, une);
     let uw = spin(spin_angle, uwe);
+    // Convert angular equatorial coordinates (RA, DEC) to
+    // cartesian equatorial coordinates in 'p', using the
+    // same orientation system as uze, une, uwe.
     let p = [cosdc * cosra, cosdc * sinra, sindc];
+    // Use dot products of p with the zenith, north, and west
+    // vectors to obtain the cartesian coordinates of the body in
+    // the observer's horizontal orientation system.
+    // pz = zenith component [-1, +1]
+    // pn = north  component [-1, +1]
+    // pw = west   component [-1, +1]
     const pz = p[0] * uz[0] + p[1] * uz[1] + p[2] * uz[2];
     const pn = p[0] * un[0] + p[1] * un[1] + p[2] * un[2];
     const pw = p[0] * uw[0] + p[1] * uw[1] + p[2] * uw[2];
+    // proj is the "shadow" of the body vector along the observer's flat ground.
     let proj = Math.sqrt(pn * pn + pw * pw);
-    let az = 0;
+    // Calculate az = azimuth (compass direction clockwise from East.)
+    let az;
     if (proj > 0) {
+        // If the body is not exactly straight up/down, it has an azimuth.
+        // Invert the angle to produce degrees eastward from north.
         az = -Math.atan2(pw, pn) * RAD2DEG;
         if (az < 0)
             az += 360;
-        if (az >= 360)
-            az -= 360;
     }
+    else {
+        // The body is straight up/down, so it does not have an azimuth.
+        // Report an arbitrary but reasonable value.
+        az = 0;
+    }
+    // zd = the angle of the body away from the observer's zenith, in degrees.
     let zd = Math.atan2(proj, pz) * RAD2DEG;
     let out_ra = ra;
     let out_dec = dec;
@@ -1969,9 +2004,6 @@ function Horizon(date, observer, ra, dec, refraction) {
                 if (out_ra < 0) {
                     out_ra += 24;
                 }
-                if (out_ra >= 24) {
-                    out_ra -= 24;
-                }
             }
             else {
                 out_ra = 0;
diff --git a/source/js/astronomy.browser.min.js b/source/js/astronomy.browser.min.js
index e067728d..c31c9900 100644
--- a/source/js/astronomy.browser.min.js
+++ b/source/js/astronomy.browser.min.js
@@ -60,141 +60,141 @@ m=-m*l*a+n*f*e*a+c*n*k;l*=k;n=-k*e*c-a*f;a=-k*e*a+f*c;return 0===b?new M([[h,d,q
 a.rot[0][2]*c[0]+a.rot[1][2]*c[1]+a.rot[2][2]*c[2]]}function $a(a,b){a=Ba(a);var c=.017453292519943295*a.mobl,d=.017453292519943295*a.tobl,e=4.84813681109536E-6*a.dpsi;a=Math.cos(c);c=Math.sin(c);var h=Math.cos(d),l=Math.sin(d);d=Math.cos(e);var k=Math.sin(e);e=-k*a;var f=-k*c,m=k*h,n=d*a*h+c*l,q=d*c*h-a*l;k*=l;var u=d*a*l-c*h;a=d*c*l+a*h;return 0===b?new M([[d,m,k],[e,n,u],[f,q,a]]):new M([[d,e,f],[m,n,q],[k,u,a]])}function xb(a,b){var c=pa(a),d=.017453292519943295*b.latitude,e=Math.sin(d);d=Math.cos(d);
 var h=1/Math.sqrt(d*d+.9933056020041345*e*e),l=b.height/1E3,k=6378.1366*h+l;b=.017453292519943295*(15*c+b.longitude);e=Za(a,-1,[k*d*Math.cos(b)/1.4959787069098932E8,k*d*Math.sin(b)/1.4959787069098932E8,(6335.438815127603*h+l)*e/1.4959787069098932E8]);return Ga(a.tt,e,0)}function xc(a){if(!(a instanceof Array)||3!==a.length)return!1;for(var b=0;3>b;++b){if(!(a[b]instanceof Array)||3!==a[b].length)return!1;for(var c=0;3>c;++c)if(!Number.isFinite(a[b][c]))return!1}return!0}function yb(a){var b=a[0]*
 a[0]+a[1]*a[1],c=Math.sqrt(b+a[2]*a[2]);if(0===b){if(0===a[2])throw"Indeterminate sky coordinates";return 0>a[2]?{ra:0,dec:-90,dist:c}:{ra:0,dec:90,dist:c}}var d=Math.atan2(a[1],a[0])/.2617993877991494;0>d&&(d+=24);return new Ha(d,Math.atan2(a[2],Math.sqrt(b))/.017453292519943295,c)}function ha(a,b){var c=.017453292519943295*a;a=Math.cos(c);c=Math.sin(c);return[a*b[0]+c*b[1]+0*b[2],-c*b[0]+a*b[1]+0*b[2],0*b[0]+0*b[1]+1*b[2]]}function Ia(a,b,c,d,e){a=y(a);ia(b);r(c);r(d);var h=Math.sin(.017453292519943295*
-b.latitude),l=Math.cos(.017453292519943295*b.latitude),k=Math.sin(.017453292519943295*b.longitude),f=Math.cos(.017453292519943295*b.longitude);b=Math.sin(.017453292519943295*d);var m=Math.cos(.017453292519943295*d),n=Math.sin(.2617993877991494*c),q=Math.cos(.2617993877991494*c),u=[l*f,l*k,h];h=[-h*f,-h*k,l];k=[k,-f,0];l=-15*pa(a);a=ha(l,u);u=ha(l,h);k=ha(l,k);b=[m*q,m*n,b];n=b[0]*a[0]+b[1]*a[1]+b[2]*a[2];u=b[0]*u[0]+b[1]*u[1]+b[2]*u[2];k=b[0]*k[0]+b[1]*k[1]+b[2]*k[2];q=Math.sqrt(u*u+k*k);m=0;0<q&&
-(m=57.29577951308232*-Math.atan2(k,u),0>m&&(m+=360),360<=m&&(m-=360));n=57.29577951308232*Math.atan2(q,n);q=d;if(e&&(d=n,e=qa(e,90-n),n-=e,0<e&&3E-4<n)){c=Math.sin(.017453292519943295*n);q=Math.cos(.017453292519943295*n);u=Math.sin(.017453292519943295*d);d=Math.cos(.017453292519943295*d);e=[];for(k=0;3>k;++k)e.push((b[k]-d*a[k])/u*c+a[k]*q);q=Math.sqrt(e[0]*e[0]+e[1]*e[1]);0<q?(c=57.29577951308232*Math.atan2(e[1],e[0])/15,0>c&&(c+=24),24<=c&&(c-=24)):c=0;q=57.29577951308232*Math.atan2(e[2],q)}return new zb(m,
-90-n,c,q)}function ia(a){if(!(a instanceof Ab))throw"Not an instance of the Observer class: "+a;r(a.latitude);r(a.longitude);r(a.height);if(-90>a.latitude||90<a.latitude)throw"Latitude "+a.latitude+" is out of range. Must be -90..+90.";return a}function Bb(a){a=y(a).AddDays(-.005775518331089121);var b=N(F.Earth,a);b=Ga(0,[-b.x,-b.y,-b.z],a.tt);var c=$jscomp.makeIterator(Za(a,0,b));b=c.next().value;var d=c.next().value;c=c.next().value;a=.017453292519943295*Ba(a).tobl;return Cb(b,d,c,Math.cos(a),Math.sin(a))}
-function Ja(a,b,c,d,e){ia(c);x(d);x(e);b=y(b);c=xb(b,c);a=W(a,b,e);a=[a.x-c[0],a.y-c[1],a.z-c[2]];if(!d)return yb(a);d=Ga(0,a,b.tt);d=Za(b,0,d);return yb(d)}function Cb(a,b,c,d,e){var h=b*d+c*e;b=-b*e+c*d;c=Math.sqrt(a*a+h*h);d=0;0<c&&(d=57.29577951308232*Math.atan2(h,a),0>d&&(d+=360));return new Db(a,h,b,57.29577951308232*Math.atan2(b,c),d)}function ra(a,b,c){void 0===Ka&&(Ka=.017453292519943295*Ba(y(ab)).mobl,Eb=Math.cos(Ka),Fb=Math.sin(Ka));r(a);r(b);r(c);return Cb(a,b,c,Eb,Fb)}function X(a){a=
-y(a);var b=S(a),c=b.distance_au*Math.cos(b.geo_eclip_lat);b=[c*Math.cos(b.geo_eclip_lon),c*Math.sin(b.geo_eclip_lon),b.distance_au*Math.sin(b.geo_eclip_lat)];var d=.017453292519943295*na(a);c=Math.cos(d);d=Math.sin(d);b=Ga(a.tt,[b[0],b[1]*c-b[2]*d,b[1]*d+b[2]*c],0);return new B(b[0],b[1],b[2],a)}function ba(a,b){var c=1,d=0;a=$jscomp.makeIterator(a);for(var e=a.next();!e.done;e=a.next()){var h=0;e=$jscomp.makeIterator(e.value);for(var l=e.next();!l.done;l=e.next()){var k=$jscomp.makeIterator(l.value);
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-sc;g.Seasons=function(a){function b(l,k,f){k=new Date(Date.UTC(a,k-1,f));l=Lb(l,k,4);if(!l)throw"Cannot find season change near "+k.toISOString();return l}a instanceof Date&&Number.isFinite(a.getTime())&&(a=a.getUTCFullYear());if(!Number.isSafeInteger(a))throw"Cannot calculate seasons because year argument "+a+" is neither a Date nor a safe integer.";var c=b(0,3,19),d=b(90,6,19),e=b(180,9,21),h=b(270,12,20);return new sc(c,d,e,h)};var Rb=function(a,b,c,d){this.time=a;this.visibility=b;this.elongation=
-c;this.ecliptic_separation=d};g.ElongationEvent=Rb;g.Elongation=Qb;g.SearchMaxElongation=function(a,b){function c(m){var n=m.AddDays(-.005);m=m.AddDays(.005);n=ja(a,n);m=ja(a,m);return(n-m)/.01}b=y(b);var d={Mercury:{s1:50,s2:85},Venus:{s1:40,s2:50}}[a];if(!d)throw"SearchMaxElongation works for Mercury and Venus only.";for(var e=0;2>=++e;){var h=ea(a,b),l=ea("Earth",b),k=ua(h-l),f=h=l=void 0;k>=-d.s1&&k<+d.s1?(f=0,l=+d.s1,h=+d.s2):k>=+d.s2||k<-d.s2?(f=0,l=-d.s2,h=-d.s1):0<=k?(f=-va(a)/4,l=+d.s1,h=
-+d.s2):(f=-va(a)/4,l=-d.s2,h=-d.s1);k=b.AddDays(f);l=ka(a,l,k);h=ka(a,h,l);k=c(l);if(0<=k)throw"SearchMaxElongation: internal error: m1 = "+k;f=c(h);if(0>=f)throw"SearchMaxElongation: internal error: m2 = "+f;k=E(c,l,h,{init_f1:k,init_f2:f,dt_tolerance_seconds:10});if(!k)throw"SearchMaxElongation: failed search iter "+e+" (t1="+l.toString()+", t2="+h.toString()+")";if(k.tt>=b.tt)return Qb(a,k);b=h.AddDays(1)}throw"SearchMaxElongation: failed to find event after 2 tries.";};g.SearchPeakMagnitude=function(a,
-b){function c(f){var m=f.AddDays(-.005);f=f.AddDays(.005);m=Qa(a,m).mag;return(Qa(a,f).mag-m)/.01}if("Venus"!==a)throw"SearchPeakMagnitude currently works for Venus only.";b=y(b);for(var d=0;2>=++d;){var e=ea(a,b),h=ea("Earth",b),l=ua(e-h),k=e=h=void 0;-10<=l&&10>l?(k=0,h=10,e=30):30<=l||-30>l?(k=0,h=-30,e=-10):0<=l?(k=-va(a)/4,h=10,e=30):(k=-va(a)/4,h=-30,e=-10);l=b.AddDays(k);h=ka(a,h,l);e=ka(a,e,h);l=c(h);if(0<=l)throw"SearchPeakMagnitude: internal error: m1 = "+l;k=c(e);if(0>=k)throw"SearchPeakMagnitude: internal error: m2 = "+
-k;l=E(c,h,e,{init_f1:l,init_f2:k,dt_tolerance_seconds:10});if(!l)throw"SearchPeakMagnitude: failed search iter "+d+" (t1="+h.toString()+", t2="+e.toString()+")";if(l.tt>=b.tt)return Qa(a,l);b=e.AddDays(1)}throw"SearchPeakMagnitude: failed to find event after 2 tries.";};var ya=function(a,b,c){this.time=a;this.kind=b;this.dist_au=c;this.dist_km=1.4959787069098932E8*c};g.Apsis=ya;g.SearchLunarApsis=Sb;g.NextLunarApsis=function(a){var b=Sb(a.time.AddDays(11));if(1!==b.kind+a.kind)throw"NextLunarApsis INTERNAL ERROR: did not find alternating apogee/perigee: prev="+
-a.kind+" @ "+a.time.toString()+", next="+b.kind+" @ "+b.time.toString();return b};g.SearchPlanetApsis=Ub;g.NextPlanetApsis=function(a,b){if(0!==b.kind&&1!==b.kind)throw"Invalid apsis kind: "+b.kind;var c=b.time.AddDays(.25*Y[a].OrbitalPeriod);a=Ub(a,c);if(1!==a.kind+b.kind)throw"Internal error: previous apsis was "+b.kind+", but found "+a.kind+" for next apsis.";return a};g.InverseRotation=la;g.CombineRotation=ma;g.VectorFromSphere=ib;g.VectorFromEquator=Vb;g.EquatorFromVector=Wb;g.SphereFromVector=
-jb;g.HorizonFromVector=function(a,b){a=jb(a);a.lon=Xb(a.lon);a.lat+=qa(b,a.lat);return a};g.VectorFromHorizon=function(a,b,c){var d=Xb(a.lon);c=a.lat+Yb(c,a.lat);a=new Ra(c,d,a.dist);return ib(a,b)};g.Refraction=qa;g.InverseRefraction=Yb;g.RotateVector=za;g.Rotation_EQJ_ECL=Zb;g.Rotation_ECL_EQJ=function(){return new M([[1,0,0],[0,.9174821430670688,.3977769691083922],[0,-.3977769691083922,.9174821430670688]])};g.Rotation_EQJ_EQD=kb;g.Rotation_EQD_EQJ=lb;g.Rotation_EQD_HOR=mb;g.Rotation_HOR_EQD=$b;
-g.Rotation_HOR_EQJ=ac;g.Rotation_EQJ_HOR=function(a,b){a=ac(a,b);return la(a)};g.Rotation_EQD_ECL=bc;g.Rotation_ECL_EQD=cc;g.Rotation_ECL_HOR=dc;g.Rotation_HOR_ECL=function(a,b){a=dc(a,b);return la(a)};var Hc=[["And","Andromeda"],["Ant","Antila"],["Aps","Apus"],["Aql","Aquila"],["Aqr","Aquarius"],["Ara","Ara"],["Ari","Aries"],["Aur","Auriga"],["Boo","Bootes"],["Cae","Caelum"],["Cam","Camelopardis"],["Cap","Capricornus"],["Car","Carina"],["Cas","Cassiopeia"],["Cen","Centaurus"],["Cep","Cepheus"],["Cet",
-"Cetus"],["Cha","Chamaeleon"],["Cir","Circinus"],["CMa","Canis Major"],["CMi","Canis Minor"],["Cnc","Cancer"],["Col","Columba"],["Com","Coma Berenices"],["CrA","Corona Australis"],["CrB","Corona Borealis"],["Crt","Crater"],["Cru","Crux"],["Crv","Corvus"],["CVn","Canes Venatici"],["Cyg","Cygnus"],["Del","Delphinus"],["Dor","Dorado"],["Dra","Draco"],["Equ","Equuleus"],["Eri","Eridanus"],["For","Fornax"],["Gem","Gemini"],["Gru","Grus"],["Her","Hercules"],["Hor","Horologium"],["Hya","Hydra"],["Hyi","Hydrus"],
-["Ind","Indus"],["Lac","Lacerta"],["Leo","Leo"],["Lep","Lepus"],["Lib","Libra"],["LMi","Leo Minor"],["Lup","Lupus"],["Lyn","Lynx"],["Lyr","Lyra"],["Men","Mensa"],["Mic","Microscopium"],["Mon","Monoceros"],["Mus","Musca"],["Nor","Norma"],["Oct","Octans"],["Oph","Ophiuchus"],["Ori","Orion"],["Pav","Pavo"],["Peg","Pegasus"],["Per","Perseus"],["Phe","Phoenix"],["Pic","Pictor"],["PsA","Pisces Austrinus"],["Psc","Pisces"],["Pup","Puppis"],["Pyx","Pyxis"],["Ret","Reticulum"],["Scl","Sculptor"],["Sco","Scorpius"],
-["Sct","Scutum"],["Ser","Serpens"],["Sex","Sextans"],["Sge","Sagitta"],["Sgr","Sagittarius"],["Tau","Taurus"],["Tel","Telescopium"],["TrA","Triangulum Australe"],["Tri","Triangulum"],["Tuc","Tucana"],["UMa","Ursa Major"],["UMi","Ursa Minor"],["Vel","Vela"],["Vir","Virgo"],["Vol","Volans"],["Vul","Vulpecula"]],Ic=[[83,0,8640,2112],[83,2880,5220,2076],[83,7560,8280,2068],[83,6480,7560,2064],[15,0,2880,2040],[10,3300,3840,1968],[15,0,1800,1920],[10,3840,5220,1920],[83,6300,6480,1920],[33,7260,7560,1920],
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-[60,6480,7680,-1800],[43,7680,8400,-1800],[81,8400,8640,-1800],[81,270,480,-1824],[42,0,1260,-1980],[17,2760,4920,-1980],[2,4920,6480,-1980],[52,1260,2760,-2040],[57,0,8640,-2160]],qb,tc,uc=function(a,b,c,d){this.symbol=a;this.name=b;this.ra1875=c;this.dec1875=d};g.ConstellationInfo=uc;g.Constellation=function(a,b){r(a);r(b);if(-90>b||90<b)throw"Invalid declination angle. Must be -90..+90.";a%=24;0>a&&(a+=24);qb||(qb=kb(new P(-45655.74141261017)),tc=new P(0));a=new Ha(a,b,1);a=Vb(a,tc);a=za(qb,a);
-a=Wb(a);b=10/240;for(var c=b/15,d=$jscomp.makeIterator(Ic),e=d.next();!e.done;e=d.next()){e=e.value;var h=e[1]*c,l=e[2]*c;if(e[3]*b<=a.dec&&h<=a.ra&&a.ra<l)return b=Hc[e[0]],new uc(b[0],b[1],a.ra,a.dec)}throw"Unable to find constellation for given coordinates.";};var gc=function(a,b,c,d,e){this.kind=a;this.peak=b;this.sd_penum=c;this.sd_partial=d;this.sd_total=e};g.LunarEclipseInfo=gc;var Bc=function(a,b,c,d,e,h,l){this.time=a;this.u=b;this.r=c;this.k=d;this.p=e;this.target=h;this.dir=l};g.SearchLunarEclipse=
-fc;var ic=function(a,b,c,d,e){this.kind=a;this.peak=b;this.distance=c;this.latitude=d;this.longitude=e};g.GlobalSolarEclipseInfo=ic;g.NextLunarEclipse=function(a){a=a.AddDays(10);return fc(a)};g.SearchGlobalSolarEclipse=hc;g.NextGlobalSolarEclipse=function(a){a=a.AddDays(10);return hc(a)};var mc=function(a,b){this.time=a;this.altitude=b};g.EclipseEvent=mc;var oc=function(a,b,c,d,e,h){this.kind=a;this.partial_begin=b;this.total_begin=c;this.peak=d;this.total_end=e;this.partial_end=h};g.LocalSolarEclipseInfo=
-oc;g.SearchLocalSolarEclipse=nc;g.NextLocalSolarEclipse=function(a,b){a=a.AddDays(10);return nc(a,b)};var rc=function(a,b,c,d){this.start=a;this.peak=b;this.finish=c;this.separation=d};g.TransitInfo=rc;g.SearchTransit=qc;g.NextTransit=function(a,b){b=b.AddDays(100);return qc(a,b)}},{}]},{},[1])(1)});
+b.latitude),l=Math.cos(.017453292519943295*b.latitude),k=Math.sin(.017453292519943295*b.longitude),f=Math.cos(.017453292519943295*b.longitude);b=Math.sin(.017453292519943295*d);var m=Math.cos(.017453292519943295*d),n=Math.sin(.2617993877991494*c),q=Math.cos(.2617993877991494*c),u=[l*f,l*k,h];h=[-h*f,-h*k,l];k=[k,-f,0];l=-15*pa(a);a=ha(l,u);u=ha(l,h);k=ha(l,k);b=[m*q,m*n,b];n=b[0]*a[0]+b[1]*a[1]+b[2]*a[2];m=b[0]*u[0]+b[1]*u[1]+b[2]*u[2];u=b[0]*k[0]+b[1]*k[1]+b[2]*k[2];q=Math.sqrt(m*m+u*u);0<q?(m=57.29577951308232*
+-Math.atan2(u,m),0>m&&(m+=360)):m=0;n=57.29577951308232*Math.atan2(q,n);q=d;if(e&&(d=n,e=qa(e,90-n),n-=e,0<e&&3E-4<n)){c=Math.sin(.017453292519943295*n);q=Math.cos(.017453292519943295*n);u=Math.sin(.017453292519943295*d);d=Math.cos(.017453292519943295*d);e=[];for(k=0;3>k;++k)e.push((b[k]-d*a[k])/u*c+a[k]*q);q=Math.sqrt(e[0]*e[0]+e[1]*e[1]);0<q?(c=57.29577951308232*Math.atan2(e[1],e[0])/15,0>c&&(c+=24)):c=0;q=57.29577951308232*Math.atan2(e[2],q)}return new zb(m,90-n,c,q)}function ia(a){if(!(a instanceof
+Ab))throw"Not an instance of the Observer class: "+a;r(a.latitude);r(a.longitude);r(a.height);if(-90>a.latitude||90<a.latitude)throw"Latitude "+a.latitude+" is out of range. Must be -90..+90.";return a}function Bb(a){a=y(a).AddDays(-.005775518331089121);var b=N(F.Earth,a);b=Ga(0,[-b.x,-b.y,-b.z],a.tt);var c=$jscomp.makeIterator(Za(a,0,b));b=c.next().value;var d=c.next().value;c=c.next().value;a=.017453292519943295*Ba(a).tobl;return Cb(b,d,c,Math.cos(a),Math.sin(a))}function Ja(a,b,c,d,e){ia(c);x(d);
+x(e);b=y(b);c=xb(b,c);a=W(a,b,e);a=[a.x-c[0],a.y-c[1],a.z-c[2]];if(!d)return yb(a);d=Ga(0,a,b.tt);d=Za(b,0,d);return yb(d)}function Cb(a,b,c,d,e){var h=b*d+c*e;b=-b*e+c*d;c=Math.sqrt(a*a+h*h);d=0;0<c&&(d=57.29577951308232*Math.atan2(h,a),0>d&&(d+=360));return new Db(a,h,b,57.29577951308232*Math.atan2(b,c),d)}function ra(a,b,c){void 0===Ka&&(Ka=.017453292519943295*Ba(y(ab)).mobl,Eb=Math.cos(Ka),Fb=Math.sin(Ka));r(a);r(b);r(c);return Cb(a,b,c,Eb,Fb)}function X(a){a=y(a);var b=S(a),c=b.distance_au*Math.cos(b.geo_eclip_lat);
+b=[c*Math.cos(b.geo_eclip_lon),c*Math.sin(b.geo_eclip_lon),b.distance_au*Math.sin(b.geo_eclip_lat)];var d=.017453292519943295*na(a);c=Math.cos(d);d=Math.sin(d);b=Ga(a.tt,[b[0],b[1]*c-b[2]*d,b[1]*d+b[2]*c],0);return new B(b[0],b[1],b[2],a)}function ba(a,b){var c=1,d=0;a=$jscomp.makeIterator(a);for(var e=a.next();!e.done;e=a.next()){var h=0;e=$jscomp.makeIterator(e.value);for(var l=e.next();!l.done;l=e.next()){var k=$jscomp.makeIterator(l.value);l=k.next().value;var f=k.next().value;k=k.next().value;
+h+=l*Math.cos(f+b*k)}d+=c*h;c*=b}return d}function bb(a,b){var c=1,d=0,e=0,h=0;a=$jscomp.makeIterator(a);for(var l=a.next();!l.done;l=a.next()){var k=0,f=0;l=$jscomp.makeIterator(l.value);for(var m=l.next();!m.done;m=l.next()){var n=$jscomp.makeIterator(m.value);m=n.next().value;var q=n.next().value;n=n.next().value;q+=b*n;k+=m*n*Math.sin(q);0<h&&(f+=m*Math.cos(q))}e+=h*d*f-c*k;d=c;c*=b;++h}return e}function cb(a){return new C(a[0]+4.4036E-7*a[1]-1.90919E-7*a[2],-4.79966E-7*a[0]+.917482137087*a[1]-
+.397776982902*a[2],.397776982902*a[1]+.917482137087*a[2])}function Gb(a,b,c){var d=c*Math.cos(b);return[d*Math.cos(a),d*Math.sin(a),c*Math.sin(b)]}function N(a,b){var c=b.tt/365250,d=ba(a[0],c),e=ba(a[1],c);a=ba(a[2],c);d=Gb(d,e,a);return cb(d).ToAstroVector(b)}function La(a,b,c,d){d/=d+2.959122082855911E-4;b=N(F[c],b);a.x+=d*b.x;a.y+=d*b.y;a.z+=d*b.z}function Ma(a,b,c,d){d/=d+2.959122082855911E-4;var e=F[c],h=b/365250;c=ba(e[0],h);var l=ba(e[1],h),k=ba(e[2],h),f=bb(e[0],h),m=bb(e[1],h);h=bb(e[2],
+h);var n=Math.cos(c),q=Math.sin(c),u=Math.cos(l),w=Math.sin(l);e=+(h*u*n)-k*w*n*m-k*u*q*f;f=+(h*u*q)-k*w*q*m+k*u*n*f;m=+(h*w)+k*u*m;c=Gb(c,l,k);l=[e/365250,f/365250,m/365250];c=cb(c);l=cb(l);b=new Na(b,c,l);a.r.incr(b.r.mul(d));a.v.incr(b.v.mul(d));return b}function sa(a,b,c){a=c.sub(a);c=a.quadrature();return a.mul(b/(c*Math.sqrt(c)))}function Oa(a,b,c,d){return new C(b.x+a*(c.x+a*d.x/2),b.y+a*(c.y+a*d.y/2),b.z+a*(c.z+a*d.z/2))}function db(a,b){var c=a-b.tt,d=new Pa(a),e=Oa(c,b.r,b.v,b.a),h=d.Acceleration(e).mean(b.a);
+e=Oa(c,b.r,b.v,h);b=b.v.add(h.mul(c));c=d.Acceleration(e);a=new Hb(a,e,b,c);return new Ib(d,a)}function Jb(a,b){a=Math.floor(a);return 0>a?0:a>=b?b-1:a}function eb(a){var b=$jscomp.makeIterator(a);a=b.next().value;var c=$jscomp.makeIterator(b.next().value);var d=c.next().value;var e=c.next().value;c=c.next().value;var h=$jscomp.makeIterator(b.next().value);b=h.next().value;var l=h.next().value;h=h.next().value;d=new Na(a,new C(d,e,c),new C(b,l,h));a=new Pa(d.tt);e=d.r.add(a.Sun.r);c=d.v.add(a.Sun.v);
+b=a.Acceleration(e);d=new Hb(d.tt,e,c,b);return new Ib(a,d)}function Kb(a,b,c){a=eb(a);for(var d=Math.ceil((b-a.grav.tt)/c),e=0;e<d;++e)a=db(e+1===d?b:a.grav.tt+c,a.grav);return a}function ta(a,b){b=y(b);if(a in F)return N(F[a],b);if("Pluto"===a){a=b.tt;var c=ca[0][0];if(a<c||a>ca[40][0])a=null;else{a=Jb((a-c)/36500,40);if(!fb[a]){c=fb[a]=[];c[0]=eb(ca[a]).grav;c[146]=eb(ca[a+1]).grav;var d,e=c[0].tt;for(d=1;146>d;++d)c[d]=db(e+=250,c[d-1]).grav;e=c[146].tt;var h=[];h[146]=c[146];for(d=145;0<d;--d)h[d]=
+db(e-=250,h[d+1]).grav;for(d=145;0<d;--d)e=d/146,c[d].r=c[d].r.mul(1-e).add(h[d].r.mul(e)),c[d].v=c[d].v.mul(1-e).add(h[d].v.mul(e)),c[d].a=c[d].a.mul(1-e).add(h[d].a.mul(e))}a=fb[a]}(c=a)?(d=Jb((b.tt-c[0].tt)/250,146),a=c[d],d=c[d+1],h=a.a.mean(d.a),c=Oa(b.tt-a.tt,a.r,a.v,h),d=Oa(b.tt-d.tt,d.r,d.v,h),a=(b.tt-a.tt)/250,a=c.mul(1-a).add(d.mul(a)),c=new Pa(b.tt)):(c=b.tt<ca[0][0]?Kb(ca[0],b.tt,-250):Kb(ca[40],b.tt,250),a=c.grav.r,c=c.bary);return a.sub(c.Sun.r).ToAstroVector(b)}if("Sun"===a)return new B(0,
+0,0,b);if("Moon"===a)return a=N(F.Earth,b),c=X(b),new B(a.x+c.x,a.y+c.y,a.z+c.z,b);if("EMB"===a)return a=N(F.Earth,b),c=X(b),new B(a.x+c.x/82.30056,a.y+c.y/82.30056,a.z+c.z/82.30056,b);if("SSB"===a)return a=new B(0,0,0,b),La(a,b,"Jupiter",2.825345909524226E-7),La(a,b,"Saturn",8.459715185680659E-8),La(a,b,"Uranus",1.292024916781969E-8),La(a,b,"Neptune",1.524358900784276E-8),a;throw'HelioVector: Unknown body "'+a+'"';}function da(a,b){b=y(b);return a in F?ba(F[a][2],b.tt/365250):ta(a,b).Length()}function W(a,
+b,c){x(c);b=y(b);if("Moon"===a)return X(b);if("Earth"===a)return new B(0,0,0,b);for(var d=null,e,h=0,l=b,k=0;10>k;++k){e=ta(a,l);c?d=N(F.Earth,l):d||(d=N(F.Earth,b));e=new B(e.x-d.x,e.y-d.y,e.z-d.z,b);var f=b.AddDays(-e.Length()/173.1446326846693);h=Math.abs(f.tt-l.tt);if(1E-9>h)return e;l=f}throw"Light-travel time solver did not converge: dt="+h;}function yc(a,b,c,d,e){var h=(e+c)/2-d;c=(e-c)/2;if(0==h){if(0==c)return null;d=-d/c;if(-1>d||1<d)return null}else{d=c*c-4*h*d;if(0>=d)return null;e=Math.sqrt(d);
+d=(-c+e)/(2*h);e=(-c-e)/(2*h);if(-1<=d&&1>=d){if(-1<=e&&1>=e)return null}else if(-1<=e&&1>=e)d=e;else return null}return{x:d,t:a+d*b,df_dt:(2*h*d+c)/b}}function E(a,b,c,d){var e=r(d&&d.dt_tolerance_seconds||1);e=Math.abs(e/86400);var h=d&&d.init_f1||a(b),l=d&&d.init_f2||a(c),k=NaN,f=0;d=d&&d.iter_limit||20;for(var m=!0;;){if(++f>d)throw"Excessive iteration in Search()";var n=new P(b.ut+.5*(c.ut-b.ut)),q=n.ut-b.ut;if(Math.abs(q)<e)return n;m?k=a(n):m=!0;var u=yc(n.ut,c.ut-n.ut,h,k,l);if(u){var w=y(u.t),
+H=a(w);if(0!==u.df_dt){if(Math.abs(H/u.df_dt)<e)return w;u=1.2*Math.abs(H/u.df_dt);if(u<q/10&&(q=w.AddDays(-u),w=w.AddDays(+u),0>(q.ut-b.ut)*(q.ut-c.ut)&&0>(w.ut-b.ut)*(w.ut-c.ut))){u=a(q);var z=a(w);if(0>u&&0<=z){h=u;l=z;b=q;c=w;k=H;m=!1;continue}}}}if(0>h&&0<=k)c=n,l=k;else if(0>k&&0<=l)b=n,h=k;else return null}}function ua(a){for(;-180>=a;)a+=360;for(;180<a;)a-=360;return a}function Lb(a,b,c){r(a);r(c);b=y(b);c=b.AddDays(c);return E(function(d){d=Bb(d);return ua(d.elon-a)},b,c)}function gb(a,b){if("Earth"===
+a)throw"The Earth does not have a longitude as seen from itself.";b=y(b);a=W(a,b,!1);a=ra(a.x,a.y,a.z);b=W("Sun",b,!1);b=ra(b.x,b.y,b.z);for(b=a.elon-b.elon;0>b;)b+=360;for(;360<=b;)b-=360;return b}function ja(a,b){if("Earth"==a)throw"The Earth does not have an angle as seen from itself.";var c=W("Sun",b,!0);a=W(a,b,!0);return O(c,a)}function ea(a,b){if("Sun"===a)throw"Cannot calculate heliocentric longitude of the Sun.";a=ta(a,b);return ra(a.x,a.y,a.z).elon}function Qa(a,b){if("Earth"===a)throw"The illumination of the Earth is not defined.";
+var c=y(b),d=N(F.Earth,c);if("Sun"===a){var e=new B(-d.x,-d.y,-d.z,c);b=new B(0,0,0,c);d=0}else"Moon"===a?(e=X(c),b=new B(d.x+e.x,d.y+e.y,d.z+e.z,c)):(b=ta(a,b),e=new B(b.x-d.x,b.y-d.y,b.z-d.z,c)),d=O(e,b);var h=e.Length(),l=b.Length();if("Sun"===a)a=zc+5*Math.log10(h);else if("Moon"===a){a=.017453292519943295*d;var k=a*a;a=-12.717+1.49*Math.abs(a)+.0431*k*k;a+=5*Math.log10(h/.002573570052980638*l)}else if("Saturn"===a){a=d;var f=ra(e.x,e.y,e.z);k=.017453292519943295*f.elat;f=Math.asin(Math.sin(k)*
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+-6.87;break;case "Pluto":a=-1;k=4;break;default:throw"VisualMagnitude: unsupported body "+a;}var q=d/100;a=a+q*(k+q*(m+q*n))+5*Math.log10(l*h)}return new Mb(c,a,d,l,h,e,b,f)}function va(a){if("Earth"===a)throw"The Earth does not have a synodic period as seen from itself.";if("Moon"===a)return 29.530588;var b=Y[a];if(!b)throw"Not a valid planet name: "+a;a=Y.Earth.OrbitalPeriod;return Math.abs(a/(a/b.OrbitalPeriod-1))}function ka(a,b,c){function d(m){var n=ea(a,m);m=ea("Earth",m);return ua(h*(m-n)-
+b)}r(b);var e=Y[a];if(!e)throw"Cannot search relative longitude because body is not a planet: "+a;if("Earth"===a)throw"Cannot search relative longitude for the Earth (it is always 0)";var h=e.OrbitalPeriod>Y.Earth.OrbitalPeriod?1:-1;e=va(a);c=y(c);var l=d(c);0<l&&(l-=360);for(var k=0;100>k;++k){var f=-l/360*e;c=c.AddDays(f);if(1>86400*Math.abs(f))return c;f=l;l=d(c);30>Math.abs(f)&&f!==l&&(f/=f-l,.5<f&&2>f&&(e*=f))}throw"Relative longitude search failed to converge for "+a+" near "+c.toString()+" (error_angle = "+
+l+").";}function hb(a){return gb("Moon",a)}function wa(a,b,c){function d(l){l=hb(l);return ua(l-a)}r(a);r(c);b=y(b);var e=d(b);0<e&&(e-=360);var h=-(29.530588*e)/360;e=h-1.5;if(e>c)return null;c=Math.min(c,h+1.5);e=b.AddDays(e);b=b.AddDays(c);return E(d,e,b)}function Nb(a){var b=hb(a);b=(Math.floor(b/90)+1)%4;a=wa(90*b,a,10);if(!a)throw"Cannot find moon quarter";return new Ob(b,a)}function xa(a,b,c,d){ia(b);d=y(d);var e=0;if("Earth"===a)throw"Cannot search for hour angle of the Earth.";r(c);if(0>
+c||24<=c)throw"Invalid hour angle "+c;for(;;){++e;var h=pa(d),l=Ja(a,d,b,!0,!0);h=(c+l.ra-b.longitude/15-h)%24;1===e?0>h&&(h+=24):-12>h?h+=24:12<h&&(h-=24);if(.1>3600*Math.abs(h))return a=Ia(d,b,l.ra,l.dec,"normal"),new Pb(d,a);d=d.AddDays(h/24*.9972695717592592)}}function Qb(a,b){b=y(b);var c=gb(a,b);if(180<c){var d="morning";c=360-c}else d="evening";a=ja(a,b);return new Rb(b,d,a,c)}function Sb(a){function b(k){var f=k.AddDays(-5E-4);k=k.AddDays(5E-4);f=S(f).distance_au;return(S(k).distance_au-f)/
+.001}function c(k){return-b(k)}a=y(a);for(var d=b(a),e=0;59.061176>5*e;++e){var h=a.AddDays(5),l=b(h);if(0>=d*l){if(0>d||0<l){a=E(b,a,h,{init_f1:d,init_f2:l});if(!a)throw"SearchLunarApsis INTERNAL ERROR: perigee search failed!";d=S(a).distance_au;return new ya(a,0,d)}if(0<d||0>l){a=E(c,a,h,{init_f1:-d,init_f2:-l});if(!a)throw"SearchLunarApsis INTERNAL ERROR: apogee search failed!";d=S(a).distance_au;return new ya(a,1,d)}throw"SearchLunarApsis INTERNAL ERROR: cannot classify apsis event!";}a=h;d=l}throw"SearchLunarApsis INTERNAL ERROR: could not find apsis within 2 synodic months of start date.";
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+d),4*d);if(c.time.tt>=b.tt)return a.time.tt>=b.tt&&a.time.tt<c.time.tt?a:c;if(a.time.tt>=b.tt)return a;throw"Internal error: failed to find Neptune apsis.";}function Ub(a,b){function c(n){var q=n.AddDays(-5E-4);n=n.AddDays(5E-4);q=da(a,q);return(da(a,n)-q)/.001}function d(n){return-c(n)}if("Neptune"===a||"Pluto"===a)return Ac(a,b);for(var e=Y[a].OrbitalPeriod,h=e/6,l=c(b),k=0;k*h<2*e;++k){var f=b.AddDays(h),m=c(f);if(0>=l*m){e=h=void 0;if(0>l||0<m)h=c,e=0;else if(0<l||0>m)h=d,e=1;else throw"Internal error with slopes in SearchPlanetApsis";
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+b.rot[2][2]*a.rot[2][2]]])}function ib(a,b){var c=.017453292519943295*a.lat,d=.017453292519943295*a.lon,e=a.dist*Math.cos(c);return new B(e*Math.cos(d),e*Math.sin(d),a.dist*Math.sin(c),b)}function Vb(a,b){return ib(new Ra(a.dec,15*a.ra,a.dist),b)}function Wb(a){a=jb(a);return new Ha(a.lon/15,a.lat,a.dist)}function jb(a){var b=a.x*a.x+a.y*a.y,c=Math.sqrt(b+a.z*a.z);if(0===b){if(0===a.z)throw"Zero-length vector not allowed.";var d=0;a=0>a.z?-90:90}else d=57.29577951308232*Math.atan2(a.y,a.x),0>d&&(d+=
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+a.x,this.y-a.y,this.z-a.z)};C.prototype.incr=function(a){this.x+=a.x;this.y+=a.y;this.z+=a.z};C.prototype.decr=function(a){this.x-=a.x;this.y-=a.y;this.z-=a.z};C.prototype.mul=function(a){return new C(a*this.x,a*this.y,a*this.z)};C.prototype.div=function(a){return new C(this.x/a,this.y/a,this.z/a)};C.prototype.mean=function(a){return new C((this.x+a.x)/2,(this.y+a.y)/2,(this.z+a.z)/2)};var Na=function(a,b,c){this.tt=a;this.r=b;this.v=c},Pa=function(a){var b=new Na(a,new C(0,0,0),new C(0,0,0));this.Jupiter=
+Ma(b,a,"Jupiter",2.825345909524226E-7);this.Saturn=Ma(b,a,"Saturn",8.459715185680659E-8);this.Uranus=Ma(b,a,"Uranus",1.292024916781969E-8);this.Neptune=Ma(b,a,"Neptune",1.524358900784276E-8);this.Jupiter.r.decr(b.r);this.Jupiter.v.decr(b.v);this.Saturn.r.decr(b.r);this.Saturn.v.decr(b.v);this.Uranus.r.decr(b.r);this.Uranus.v.decr(b.v);this.Neptune.r.decr(b.r);this.Neptune.v.decr(b.v);this.Sun=new Na(a,b.r.mul(-1),b.v.mul(-1))};Pa.prototype.Acceleration=function(a){var b=sa(a,2.959122082855911E-4,
+this.Sun.r);b.incr(sa(a,2.825345909524226E-7,this.Jupiter.r));b.incr(sa(a,8.459715185680659E-8,this.Saturn.r));b.incr(sa(a,1.292024916781969E-8,this.Uranus.r));b.incr(sa(a,1.524358900784276E-8,this.Neptune.r));return b};var Hb=function(a,b,c,d){this.tt=a;this.r=b;this.v=c;this.a=d},Ib=function(a,b){this.bary=a;this.grav=b},fb=[];g.HelioVector=ta;g.HelioDistance=da;g.GeoVector=W;g.Search=E;g.SearchSunLongitude=Lb;g.LongitudeFromSun=gb;g.AngleFromSun=ja;g.EclipticLongitude=ea;var Mb=function(a,b,c,
+d,e,h,l,k){this.time=a;this.mag=b;this.phase_angle=c;this.helio_dist=d;this.geo_dist=e;this.gc=h;this.hc=l;this.ring_tilt=k;this.phase_fraction=(1+Math.cos(.017453292519943295*c))/2};g.IlluminationInfo=Mb;g.Illumination=Qa;g.SearchRelativeLongitude=ka;g.MoonPhase=hb;g.SearchMoonPhase=wa;var Ob=function(a,b){this.quarter=a;this.time=b};g.MoonQuarter=Ob;g.SearchMoonQuarter=Nb;g.NextMoonQuarter=function(a){a=new Date(a.time.date.getTime()+5184E5);return Nb(a)};g.SearchRiseSet=function(a,b,c,d,e){function h(w){var H=
+Ja(a,w,b,!0,!0);w=Ia(w,b,H.ra,H.dec).altitude+l/H.dist*57.29577951308232+Gc;return c*w}ia(b);r(e);a:switch(a){case "Sun":var l=.0046504672612422675;break a;case "Moon":l=1.1618480877914597E-5;break a;default:l=0}if("Earth"===a)throw"Cannot find rise or set time of the Earth.";if(1===c){var k=12;var f=0}else if(-1===c)k=0,f=12;else throw"SearchRiseSet: Invalid direction parameter "+c+" -- must be +1 or -1";d=y(d);var m=h(d);var n;if(0<m){m=xa(a,b,k,d);var q=m.time;m=h(q)}else q=d;var u=xa(a,b,f,q);
+for(n=h(u.time);;){if(0>=m&&0<n&&(q=E(h,q,u.time,{init_f1:m,init_f2:n})))return q;m=xa(a,b,k,u.time);u=xa(a,b,f,m.time);if(m.time.ut>=d.ut+e)return null;q=m.time;m=h(m.time);n=h(u.time)}};var Pb=function(a,b){this.time=a;this.hor=b};g.HourAngleEvent=Pb;g.SearchHourAngle=xa;var sc=function(a,b,c,d){this.mar_equinox=a;this.jun_solstice=b;this.sep_equinox=c;this.dec_solstice=d};g.SeasonInfo=sc;g.Seasons=function(a){function b(l,k,f){k=new Date(Date.UTC(a,k-1,f));l=Lb(l,k,4);if(!l)throw"Cannot find season change near "+
+k.toISOString();return l}a instanceof Date&&Number.isFinite(a.getTime())&&(a=a.getUTCFullYear());if(!Number.isSafeInteger(a))throw"Cannot calculate seasons because year argument "+a+" is neither a Date nor a safe integer.";var c=b(0,3,19),d=b(90,6,19),e=b(180,9,21),h=b(270,12,20);return new sc(c,d,e,h)};var Rb=function(a,b,c,d){this.time=a;this.visibility=b;this.elongation=c;this.ecliptic_separation=d};g.ElongationEvent=Rb;g.Elongation=Qb;g.SearchMaxElongation=function(a,b){function c(m){var n=m.AddDays(-.005);
+m=m.AddDays(.005);n=ja(a,n);m=ja(a,m);return(n-m)/.01}b=y(b);var d={Mercury:{s1:50,s2:85},Venus:{s1:40,s2:50}}[a];if(!d)throw"SearchMaxElongation works for Mercury and Venus only.";for(var e=0;2>=++e;){var h=ea(a,b),l=ea("Earth",b),k=ua(h-l),f=h=l=void 0;k>=-d.s1&&k<+d.s1?(f=0,l=+d.s1,h=+d.s2):k>=+d.s2||k<-d.s2?(f=0,l=-d.s2,h=-d.s1):0<=k?(f=-va(a)/4,l=+d.s1,h=+d.s2):(f=-va(a)/4,l=-d.s2,h=-d.s1);k=b.AddDays(f);l=ka(a,l,k);h=ka(a,h,l);k=c(l);if(0<=k)throw"SearchMaxElongation: internal error: m1 = "+
+k;f=c(h);if(0>=f)throw"SearchMaxElongation: internal error: m2 = "+f;k=E(c,l,h,{init_f1:k,init_f2:f,dt_tolerance_seconds:10});if(!k)throw"SearchMaxElongation: failed search iter "+e+" (t1="+l.toString()+", t2="+h.toString()+")";if(k.tt>=b.tt)return Qb(a,k);b=h.AddDays(1)}throw"SearchMaxElongation: failed to find event after 2 tries.";};g.SearchPeakMagnitude=function(a,b){function c(f){var m=f.AddDays(-.005);f=f.AddDays(.005);m=Qa(a,m).mag;return(Qa(a,f).mag-m)/.01}if("Venus"!==a)throw"SearchPeakMagnitude currently works for Venus only.";
+b=y(b);for(var d=0;2>=++d;){var e=ea(a,b),h=ea("Earth",b),l=ua(e-h),k=e=h=void 0;-10<=l&&10>l?(k=0,h=10,e=30):30<=l||-30>l?(k=0,h=-30,e=-10):0<=l?(k=-va(a)/4,h=10,e=30):(k=-va(a)/4,h=-30,e=-10);l=b.AddDays(k);h=ka(a,h,l);e=ka(a,e,h);l=c(h);if(0<=l)throw"SearchPeakMagnitude: internal error: m1 = "+l;k=c(e);if(0>=k)throw"SearchPeakMagnitude: internal error: m2 = "+k;l=E(c,h,e,{init_f1:l,init_f2:k,dt_tolerance_seconds:10});if(!l)throw"SearchPeakMagnitude: failed search iter "+d+" (t1="+h.toString()+
+", t2="+e.toString()+")";if(l.tt>=b.tt)return Qa(a,l);b=e.AddDays(1)}throw"SearchPeakMagnitude: failed to find event after 2 tries.";};var ya=function(a,b,c){this.time=a;this.kind=b;this.dist_au=c;this.dist_km=1.4959787069098932E8*c};g.Apsis=ya;g.SearchLunarApsis=Sb;g.NextLunarApsis=function(a){var b=Sb(a.time.AddDays(11));if(1!==b.kind+a.kind)throw"NextLunarApsis INTERNAL ERROR: did not find alternating apogee/perigee: prev="+a.kind+" @ "+a.time.toString()+", next="+b.kind+" @ "+b.time.toString();
+return b};g.SearchPlanetApsis=Ub;g.NextPlanetApsis=function(a,b){if(0!==b.kind&&1!==b.kind)throw"Invalid apsis kind: "+b.kind;var c=b.time.AddDays(.25*Y[a].OrbitalPeriod);a=Ub(a,c);if(1!==a.kind+b.kind)throw"Internal error: previous apsis was "+b.kind+", but found "+a.kind+" for next apsis.";return a};g.InverseRotation=la;g.CombineRotation=ma;g.VectorFromSphere=ib;g.VectorFromEquator=Vb;g.EquatorFromVector=Wb;g.SphereFromVector=jb;g.HorizonFromVector=function(a,b){a=jb(a);a.lon=Xb(a.lon);a.lat+=qa(b,
+a.lat);return a};g.VectorFromHorizon=function(a,b,c){var d=Xb(a.lon);c=a.lat+Yb(c,a.lat);a=new Ra(c,d,a.dist);return ib(a,b)};g.Refraction=qa;g.InverseRefraction=Yb;g.RotateVector=za;g.Rotation_EQJ_ECL=Zb;g.Rotation_ECL_EQJ=function(){return new M([[1,0,0],[0,.9174821430670688,.3977769691083922],[0,-.3977769691083922,.9174821430670688]])};g.Rotation_EQJ_EQD=kb;g.Rotation_EQD_EQJ=lb;g.Rotation_EQD_HOR=mb;g.Rotation_HOR_EQD=$b;g.Rotation_HOR_EQJ=ac;g.Rotation_EQJ_HOR=function(a,b){a=ac(a,b);return la(a)};
+g.Rotation_EQD_ECL=bc;g.Rotation_ECL_EQD=cc;g.Rotation_ECL_HOR=dc;g.Rotation_HOR_ECL=function(a,b){a=dc(a,b);return la(a)};var Hc=[["And","Andromeda"],["Ant","Antila"],["Aps","Apus"],["Aql","Aquila"],["Aqr","Aquarius"],["Ara","Ara"],["Ari","Aries"],["Aur","Auriga"],["Boo","Bootes"],["Cae","Caelum"],["Cam","Camelopardis"],["Cap","Capricornus"],["Car","Carina"],["Cas","Cassiopeia"],["Cen","Centaurus"],["Cep","Cepheus"],["Cet","Cetus"],["Cha","Chamaeleon"],["Cir","Circinus"],["CMa","Canis Major"],["CMi",
+"Canis Minor"],["Cnc","Cancer"],["Col","Columba"],["Com","Coma Berenices"],["CrA","Corona Australis"],["CrB","Corona Borealis"],["Crt","Crater"],["Cru","Crux"],["Crv","Corvus"],["CVn","Canes Venatici"],["Cyg","Cygnus"],["Del","Delphinus"],["Dor","Dorado"],["Dra","Draco"],["Equ","Equuleus"],["Eri","Eridanus"],["For","Fornax"],["Gem","Gemini"],["Gru","Grus"],["Her","Hercules"],["Hor","Horologium"],["Hya","Hydra"],["Hyi","Hydrus"],["Ind","Indus"],["Lac","Lacerta"],["Leo","Leo"],["Lep","Lepus"],["Lib",
+"Libra"],["LMi","Leo Minor"],["Lup","Lupus"],["Lyn","Lynx"],["Lyr","Lyra"],["Men","Mensa"],["Mic","Microscopium"],["Mon","Monoceros"],["Mus","Musca"],["Nor","Norma"],["Oct","Octans"],["Oph","Ophiuchus"],["Ori","Orion"],["Pav","Pavo"],["Peg","Pegasus"],["Per","Perseus"],["Phe","Phoenix"],["Pic","Pictor"],["PsA","Pisces Austrinus"],["Psc","Pisces"],["Pup","Puppis"],["Pyx","Pyxis"],["Ret","Reticulum"],["Scl","Sculptor"],["Sco","Scorpius"],["Sct","Scutum"],["Ser","Serpens"],["Sex","Sextans"],["Sge","Sagitta"],
+["Sgr","Sagittarius"],["Tau","Taurus"],["Tel","Telescopium"],["TrA","Triangulum Australe"],["Tri","Triangulum"],["Tuc","Tucana"],["UMa","Ursa Major"],["UMi","Ursa Minor"],["Vel","Vela"],["Vir","Virgo"],["Vol","Volans"],["Vul","Vulpecula"]],Ic=[[83,0,8640,2112],[83,2880,5220,2076],[83,7560,8280,2068],[83,6480,7560,2064],[15,0,2880,2040],[10,3300,3840,1968],[15,0,1800,1920],[10,3840,5220,1920],[83,6300,6480,1920],[33,7260,7560,1920],[15,0,1263,1848],[10,4140,4890,1848],[83,5952,6300,1800],[15,7260,
+7440,1800],[10,2868,3300,1764],[33,3300,4080,1764],[83,4680,5952,1680],[13,1116,1230,1632],[33,7350,7440,1608],[33,4080,4320,1596],[15,0,120,1584],[83,5040,5640,1584],[15,8490,8640,1584],[33,4320,4860,1536],[33,4860,5190,1512],[15,8340,8490,1512],[10,2196,2520,1488],[33,7200,7350,1476],[15,7393.2,7416,1462],[10,2520,2868,1440],[82,2868,3030,1440],[33,7116,7200,1428],[15,7200,7393.2,1428],[15,8232,8340,1418],[13,0,876,1404],[33,6990,7116,1392],[13,612,687,1380],[13,876,1116,1368],[10,1116,1140,1368],
+[15,8034,8232,1350],[10,1800,2196,1344],[82,5052,5190,1332],[33,5190,6990,1332],[10,1140,1200,1320],[15,7968,8034,1320],[15,7416,7908,1316],[13,0,612,1296],[50,2196,2340,1296],[82,4350,4860,1272],[33,5490,5670,1272],[15,7908,7968,1266],[10,1200,1800,1260],[13,8232,8400,1260],[33,5670,6120,1236],[62,735,906,1212],[33,6120,6564,1212],[13,0,492,1200],[62,492,600,1200],[50,2340,2448,1200],[13,8400,8640,1200],[82,4860,5052,1164],[13,0,402,1152],[13,8490,8640,1152],[39,6543,6564,1140],[33,6564,6870,1140],
+[30,6870,6900,1140],[62,600,735,1128],[82,3030,3300,1128],[13,60,312,1104],[82,4320,4350,1080],[50,2448,2652,1068],[30,7887,7908,1056],[30,7875,7887,1050],[30,6900,6984,1044],[82,3300,3660,1008],[82,3660,3882,960],[8,5556,5670,960],[39,5670,5880,960],[50,3330,3450,954],[0,0,906,882],[62,906,924,882],[51,6969,6984,876],[62,1620,1689,864],[30,7824,7875,864],[44,7875,7920,864],[7,2352,2652,852],[50,2652,2790,852],[0,0,720,840],[44,7920,8214,840],[44,8214,8232,828],[0,8232,8460,828],[62,924,978,816],
+[82,3882,3960,816],[29,4320,4440,816],[50,2790,3330,804],[48,3330,3558,804],[0,258,507,792],[8,5466,5556,792],[0,8460,8550,770],[29,4440,4770,768],[0,8550,8640,752],[29,5025,5052,738],[80,870,978,736],[62,978,1620,736],[7,1620,1710,720],[51,6543,6969,720],[82,3960,4320,696],[30,7080,7530,696],[7,1710,2118,684],[48,3558,3780,684],[29,4770,5025,684],[0,0,24,672],[80,507,600,672],[7,2118,2352,672],[37,2838,2880,672],[30,7530,7824,672],[30,6933,7080,660],[80,690,870,654],[25,5820,5880,648],[8,5430,5466,
+624],[25,5466,5820,624],[51,6612,6792,624],[48,3870,3960,612],[51,6792,6933,612],[80,600,690,600],[66,258,306,570],[48,3780,3870,564],[87,7650,7710,564],[77,2052,2118,548],[0,24,51,528],[73,5730,5772,528],[37,2118,2238,516],[87,7140,7290,510],[87,6792,6930,506],[0,51,306,504],[87,7290,7404,492],[37,2811,2838,480],[87,7404,7650,468],[87,6930,7140,460],[6,1182,1212,456],[75,6792,6840,444],[59,2052,2076,432],[37,2238,2271,420],[75,6840,7140,388],[77,1788,1920,384],[39,5730,5790,384],[75,7140,7290,378],
+[77,1662,1788,372],[77,1920,2016,372],[23,4620,4860,360],[39,6210,6570,344],[23,4272,4620,336],[37,2700,2811,324],[39,6030,6210,308],[61,0,51,300],[77,2016,2076,300],[37,2520,2700,300],[61,7602,7680,300],[37,2271,2496,288],[39,6570,6792,288],[31,7515,7578,284],[61,7578,7602,284],[45,4146,4272,264],[59,2247,2271,240],[37,2496,2520,240],[21,2811,2853,240],[61,8580,8640,240],[6,600,1182,238],[31,7251,7308,204],[8,4860,5430,192],[61,8190,8580,180],[21,2853,3330,168],[45,3330,3870,168],[58,6570,6718.4,
+150],[3,6718.4,6792,150],[31,7500,7515,144],[20,2520,2526,132],[73,6570,6633,108],[39,5790,6030,96],[58,6570,6633,72],[61,7728,7800,66],[66,0,720,48],[73,6690,6792,48],[31,7308,7500,48],[34,7500,7680,48],[61,7680,7728,48],[61,7920,8190,48],[61,7800,7920,42],[20,2526,2592,36],[77,1290,1662,0],[59,1662,1680,0],[20,2592,2910,0],[85,5280,5430,0],[58,6420,6570,0],[16,954,1182,-42],[77,1182,1290,-42],[73,5430,5856,-78],[59,1680,1830,-96],[59,2100,2247,-96],[73,6420,6468,-96],[73,6570,6690,-96],[3,6690,
+6792,-96],[66,8190,8580,-96],[45,3870,4146,-144],[85,4146,4260,-144],[66,0,120,-168],[66,8580,8640,-168],[85,5130,5280,-192],[58,5730,5856,-192],[3,7200,7392,-216],[4,7680,7872,-216],[58,6180,6468,-240],[54,2100,2910,-264],[35,1770,1830,-264],[59,1830,2100,-264],[41,2910,3012,-264],[74,3450,3870,-264],[85,4260,4620,-264],[58,6330,6360,-280],[3,6792,7200,-288.8],[35,1740,1770,-348],[4,7392,7680,-360],[73,6180,6570,-384],[72,6570,6792,-384],[41,3012,3090,-408],[58,5856,5895,-438],[41,3090,3270,-456],
+[26,3870,3900,-456],[71,5856,5895,-462],[47,5640,5730,-480],[28,4530,4620,-528],[85,4620,5130,-528],[41,3270,3510,-576],[16,600,954,-585.2],[35,954,1350,-585.2],[26,3900,4260,-588],[28,4260,4530,-588],[47,5130,5370,-588],[58,5856,6030,-590],[16,0,600,-612],[11,7680,7872,-612],[4,7872,8580,-612],[16,8580,8640,-612],[41,3510,3690,-636],[35,1692,1740,-654],[46,1740,2202,-654],[11,7200,7680,-672],[41,3690,3810,-700],[41,4530,5370,-708],[47,5370,5640,-708],[71,5640,5760,-708],[35,1650,1692,-720],[58,6030,
+6336,-720],[76,6336,6420,-720],[41,3810,3900,-748],[19,2202,2652,-792],[41,4410,4530,-792],[41,3900,4410,-840],[36,1260,1350,-864],[68,3012,3372,-882],[35,1536,1650,-888],[76,6420,6900,-888],[65,7680,8280,-888],[70,8280,8400,-888],[36,1080,1260,-950],[1,3372,3960,-954],[70,0,600,-960],[36,600,1080,-960],[35,1392,1536,-960],[70,8400,8640,-960],[14,5100,5370,-1008],[49,5640,5760,-1008],[71,5760,5911.5,-1008],[9,1740,1800,-1032],[22,1800,2370,-1032],[67,2880,3012,-1032],[35,1230,1392,-1056],[71,5911.5,
+6420,-1092],[24,6420,6900,-1092],[76,6900,7320,-1092],[53,7320,7680,-1092],[35,1080,1230,-1104],[9,1620,1740,-1116],[49,5520,5640,-1152],[63,0,840,-1156],[35,960,1080,-1176],[40,1470,1536,-1176],[9,1536,1620,-1176],[38,7680,7920,-1200],[67,2160,2880,-1218],[84,2880,2940,-1218],[35,870,960,-1224],[40,1380,1470,-1224],[63,0,660,-1236],[12,2160,2220,-1260],[84,2940,3042,-1272],[40,1260,1380,-1276],[32,1380,1440,-1276],[63,0,570,-1284],[35,780,870,-1296],[64,1620,1800,-1296],[49,5418,5520,-1296],[84,
+3042,3180,-1308],[12,2220,2340,-1320],[14,4260,4620,-1320],[49,5100,5418,-1320],[56,5418,5520,-1320],[32,1440,1560,-1356],[84,3180,3960,-1356],[14,3960,4050,-1356],[5,6300,6480,-1368],[78,6480,7320,-1368],[38,7920,8400,-1368],[40,1152,1260,-1380],[64,1800,1980,-1380],[12,2340,2460,-1392],[63,0,480,-1404],[35,480,780,-1404],[63,8400,8640,-1404],[32,1560,1650,-1416],[56,5520,5911.5,-1440],[43,7320,7680,-1440],[64,1980,2160,-1464],[18,5460,5520,-1464],[5,5911.5,5970,-1464],[18,5370,5460,-1526],[5,5970,
+6030,-1526],[64,2160,2460,-1536],[12,2460,3252,-1536],[14,4050,4260,-1536],[27,4260,4620,-1536],[14,4620,5232,-1536],[18,4860,4920,-1560],[5,6030,6060,-1560],[40,780,1152,-1620],[69,1152,1650,-1620],[18,5310,5370,-1620],[5,6060,6300,-1620],[60,6300,6480,-1620],[81,7920,8400,-1620],[32,1650,2370,-1680],[18,4920,5310,-1680],[79,5310,6120,-1680],[81,0,480,-1800],[42,1260,1650,-1800],[86,2370,3252,-1800],[12,3252,4050,-1800],[55,4050,4920,-1800],[60,6480,7680,-1800],[43,7680,8400,-1800],[81,8400,8640,
+-1800],[81,270,480,-1824],[42,0,1260,-1980],[17,2760,4920,-1980],[2,4920,6480,-1980],[52,1260,2760,-2040],[57,0,8640,-2160]],qb,tc,uc=function(a,b,c,d){this.symbol=a;this.name=b;this.ra1875=c;this.dec1875=d};g.ConstellationInfo=uc;g.Constellation=function(a,b){r(a);r(b);if(-90>b||90<b)throw"Invalid declination angle. Must be -90..+90.";a%=24;0>a&&(a+=24);qb||(qb=kb(new P(-45655.74141261017)),tc=new P(0));a=new Ha(a,b,1);a=Vb(a,tc);a=za(qb,a);a=Wb(a);b=10/240;for(var c=b/15,d=$jscomp.makeIterator(Ic),
+e=d.next();!e.done;e=d.next()){e=e.value;var h=e[1]*c,l=e[2]*c;if(e[3]*b<=a.dec&&h<=a.ra&&a.ra<l)return b=Hc[e[0]],new uc(b[0],b[1],a.ra,a.dec)}throw"Unable to find constellation for given coordinates.";};var gc=function(a,b,c,d,e){this.kind=a;this.peak=b;this.sd_penum=c;this.sd_partial=d;this.sd_total=e};g.LunarEclipseInfo=gc;var Bc=function(a,b,c,d,e,h,l){this.time=a;this.u=b;this.r=c;this.k=d;this.p=e;this.target=h;this.dir=l};g.SearchLunarEclipse=fc;var ic=function(a,b,c,d,e){this.kind=a;this.peak=
+b;this.distance=c;this.latitude=d;this.longitude=e};g.GlobalSolarEclipseInfo=ic;g.NextLunarEclipse=function(a){a=a.AddDays(10);return fc(a)};g.SearchGlobalSolarEclipse=hc;g.NextGlobalSolarEclipse=function(a){a=a.AddDays(10);return hc(a)};var mc=function(a,b){this.time=a;this.altitude=b};g.EclipseEvent=mc;var oc=function(a,b,c,d,e,h){this.kind=a;this.partial_begin=b;this.total_begin=c;this.peak=d;this.total_end=e;this.partial_end=h};g.LocalSolarEclipseInfo=oc;g.SearchLocalSolarEclipse=nc;g.NextLocalSolarEclipse=
+function(a,b){a=a.AddDays(10);return nc(a,b)};var rc=function(a,b,c,d){this.start=a;this.peak=b;this.finish=c;this.separation=d};g.TransitInfo=rc;g.SearchTransit=qc;g.NextTransit=function(a,b){b=b.AddDays(100);return qc(a,b)}},{}]},{},[1])(1)});
diff --git a/source/js/astronomy.js b/source/js/astronomy.js
index 690534ee..cc5d843d 100644
--- a/source/js/astronomy.js
+++ b/source/js/astronomy.js
@@ -1564,7 +1564,7 @@ function sidereal_time(time) {
     if (gst < 0) {
         gst += 24;
     }
-    return gst;
+    return gst; // return sidereal hours in the half-open range [0, 24).
 }
 function terra(observer, st) {
     const df = 1 - 0.003352819697896; // flattening of the Earth
@@ -1926,26 +1926,61 @@ function Horizon(date, observer, ra, dec, refraction) {
     const cosdc = Math.cos(dec * DEG2RAD);
     const sinra = Math.sin(ra * 15 * DEG2RAD);
     const cosra = Math.cos(ra * 15 * DEG2RAD);
+    // Calculate three mutually perpendicular unit vectors
+    // in equatorial coordinates: uze, une, uwe.
+    //
+    // uze = The direction of the observer's local zenith (straight up).
+    // une = The direction toward due north on the observer's horizon.
+    // uwe = The direction toward due west on the observer's horizon.
+    //
+    // HOWEVER, these are uncorrected for the Earth's rotation due to the time of day.
+    //
+    // The components of these 3 vectors are as follows:
+    // x = direction from center of Earth toward 0 degrees longitude (the prime meridian) on equator.
+    // y = direction from center of Earth toward 90 degrees west longitude on equator.
+    // z = direction from center of Earth toward the north pole.
     let uze = [coslat * coslon, coslat * sinlon, sinlat];
     let une = [-sinlat * coslon, -sinlat * sinlon, coslat];
     let uwe = [sinlon, -coslon, 0];
+    // Correct the vectors uze, une, uwe for the Earth's rotation by calculating
+    // sideral time. Call spin() for each uncorrected vector to rotate about
+    // the Earth's axis to yield corrected unit vectors uz, un, uw.
+    // Multiply sidereal hours by -15 to convert to degrees and flip eastward
+    // rotation of the Earth to westward apparent movement of objects with time.
     const spin_angle = -15 * sidereal_time(time);
     let uz = spin(spin_angle, uze);
     let un = spin(spin_angle, une);
     let uw = spin(spin_angle, uwe);
+    // Convert angular equatorial coordinates (RA, DEC) to
+    // cartesian equatorial coordinates in 'p', using the
+    // same orientation system as uze, une, uwe.
     let p = [cosdc * cosra, cosdc * sinra, sindc];
+    // Use dot products of p with the zenith, north, and west
+    // vectors to obtain the cartesian coordinates of the body in
+    // the observer's horizontal orientation system.
+    // pz = zenith component [-1, +1]
+    // pn = north  component [-1, +1]
+    // pw = west   component [-1, +1]
     const pz = p[0] * uz[0] + p[1] * uz[1] + p[2] * uz[2];
     const pn = p[0] * un[0] + p[1] * un[1] + p[2] * un[2];
     const pw = p[0] * uw[0] + p[1] * uw[1] + p[2] * uw[2];
+    // proj is the "shadow" of the body vector along the observer's flat ground.
     let proj = Math.sqrt(pn * pn + pw * pw);
-    let az = 0;
+    // Calculate az = azimuth (compass direction clockwise from East.)
+    let az;
     if (proj > 0) {
+        // If the body is not exactly straight up/down, it has an azimuth.
+        // Invert the angle to produce degrees eastward from north.
         az = -Math.atan2(pw, pn) * RAD2DEG;
         if (az < 0)
             az += 360;
-        if (az >= 360)
-            az -= 360;
     }
+    else {
+        // The body is straight up/down, so it does not have an azimuth.
+        // Report an arbitrary but reasonable value.
+        az = 0;
+    }
+    // zd = the angle of the body away from the observer's zenith, in degrees.
     let zd = Math.atan2(proj, pz) * RAD2DEG;
     let out_ra = ra;
     let out_dec = dec;
@@ -1968,9 +2003,6 @@ function Horizon(date, observer, ra, dec, refraction) {
                 if (out_ra < 0) {
                     out_ra += 24;
                 }
-                if (out_ra >= 24) {
-                    out_ra -= 24;
-                }
             }
             else {
                 out_ra = 0;
diff --git a/source/js/astronomy.min.js b/source/js/astronomy.min.js
index d791c341..c101b7a8 100644
--- a/source/js/astronomy.min.js
+++ b/source/js/astronomy.min.js
@@ -123,9 +123,9 @@ var Vector=function(a,b,c,d){this.x=a;this.y=b;this.z=c;this.t=d};Vector.prototy
 function IsValidRotationArray(a){if(!(a instanceof Array)||3!==a.length)return!1;for(var b=0;3>b;++b){if(!(a[b]instanceof Array)||3!==a[b].length)return!1;for(var c=0;3>c;++c)if(!Number.isFinite(a[b][c]))return!1}return!0}var RotationMatrix=function(a){this.rot=a};exports.RotationMatrix=RotationMatrix;function MakeRotation(a){if(!IsValidRotationArray(a))throw"Argument must be a [3][3] array of numbers";return new RotationMatrix(a)}exports.MakeRotation=MakeRotation;
 var HorizontalCoordinates=function(a,b,c,d){this.azimuth=VerifyNumber(a);this.altitude=VerifyNumber(b);this.ra=VerifyNumber(c);this.dec=VerifyNumber(d)};exports.HorizontalCoordinates=HorizontalCoordinates;var EclipticCoordinates=function(a,b,c,d,e){this.ex=VerifyNumber(a);this.ey=VerifyNumber(b);this.ez=VerifyNumber(c);this.elat=VerifyNumber(d);this.elon=VerifyNumber(e)};exports.EclipticCoordinates=EclipticCoordinates;
 function vector2radec(a){var b=a[0]*a[0]+a[1]*a[1],c=Math.sqrt(b+a[2]*a[2]);if(0===b){if(0===a[2])throw"Indeterminate sky coordinates";return 0>a[2]?{ra:0,dec:-90,dist:c}:{ra:0,dec:90,dist:c}}var d=Math.atan2(a[1],a[0])/(15*DEG2RAD);0>d&&(d+=24);return new EquatorialCoordinates(d,Math.atan2(a[2],Math.sqrt(b))/DEG2RAD,c)}function spin(a,b){var c=a*DEG2RAD;a=Math.cos(c);c=Math.sin(c);return[a*b[0]+c*b[1]+0*b[2],-c*b[0]+a*b[1]+0*b[2],0*b[0]+0*b[1]+1*b[2]]}
-function Horizon(a,b,c,d,e){a=MakeTime(a);VerifyObserver(b);VerifyNumber(c);VerifyNumber(d);var f=Math.sin(b.latitude*DEG2RAD),g=Math.cos(b.latitude*DEG2RAD),k=Math.sin(b.longitude*DEG2RAD),h=Math.cos(b.longitude*DEG2RAD);b=Math.sin(d*DEG2RAD);var l=Math.cos(d*DEG2RAD),m=Math.sin(15*c*DEG2RAD),n=Math.cos(15*c*DEG2RAD),p=[g*h,g*k,f];f=[-f*h,-f*k,g];k=[k,-h,0];g=-15*sidereal_time(a);a=spin(g,p);p=spin(g,f);k=spin(g,k);b=[l*n,l*m,b];m=b[0]*a[0]+b[1]*a[1]+b[2]*a[2];p=b[0]*p[0]+b[1]*p[1]+b[2]*p[2];k=b[0]*
-k[0]+b[1]*k[1]+b[2]*k[2];n=Math.sqrt(p*p+k*k);l=0;0<n&&(l=-Math.atan2(k,p)*RAD2DEG,0>l&&(l+=360),360<=l&&(l-=360));m=Math.atan2(n,m)*RAD2DEG;n=d;if(e&&(d=m,e=Refraction(e,90-m),m-=e,0<e&&3E-4<m)){c=Math.sin(m*DEG2RAD);n=Math.cos(m*DEG2RAD);p=Math.sin(d*DEG2RAD);d=Math.cos(d*DEG2RAD);e=[];for(k=0;3>k;++k)e.push((b[k]-d*a[k])/p*c+a[k]*n);n=Math.sqrt(e[0]*e[0]+e[1]*e[1]);0<n?(c=Math.atan2(e[1],e[0])*RAD2DEG/15,0>c&&(c+=24),24<=c&&(c-=24)):c=0;n=Math.atan2(e[2],n)*RAD2DEG}return new HorizontalCoordinates(l,
-90-m,c,n)}exports.Horizon=Horizon;function VerifyObserver(a){if(!(a instanceof Observer))throw"Not an instance of the Observer class: "+a;VerifyNumber(a.latitude);VerifyNumber(a.longitude);VerifyNumber(a.height);if(-90>a.latitude||90<a.latitude)throw"Latitude "+a.latitude+" is out of range. Must be -90..+90.";return a}var Observer=function(a,b,c){this.latitude=a;this.longitude=b;this.height=c;VerifyObserver(this)};exports.Observer=Observer;
+function Horizon(a,b,c,d,e){a=MakeTime(a);VerifyObserver(b);VerifyNumber(c);VerifyNumber(d);var f=Math.sin(b.latitude*DEG2RAD),g=Math.cos(b.latitude*DEG2RAD),k=Math.sin(b.longitude*DEG2RAD),h=Math.cos(b.longitude*DEG2RAD);b=Math.sin(d*DEG2RAD);var l=Math.cos(d*DEG2RAD),m=Math.sin(15*c*DEG2RAD),n=Math.cos(15*c*DEG2RAD),p=[g*h,g*k,f];f=[-f*h,-f*k,g];k=[k,-h,0];g=-15*sidereal_time(a);a=spin(g,p);p=spin(g,f);k=spin(g,k);b=[l*n,l*m,b];m=b[0]*a[0]+b[1]*a[1]+b[2]*a[2];l=b[0]*p[0]+b[1]*p[1]+b[2]*p[2];p=b[0]*
+k[0]+b[1]*k[1]+b[2]*k[2];n=Math.sqrt(l*l+p*p);0<n?(l=-Math.atan2(p,l)*RAD2DEG,0>l&&(l+=360)):l=0;m=Math.atan2(n,m)*RAD2DEG;n=d;if(e&&(d=m,e=Refraction(e,90-m),m-=e,0<e&&3E-4<m)){c=Math.sin(m*DEG2RAD);n=Math.cos(m*DEG2RAD);p=Math.sin(d*DEG2RAD);d=Math.cos(d*DEG2RAD);e=[];for(k=0;3>k;++k)e.push((b[k]-d*a[k])/p*c+a[k]*n);n=Math.sqrt(e[0]*e[0]+e[1]*e[1]);0<n?(c=Math.atan2(e[1],e[0])*RAD2DEG/15,0>c&&(c+=24)):c=0;n=Math.atan2(e[2],n)*RAD2DEG}return new HorizontalCoordinates(l,90-m,c,n)}
+exports.Horizon=Horizon;function VerifyObserver(a){if(!(a instanceof Observer))throw"Not an instance of the Observer class: "+a;VerifyNumber(a.latitude);VerifyNumber(a.longitude);VerifyNumber(a.height);if(-90>a.latitude||90<a.latitude)throw"Latitude "+a.latitude+" is out of range. Must be -90..+90.";return a}var Observer=function(a,b,c){this.latitude=a;this.longitude=b;this.height=c;VerifyObserver(this)};exports.Observer=Observer;
 function SunPosition(a){a=MakeTime(a).AddDays(-1/C_AUDAY);var b=CalcVsop(vsop.Earth,a);b=precession(0,[-b.x,-b.y,-b.z],a.tt);var c=$jscomp.makeIterator(nutation(a,0,b));b=c.next().value;var d=c.next().value;c=c.next().value;a=DEG2RAD*e_tilt(a).tobl;return RotateEquatorialToEcliptic(b,d,c,Math.cos(a),Math.sin(a))}exports.SunPosition=SunPosition;
 function Equator(a,b,c,d,e){VerifyObserver(c);VerifyBoolean(d);VerifyBoolean(e);b=MakeTime(b);c=geo_pos(b,c);a=GeoVector(a,b,e);a=[a.x-c[0],a.y-c[1],a.z-c[2]];if(!d)return vector2radec(a);d=precession(0,a,b.tt);d=nutation(b,0,d);return vector2radec(d)}exports.Equator=Equator;function RotateEquatorialToEcliptic(a,b,c,d,e){var f=b*d+c*e;b=-b*e+c*d;c=Math.sqrt(a*a+f*f);d=0;0<c&&(d=RAD2DEG*Math.atan2(f,a),0>d&&(d+=360));return new EclipticCoordinates(a,f,b,RAD2DEG*Math.atan2(b,c),d)}
 function Ecliptic(a,b,c){void 0===ob2000&&(ob2000=DEG2RAD*e_tilt(MakeTime(J2000)).mobl,cos_ob2000=Math.cos(ob2000),sin_ob2000=Math.sin(ob2000));VerifyNumber(a);VerifyNumber(b);VerifyNumber(c);return RotateEquatorialToEcliptic(a,b,c,cos_ob2000,sin_ob2000)}exports.Ecliptic=Ecliptic;
diff --git a/source/js/astronomy.ts b/source/js/astronomy.ts
index 7b0ccb8f..f2f9b283 100644
--- a/source/js/astronomy.ts
+++ b/source/js/astronomy.ts
@@ -1660,7 +1660,7 @@ function sidereal_time(time: AstroTime): number {          // calculates Greenwi
     if (gst < 0) {
         gst += 24;
     }
-    return gst;
+    return gst;     // return sidereal hours in the half-open range [0, 24).
 }
 
 function terra(observer: Observer, st: number): TerraInfo {
@@ -2068,28 +2068,70 @@ export function Horizon(date: FlexibleDateTime, observer: Observer, ra: number,
     const cosdc = Math.cos(dec * DEG2RAD);
     const sinra = Math.sin(ra * 15 * DEG2RAD);
     const cosra = Math.cos(ra * 15 * DEG2RAD);
+
+    // Calculate three mutually perpendicular unit vectors
+    // in equatorial coordinates: uze, une, uwe.
+    //
+    // uze = The direction of the observer's local zenith (straight up).
+    // une = The direction toward due north on the observer's horizon.
+    // uwe = The direction toward due west on the observer's horizon.
+    //
+    // HOWEVER, these are uncorrected for the Earth's rotation due to the time of day.
+    //
+    // The components of these 3 vectors are as follows:
+    // x = direction from center of Earth toward 0 degrees longitude (the prime meridian) on equator.
+    // y = direction from center of Earth toward 90 degrees west longitude on equator.
+    // z = direction from center of Earth toward the north pole.
+
     let uze: ArrayVector = [coslat*coslon, coslat*sinlon, sinlat];
     let une: ArrayVector = [-sinlat*coslon, -sinlat*sinlon, coslat];
     let uwe: ArrayVector = [sinlon, -coslon, 0];
 
+    // Correct the vectors uze, une, uwe for the Earth's rotation by calculating
+    // sideral time. Call spin() for each uncorrected vector to rotate about
+    // the Earth's axis to yield corrected unit vectors uz, un, uw.
+    // Multiply sidereal hours by -15 to convert to degrees and flip eastward
+    // rotation of the Earth to westward apparent movement of objects with time.
+
     const spin_angle = -15 * sidereal_time(time);
     let uz = spin(spin_angle, uze);
     let un = spin(spin_angle, une);
     let uw = spin(spin_angle, uwe);
 
+    // Convert angular equatorial coordinates (RA, DEC) to
+    // cartesian equatorial coordinates in 'p', using the
+    // same orientation system as uze, une, uwe.
+
     let p = [cosdc*cosra, cosdc*sinra, sindc];
 
+    // Use dot products of p with the zenith, north, and west
+    // vectors to obtain the cartesian coordinates of the body in
+    // the observer's horizontal orientation system.
+    // pz = zenith component [-1, +1]
+    // pn = north  component [-1, +1]
+    // pw = west   component [-1, +1]
+
     const pz = p[0]*uz[0] + p[1]*uz[1] + p[2]*uz[2];
     const pn = p[0]*un[0] + p[1]*un[1] + p[2]*un[2];
     const pw = p[0]*uw[0] + p[1]*uw[1] + p[2]*uw[2];
 
+    // proj is the "shadow" of the body vector along the observer's flat ground.
     let proj = Math.sqrt(pn*pn + pw*pw);
-    let az = 0;
+
+    // Calculate az = azimuth (compass direction clockwise from East.)
+    let az: number;
     if (proj > 0) {
+        // If the body is not exactly straight up/down, it has an azimuth.
+        // Invert the angle to produce degrees eastward from north.
         az = -Math.atan2(pw, pn) * RAD2DEG;
         if (az < 0) az += 360;
-        if (az >= 360) az -= 360;
+    } else {
+        // The body is straight up/down, so it does not have an azimuth.
+        // Report an arbitrary but reasonable value.
+        az = 0;
     }
+
+    // zd = the angle of the body away from the observer's zenith, in degrees.
     let zd = Math.atan2(proj, pz) * RAD2DEG;
     let out_ra = ra;
     let out_dec = dec;
@@ -2113,9 +2155,6 @@ export function Horizon(date: FlexibleDateTime, observer: Observer, ra: number,
                 if (out_ra < 0) {
                     out_ra += 24;
                 }
-                if (out_ra >= 24) {
-                    out_ra -= 24;
-                }
             } else {
                 out_ra = 0;
             }
diff --git a/source/js/esm/astronomy.js b/source/js/esm/astronomy.js
index 848af746..adbede11 100644
--- a/source/js/esm/astronomy.js
+++ b/source/js/esm/astronomy.js
@@ -1555,7 +1555,7 @@ function sidereal_time(time) {
     if (gst < 0) {
         gst += 24;
     }
-    return gst;
+    return gst; // return sidereal hours in the half-open range [0, 24).
 }
 function terra(observer, st) {
     const df = 1 - 0.003352819697896; // flattening of the Earth
@@ -1910,26 +1910,61 @@ export function Horizon(date, observer, ra, dec, refraction) {
     const cosdc = Math.cos(dec * DEG2RAD);
     const sinra = Math.sin(ra * 15 * DEG2RAD);
     const cosra = Math.cos(ra * 15 * DEG2RAD);
+    // Calculate three mutually perpendicular unit vectors
+    // in equatorial coordinates: uze, une, uwe.
+    //
+    // uze = The direction of the observer's local zenith (straight up).
+    // une = The direction toward due north on the observer's horizon.
+    // uwe = The direction toward due west on the observer's horizon.
+    //
+    // HOWEVER, these are uncorrected for the Earth's rotation due to the time of day.
+    //
+    // The components of these 3 vectors are as follows:
+    // x = direction from center of Earth toward 0 degrees longitude (the prime meridian) on equator.
+    // y = direction from center of Earth toward 90 degrees west longitude on equator.
+    // z = direction from center of Earth toward the north pole.
     let uze = [coslat * coslon, coslat * sinlon, sinlat];
     let une = [-sinlat * coslon, -sinlat * sinlon, coslat];
     let uwe = [sinlon, -coslon, 0];
+    // Correct the vectors uze, une, uwe for the Earth's rotation by calculating
+    // sideral time. Call spin() for each uncorrected vector to rotate about
+    // the Earth's axis to yield corrected unit vectors uz, un, uw.
+    // Multiply sidereal hours by -15 to convert to degrees and flip eastward
+    // rotation of the Earth to westward apparent movement of objects with time.
     const spin_angle = -15 * sidereal_time(time);
     let uz = spin(spin_angle, uze);
     let un = spin(spin_angle, une);
     let uw = spin(spin_angle, uwe);
+    // Convert angular equatorial coordinates (RA, DEC) to
+    // cartesian equatorial coordinates in 'p', using the
+    // same orientation system as uze, une, uwe.
     let p = [cosdc * cosra, cosdc * sinra, sindc];
+    // Use dot products of p with the zenith, north, and west
+    // vectors to obtain the cartesian coordinates of the body in
+    // the observer's horizontal orientation system.
+    // pz = zenith component [-1, +1]
+    // pn = north  component [-1, +1]
+    // pw = west   component [-1, +1]
     const pz = p[0] * uz[0] + p[1] * uz[1] + p[2] * uz[2];
     const pn = p[0] * un[0] + p[1] * un[1] + p[2] * un[2];
     const pw = p[0] * uw[0] + p[1] * uw[1] + p[2] * uw[2];
+    // proj is the "shadow" of the body vector along the observer's flat ground.
     let proj = Math.sqrt(pn * pn + pw * pw);
-    let az = 0;
+    // Calculate az = azimuth (compass direction clockwise from East.)
+    let az;
     if (proj > 0) {
+        // If the body is not exactly straight up/down, it has an azimuth.
+        // Invert the angle to produce degrees eastward from north.
         az = -Math.atan2(pw, pn) * RAD2DEG;
         if (az < 0)
             az += 360;
-        if (az >= 360)
-            az -= 360;
     }
+    else {
+        // The body is straight up/down, so it does not have an azimuth.
+        // Report an arbitrary but reasonable value.
+        az = 0;
+    }
+    // zd = the angle of the body away from the observer's zenith, in degrees.
     let zd = Math.atan2(proj, pz) * RAD2DEG;
     let out_ra = ra;
     let out_dec = dec;
@@ -1952,9 +1987,6 @@ export function Horizon(date, observer, ra, dec, refraction) {
                 if (out_ra < 0) {
                     out_ra += 24;
                 }
-                if (out_ra >= 24) {
-                    out_ra -= 24;
-                }
             }
             else {
                 out_ra = 0;
diff --git a/source/python/astronomy.py b/source/python/astronomy.py
index b9df9b9b..fc7c6679 100644
--- a/source/python/astronomy.py
+++ b/source/python/astronomy.py
@@ -1416,6 +1416,7 @@ def _sidereal_time(time):
     gst = math.fmod((st/3600.0 + theta), 360.0) / 15.0
     if gst < 0.0:
         gst += 24.0
+    # return sidereal hours in the half-open range [0, 24).
     return gst
 
 
@@ -3885,29 +3886,69 @@ def Horizon(time, observer, ra, dec, refraction):
     sinra = math.sin(rarad)
     cosra = math.cos(rarad)
 
+    # Calculate three mutually perpendicular unit vectors
+    # in equatorial coordinates: uze, une, uwe.
+    #
+    # uze = The direction of the observer's local zenith (straight up).
+    # une = The direction toward due north on the observer's horizon.
+    # uwe = The direction toward due west on the observer's horizon.
+    #
+    # HOWEVER, these are uncorrected for the Earth's rotation due to the time of day.
+    #
+    # The components of these 3 vectors are as follows:
+    # [0] = x = direction from center of Earth toward 0 degrees longitude (the prime meridian) on equator.
+    # [1] = y = direction from center of Earth toward 90 degrees west longitude on equator.
+    # [2] = z = direction from center of Earth toward the north pole.
+
     uze = [coslat*coslon, coslat*sinlon, sinlat]
     une = [-sinlat*coslon, -sinlat*sinlon, coslat]
     uwe = [sinlon, -coslon, 0.0]
 
+    # Correct the vectors uze, une, uwe for the Earth's rotation by calculating
+    # sideral time. Call spin() for each uncorrected vector to rotate about
+    # the Earth's axis to yield corrected unit vectors uz, un, uw.
+    # Multiply sidereal hours by -15 to convert to degrees and flip eastward
+    # rotation of the Earth to westward apparent movement of objects with time.
+
     angle = -15.0 * _sidereal_time(time)
     uz = _spin(angle, uze)
     un = _spin(angle, une)
     uw = _spin(angle, uwe)
 
+    # Convert angular equatorial coordinates (RA, DEC) to
+    # cartesian equatorial coordinates in 'p', using the
+    # same orientation system as uze, une, uwe.
+
     p = [cosdc*cosra, cosdc*sinra, sindc]
 
+    # Use dot products of p with the zenith, north, and west
+    # vectors to obtain the cartesian coordinates of the body in
+    # the observer's horizontal orientation system.
+    #
+    # pz = zenith component [-1, +1]
+    # pn = north  component [-1, +1]
+    # pw = west   component [-1, +1]
+
     pz = p[0]*uz[0] + p[1]*uz[1] + p[2]*uz[2]
     pn = p[0]*un[0] + p[1]*un[1] + p[2]*un[2]
     pw = p[0]*uw[0] + p[1]*uw[1] + p[2]*uw[2]
 
+    # proj is the "shadow" of the body vector along the observer's flat ground.
     proj = math.sqrt(pn*pn + pw*pw)
-    az = 0.0
+
+    # Calculate az = azimuth (compass direction clockwise from East.)
     if proj > 0.0:
+        # If the body is not exactly straight up/down, it has an azimuth.
+        # Invert the angle to produce degrees eastward from north.
         az = math.degrees(-math.atan2(pw, pn))
         if az < 0:
             az += 360
-        if az >= 360:
-            az -= 360
+    else:
+        # The body is straight up/down, so it does not have an azimuth.
+        # Report an arbitrary but reasonable value.
+        az = 0.0
+
+    # zd = the angle of the body away from the observer's zenith.
     zd = math.degrees(math.atan2(proj, pz))
     hor_ra = ra
     hor_dec = dec
@@ -3930,8 +3971,6 @@ def Horizon(time, observer, ra, dec, refraction):
                 hor_ra = math.degrees(math.atan2(pr[1], pr[0])) / 15
                 if hor_ra < 0:
                     hor_ra += 24
-                if hor_ra >= 24:
-                    hor_ra -= 24
             else:
                 hor_ra = 0
             hor_dec = math.degrees(math.atan2(pr[2], proj))
diff --git a/website/src/assets/documentation.json b/website/src/assets/documentation.json
index b4d17f0c..e9b6d170 100644
--- a/website/src/assets/documentation.json
+++ b/website/src/assets/documentation.json
@@ -16281,7 +16281,7 @@
         "meta": {
             "range": [
                 72586,
-                73082
+                73139
             ],
             "filename": "astronomy.js",
             "lineno": 1553,
@@ -16464,8 +16464,8 @@
         "comment": "",
         "meta": {
             "range": [
-                73083,
-                73923
+                73140,
+                73980
             ],
             "filename": "astronomy.js",
             "lineno": 1569,
@@ -16506,8 +16506,8 @@
         "comment": "",
         "meta": {
             "range": [
-                73124,
-                73150
+                73181,
+                73207
             ],
             "filename": "astronomy.js",
             "lineno": 1570,
@@ -16531,8 +16531,8 @@
         "comment": "",
         "meta": {
             "range": [
-                73189,
-                73202
+                73246,
+                73259
             ],
             "filename": "astronomy.js",
             "lineno": 1571,
@@ -16556,8 +16556,8 @@
         "comment": "",
         "meta": {
             "range": [
-                73214,
-                73247
+                73271,
+                73304
             ],
             "filename": "astronomy.js",
             "lineno": 1572,
@@ -16581,8 +16581,8 @@
         "comment": "",
         "meta": {
             "range": [
-                73259,
-                73281
+                73316,
+                73338
             ],
             "filename": "astronomy.js",
             "lineno": 1573,
@@ -16606,8 +16606,8 @@
         "comment": "",
         "meta": {
             "range": [
-                73293,
-                73315
+                73350,
+                73372
             ],
             "filename": "astronomy.js",
             "lineno": 1574,
@@ -16631,8 +16631,8 @@
         "comment": "",
         "meta": {
             "range": [
-                73327,
-                73385
+                73384,
+                73442
             ],
             "filename": "astronomy.js",
             "lineno": 1575,
@@ -16656,8 +16656,8 @@
         "comment": "",
         "meta": {
             "range": [
-                73397,
-                73408
+                73454,
+                73465
             ],
             "filename": "astronomy.js",
             "lineno": 1576,
@@ -16681,8 +16681,8 @@
         "comment": "",
         "meta": {
             "range": [
-                73420,
-                73450
+                73477,
+                73507
             ],
             "filename": "astronomy.js",
             "lineno": 1577,
@@ -16706,8 +16706,8 @@
         "comment": "",
         "meta": {
             "range": [
-                73462,
-                73506
+                73519,
+                73563
             ],
             "filename": "astronomy.js",
             "lineno": 1578,
@@ -16731,8 +16731,8 @@
         "comment": "",
         "meta": {
             "range": [
-                73518,
-                73562
+                73575,
+                73619
             ],
             "filename": "astronomy.js",
             "lineno": 1579,
@@ -16756,8 +16756,8 @@
         "comment": "",
         "meta": {
             "range": [
-                73574,
-                73623
+                73631,
+                73680
             ],
             "filename": "astronomy.js",
             "lineno": 1580,
@@ -16781,8 +16781,8 @@
         "comment": "",
         "meta": {
             "range": [
-                73635,
-                73659
+                73692,
+                73716
             ],
             "filename": "astronomy.js",
             "lineno": 1581,
@@ -16806,8 +16806,8 @@
         "comment": "",
         "meta": {
             "range": [
-                73671,
-                73695
+                73728,
+                73752
             ],
             "filename": "astronomy.js",
             "lineno": 1582,
@@ -16831,8 +16831,8 @@
         "comment": "",
         "meta": {
             "range": [
-                73718,
-                73817
+                73775,
+                73874
             ],
             "filename": "astronomy.js",
             "lineno": 1584,
@@ -16854,8 +16854,8 @@
         "comment": "",
         "meta": {
             "range": [
-                73827,
-                73914
+                73884,
+                73971
             ],
             "filename": "astronomy.js",
             "lineno": 1585,
@@ -16877,8 +16877,8 @@
         "comment": "",
         "meta": {
             "range": [
-                73924,
-                74259
+                73981,
+                74316
             ],
             "filename": "astronomy.js",
             "lineno": 1588,
@@ -16908,8 +16908,8 @@
         "comment": "",
         "meta": {
             "range": [
-                73976,
-                74009
+                74033,
+                74066
             ],
             "filename": "astronomy.js",
             "lineno": 1589,
@@ -16933,8 +16933,8 @@
         "comment": "",
         "meta": {
             "range": [
-                74260,
-                75289
+                74317,
+                75346
             ],
             "filename": "astronomy.js",
             "lineno": 1596,
@@ -16981,8 +16981,8 @@
         "comment": "",
         "meta": {
             "range": [
-                74311,
-                74330
+                74368,
+                74387
             ],
             "filename": "astronomy.js",
             "lineno": 1597,
@@ -17006,8 +17006,8 @@
         "comment": "",
         "meta": {
             "range": [
-                74342,
-                74368
+                74399,
+                74425
             ],
             "filename": "astronomy.js",
             "lineno": 1598,
@@ -17031,8 +17031,8 @@
         "comment": "",
         "meta": {
             "range": [
-                74380,
-                74406
+                74437,
+                74463
             ],
             "filename": "astronomy.js",
             "lineno": 1599,
@@ -17056,8 +17056,8 @@
         "comment": "",
         "meta": {
             "range": [
-                74418,
-                74444
+                74475,
+                74501
             ],
             "filename": "astronomy.js",
             "lineno": 1600,
@@ -17081,8 +17081,8 @@
         "comment": "",
         "meta": {
             "range": [
-                74456,
-                74477
+                74513,
+                74534
             ],
             "filename": "astronomy.js",
             "lineno": 1601,
@@ -17106,8 +17106,8 @@
         "comment": "",
         "meta": {
             "range": [
-                74489,
-                74510
+                74546,
+                74567
             ],
             "filename": "astronomy.js",
             "lineno": 1602,
@@ -17131,8 +17131,8 @@
         "comment": "",
         "meta": {
             "range": [
-                74522,
-                74543
+                74579,
+                74600
             ],
             "filename": "astronomy.js",
             "lineno": 1603,
@@ -17156,8 +17156,8 @@
         "comment": "",
         "meta": {
             "range": [
-                74555,
-                74576
+                74612,
+                74633
             ],
             "filename": "astronomy.js",
             "lineno": 1604,
@@ -17181,8 +17181,8 @@
         "comment": "",
         "meta": {
             "range": [
-                74588,
-                74608
+                74645,
+                74665
             ],
             "filename": "astronomy.js",
             "lineno": 1605,
@@ -17206,8 +17206,8 @@
         "comment": "",
         "meta": {
             "range": [
-                74620,
-                74640
+                74677,
+                74697
             ],
             "filename": "astronomy.js",
             "lineno": 1606,
@@ -17231,8 +17231,8 @@
         "comment": "",
         "meta": {
             "range": [
-                74652,
-                74661
+                74709,
+                74718
             ],
             "filename": "astronomy.js",
             "lineno": 1607,
@@ -17256,8 +17256,8 @@
         "comment": "",
         "meta": {
             "range": [
-                74673,
-                74690
+                74730,
+                74747
             ],
             "filename": "astronomy.js",
             "lineno": 1608,
@@ -17281,8 +17281,8 @@
         "comment": "",
         "meta": {
             "range": [
-                74702,
-                74719
+                74759,
+                74776
             ],
             "filename": "astronomy.js",
             "lineno": 1609,
@@ -17306,8 +17306,8 @@
         "comment": "",
         "meta": {
             "range": [
-                74731,
-                74747
+                74788,
+                74804
             ],
             "filename": "astronomy.js",
             "lineno": 1610,
@@ -17331,8 +17331,8 @@
         "comment": "",
         "meta": {
             "range": [
-                74759,
-                74796
+                74816,
+                74853
             ],
             "filename": "astronomy.js",
             "lineno": 1611,
@@ -17356,8 +17356,8 @@
         "comment": "",
         "meta": {
             "range": [
-                74808,
-                74845
+                74865,
+                74902
             ],
             "filename": "astronomy.js",
             "lineno": 1612,
@@ -17381,8 +17381,8 @@
         "comment": "",
         "meta": {
             "range": [
-                74857,
-                74873
+                74914,
+                74930
             ],
             "filename": "astronomy.js",
             "lineno": 1613,
@@ -17406,8 +17406,8 @@
         "comment": "",
         "meta": {
             "range": [
-                74885,
-                74922
+                74942,
+                74979
             ],
             "filename": "astronomy.js",
             "lineno": 1614,
@@ -17431,8 +17431,8 @@
         "comment": "",
         "meta": {
             "range": [
-                74934,
-                74971
+                74991,
+                75028
             ],
             "filename": "astronomy.js",
             "lineno": 1615,
@@ -17456,8 +17456,8 @@
         "comment": "",
         "meta": {
             "range": [
-                75290,
-                75515
+                75347,
+                75572
             ],
             "filename": "astronomy.js",
             "lineno": 1631,
@@ -17489,8 +17489,8 @@
         "comment": "",
         "meta": {
             "range": [
-                75335,
-                75361
+                75392,
+                75418
             ],
             "filename": "astronomy.js",
             "lineno": 1632,
@@ -17514,8 +17514,8 @@
         "comment": "",
         "meta": {
             "range": [
-                75373,
-                75405
+                75430,
+                75462
             ],
             "filename": "astronomy.js",
             "lineno": 1633,
@@ -17539,8 +17539,8 @@
         "comment": "",
         "meta": {
             "range": [
-                75417,
-                75448
+                75474,
+                75505
             ],
             "filename": "astronomy.js",
             "lineno": 1634,
@@ -17564,8 +17564,8 @@
         "comment": "",
         "meta": {
             "range": [
-                75460,
-                75495
+                75517,
+                75552
             ],
             "filename": "astronomy.js",
             "lineno": 1635,
@@ -17589,8 +17589,8 @@
         "comment": "/**\n * @brief A 3D Cartesian vector with a time attached to it.\n *\n * Holds the Cartesian coordinates of a vector in 3D space,\n * along with the time at which the vector is valid.\n *\n * @property {number} x        The x-coordinate expressed in astronomical units (AU).\n * @property {number} y        The y-coordinate expressed in astronomical units (AU).\n * @property {number} z        The z-coordinate expressed in astronomical units (AU).\n * @property {AstroTime} t     The time at which the vector is valid.\n */",
         "meta": {
             "range": [
-                76031,
-                76372
+                76088,
+                76429
             ],
             "filename": "astronomy.js",
             "lineno": 1649,
@@ -17663,8 +17663,8 @@
         "comment": "",
         "meta": {
             "range": [
-                76050,
-                76161
+                76107,
+                76218
             ],
             "filename": "astronomy.js",
             "lineno": 1650,
@@ -17695,8 +17695,8 @@
         "comment": "/**\n * @brief A 3D Cartesian vector with a time attached to it.\n *\n * Holds the Cartesian coordinates of a vector in 3D space,\n * along with the time at which the vector is valid.\n *\n * @property {number} x        The x-coordinate expressed in astronomical units (AU).\n * @property {number} y        The y-coordinate expressed in astronomical units (AU).\n * @property {number} z        The z-coordinate expressed in astronomical units (AU).\n * @property {AstroTime} t     The time at which the vector is valid.\n */",
         "meta": {
             "range": [
-                76031,
-                76372
+                76088,
+                76429
             ],
             "filename": "astronomy.js",
             "lineno": 1649,
@@ -17768,8 +17768,8 @@
         "comment": "",
         "meta": {
             "range": [
-                76084,
-                76094
+                76141,
+                76151
             ],
             "filename": "astronomy.js",
             "lineno": 1651,
@@ -17793,8 +17793,8 @@
         "comment": "",
         "meta": {
             "range": [
-                76104,
-                76114
+                76161,
+                76171
             ],
             "filename": "astronomy.js",
             "lineno": 1652,
@@ -17818,8 +17818,8 @@
         "comment": "",
         "meta": {
             "range": [
-                76124,
-                76134
+                76181,
+                76191
             ],
             "filename": "astronomy.js",
             "lineno": 1653,
@@ -17843,8 +17843,8 @@
         "comment": "",
         "meta": {
             "range": [
-                76144,
-                76154
+                76201,
+                76211
             ],
             "filename": "astronomy.js",
             "lineno": 1654,
@@ -17868,8 +17868,8 @@
         "comment": "/**\n     * Returns the length of the vector in astronomical units (AU).\n     * @returns {number}\n     */",
         "meta": {
             "range": [
-                76275,
-                76370
+                76332,
+                76427
             ],
             "filename": "astronomy.js",
             "lineno": 1660,
@@ -17905,8 +17905,8 @@
         "comment": "",
         "meta": {
             "range": [
-                76373,
-                76396
+                76430,
+                76453
             ],
             "filename": "astronomy.js",
             "lineno": 1664,
@@ -17929,8 +17929,8 @@
         "comment": "/**\n * @brief Holds spherical coordinates: latitude, longitude, distance.\n *\n * Spherical coordinates represent the location of\n * a point using two angles and a distance.\n *\n * @property {number} lat       The latitude angle: -90..+90 degrees.\n * @property {number} lon       The longitude angle: 0..360 degrees.\n * @property {number} dist      Distance in AU.\n */",
         "meta": {
             "range": [
-                76764,
-                76939
+                76821,
+                76996
             ],
             "filename": "astronomy.js",
             "lineno": 1675,
@@ -17993,8 +17993,8 @@
         "comment": "",
         "meta": {
             "range": [
-                76786,
-                76937
+                76843,
+                76994
             ],
             "filename": "astronomy.js",
             "lineno": 1676,
@@ -18024,8 +18024,8 @@
         "comment": "/**\n * @brief Holds spherical coordinates: latitude, longitude, distance.\n *\n * Spherical coordinates represent the location of\n * a point using two angles and a distance.\n *\n * @property {number} lat       The latitude angle: -90..+90 degrees.\n * @property {number} lon       The longitude angle: 0..360 degrees.\n * @property {number} dist      Distance in AU.\n */",
         "meta": {
             "range": [
-                76764,
-                76939
+                76821,
+                76996
             ],
             "filename": "astronomy.js",
             "lineno": 1675,
@@ -18087,8 +18087,8 @@
         "comment": "",
         "meta": {
             "range": [
-                76824,
-                76852
+                76881,
+                76909
             ],
             "filename": "astronomy.js",
             "lineno": 1677,
@@ -18112,8 +18112,8 @@
         "comment": "",
         "meta": {
             "range": [
-                76862,
-                76890
+                76919,
+                76947
             ],
             "filename": "astronomy.js",
             "lineno": 1678,
@@ -18137,8 +18137,8 @@
         "comment": "",
         "meta": {
             "range": [
-                76900,
-                76930
+                76957,
+                76987
             ],
             "filename": "astronomy.js",
             "lineno": 1679,
@@ -18162,8 +18162,8 @@
         "comment": "",
         "meta": {
             "range": [
-                76940,
-                76969
+                76997,
+                77026
             ],
             "filename": "astronomy.js",
             "lineno": 1682,
@@ -18186,8 +18186,8 @@
         "comment": "/**\n * @brief Holds right ascension, declination, and distance of a celestial object.\n *\n * @property {number} ra\n *      Right ascension in sidereal hours: [0, 24).\n *\n * @property {number} dec\n *      Declination in degrees: [-90, +90].\n *\n * @property {number} dist\n *      Distance to the celestial object expressed in\n *      <a href=\"https://en.wikipedia.org/wiki/Astronomical_unit\">astronomical units</a> (AU).\n */",
         "meta": {
             "range": [
-                77393,
-                77577
+                77450,
+                77634
             ],
             "filename": "astronomy.js",
             "lineno": 1696,
@@ -18250,8 +18250,8 @@
         "comment": "",
         "meta": {
             "range": [
-                77427,
-                77575
+                77484,
+                77632
             ],
             "filename": "astronomy.js",
             "lineno": 1697,
@@ -18281,8 +18281,8 @@
         "comment": "/**\n * @brief Holds right ascension, declination, and distance of a celestial object.\n *\n * @property {number} ra\n *      Right ascension in sidereal hours: [0, 24).\n *\n * @property {number} dec\n *      Declination in degrees: [-90, +90].\n *\n * @property {number} dist\n *      Distance to the celestial object expressed in\n *      <a href=\"https://en.wikipedia.org/wiki/Astronomical_unit\">astronomical units</a> (AU).\n */",
         "meta": {
             "range": [
-                77393,
-                77577
+                77450,
+                77634
             ],
             "filename": "astronomy.js",
             "lineno": 1696,
@@ -18344,8 +18344,8 @@
         "comment": "",
         "meta": {
             "range": [
-                77464,
-                77490
+                77521,
+                77547
             ],
             "filename": "astronomy.js",
             "lineno": 1698,
@@ -18369,8 +18369,8 @@
         "comment": "",
         "meta": {
             "range": [
-                77500,
-                77528
+                77557,
+                77585
             ],
             "filename": "astronomy.js",
             "lineno": 1699,
@@ -18394,8 +18394,8 @@
         "comment": "",
         "meta": {
             "range": [
-                77538,
-                77568
+                77595,
+                77625
             ],
             "filename": "astronomy.js",
             "lineno": 1700,
@@ -18419,8 +18419,8 @@
         "comment": "",
         "meta": {
             "range": [
-                77578,
-                77631
+                77635,
+                77688
             ],
             "filename": "astronomy.js",
             "lineno": 1703,
@@ -18443,8 +18443,8 @@
         "comment": "",
         "meta": {
             "range": [
-                77633,
-                78007
+                77690,
+                78064
             ],
             "filename": "astronomy.js",
             "lineno": 1704,
@@ -18473,8 +18473,8 @@
         "comment": "",
         "meta": {
             "range": [
-                77760,
-                77765
+                77817,
+                77822
             ],
             "filename": "astronomy.js",
             "lineno": 1707,
@@ -18498,8 +18498,8 @@
         "comment": "",
         "meta": {
             "range": [
-                77889,
-                77894
+                77946,
+                77951
             ],
             "filename": "astronomy.js",
             "lineno": 1710,
@@ -18523,8 +18523,8 @@
         "comment": "/**\n * @brief Contains a rotation matrix that can be used to transform one coordinate system to another.\n *\n * @property {number[][]} rot\n *      A normalized 3x3 rotation matrix. For example, the identity matrix is represented\n *      as `[[1, 0, 0], [0, 1, 0], [0, 0, 1]]`.\n */",
         "meta": {
             "range": [
-                78288,
-                78365
+                78345,
+                78422
             ],
             "filename": "astronomy.js",
             "lineno": 1723,
@@ -18567,8 +18567,8 @@
         "comment": "",
         "meta": {
             "range": [
-                78315,
-                78363
+                78372,
+                78420
             ],
             "filename": "astronomy.js",
             "lineno": 1724,
@@ -18596,8 +18596,8 @@
         "comment": "/**\n * @brief Contains a rotation matrix that can be used to transform one coordinate system to another.\n *\n * @property {number[][]} rot\n *      A normalized 3x3 rotation matrix. For example, the identity matrix is represented\n *      as `[[1, 0, 0], [0, 1, 0], [0, 0, 1]]`.\n */",
         "meta": {
             "range": [
-                78288,
-                78365
+                78345,
+                78422
             ],
             "filename": "astronomy.js",
             "lineno": 1723,
@@ -18639,8 +18639,8 @@
         "comment": "",
         "meta": {
             "range": [
-                78342,
-                78356
+                78399,
+                78413
             ],
             "filename": "astronomy.js",
             "lineno": 1725,
@@ -18664,8 +18664,8 @@
         "comment": "",
         "meta": {
             "range": [
-                78366,
-                78405
+                78423,
+                78462
             ],
             "filename": "astronomy.js",
             "lineno": 1728,
@@ -18688,8 +18688,8 @@
         "comment": "/**\n * @brief Creates a rotation matrix that can be used to transform one coordinate system to another.\n *\n * This function verifies that the `rot` parameter is of the correct format:\n * a number[3][3] array. It throws an exception if `rot` is not of that shape.\n * Otherwise it creates a new {@link RotationMatrix} object based on `rot`.\n *\n * @param {number[][]} rot\n *      An array [3][3] of numbers. Defines a rotation matrix used to premultiply\n *      a 3D vector to reorient it into another coordinate system.\n *\n * @returns {RotationMatrix}\n */",
         "meta": {
             "range": [
-                78961,
-                79123
+                79018,
+                79180
             ],
             "filename": "astronomy.js",
             "lineno": 1742,
@@ -18740,8 +18740,8 @@
         "comment": "",
         "meta": {
             "range": [
-                79124,
-                79159
+                79181,
+                79216
             ],
             "filename": "astronomy.js",
             "lineno": 1747,
@@ -18764,8 +18764,8 @@
         "comment": "/**\n * @brief Represents the location of an object seen by an observer on the Earth.\n *\n * Holds azimuth (compass direction) and altitude (angle above/below the horizon)\n * of a celestial object as seen by an observer at a particular location on the Earth's surface.\n * Also holds right ascension and declination of the same object.\n * All of these coordinates are optionally adjusted for atmospheric refraction;\n * therefore the right ascension and declination values may not exactly match\n * those found inside a corresponding {@link EquatorialCoordinates} object.\n *\n * @property {number} azimuth\n *      A horizontal compass direction angle in degrees measured starting at north\n *      and increasing positively toward the east.\n *      The value is in the range [0, 360).\n *      North = 0, east = 90, south = 180, west = 270.\n *\n * @property {number} altitude\n *      A vertical angle in degrees above (positive) or below (negative) the horizon.\n *      The value is in the range [-90, +90].\n *      The altitude angle is optionally adjusted upward due to atmospheric refraction.\n *\n * @property {number} ra\n *      The right ascension of the celestial body in sidereal hours.\n *      The value is in the reange [0, 24).\n *      If `altitude` was adjusted for atmospheric reaction, `ra`\n *      is likewise adjusted.\n *\n * @property {number} dec\n *      The declination of of the celestial body in degrees.\n *      The value in the range [-90, +90].\n *      If `altitude` was adjusted for atmospheric reaction, `dec`\n *      is likewise adjusted.\n */",
         "meta": {
             "range": [
-                80719,
-                80970
+                80776,
+                81027
             ],
             "filename": "astronomy.js",
             "lineno": 1781,
@@ -18838,8 +18838,8 @@
         "comment": "",
         "meta": {
             "range": [
-                80753,
-                80968
+                80810,
+                81025
             ],
             "filename": "astronomy.js",
             "lineno": 1782,
@@ -18870,8 +18870,8 @@
         "comment": "/**\n * @brief Represents the location of an object seen by an observer on the Earth.\n *\n * Holds azimuth (compass direction) and altitude (angle above/below the horizon)\n * of a celestial object as seen by an observer at a particular location on the Earth's surface.\n * Also holds right ascension and declination of the same object.\n * All of these coordinates are optionally adjusted for atmospheric refraction;\n * therefore the right ascension and declination values may not exactly match\n * those found inside a corresponding {@link EquatorialCoordinates} object.\n *\n * @property {number} azimuth\n *      A horizontal compass direction angle in degrees measured starting at north\n *      and increasing positively toward the east.\n *      The value is in the range [0, 360).\n *      North = 0, east = 90, south = 180, west = 270.\n *\n * @property {number} altitude\n *      A vertical angle in degrees above (positive) or below (negative) the horizon.\n *      The value is in the range [-90, +90].\n *      The altitude angle is optionally adjusted upward due to atmospheric refraction.\n *\n * @property {number} ra\n *      The right ascension of the celestial body in sidereal hours.\n *      The value is in the reange [0, 24).\n *      If `altitude` was adjusted for atmospheric reaction, `ra`\n *      is likewise adjusted.\n *\n * @property {number} dec\n *      The declination of of the celestial body in degrees.\n *      The value in the range [-90, +90].\n *      If `altitude` was adjusted for atmospheric reaction, `dec`\n *      is likewise adjusted.\n */",
         "meta": {
             "range": [
-                80719,
-                80970
+                80776,
+                81027
             ],
             "filename": "astronomy.js",
             "lineno": 1781,
@@ -18943,8 +18943,8 @@
         "comment": "",
         "meta": {
             "range": [
-                80803,
-                80839
+                80860,
+                80896
             ],
             "filename": "astronomy.js",
             "lineno": 1783,
@@ -18968,8 +18968,8 @@
         "comment": "",
         "meta": {
             "range": [
-                80849,
-                80887
+                80906,
+                80944
             ],
             "filename": "astronomy.js",
             "lineno": 1784,
@@ -18993,8 +18993,8 @@
         "comment": "",
         "meta": {
             "range": [
-                80897,
-                80923
+                80954,
+                80980
             ],
             "filename": "astronomy.js",
             "lineno": 1785,
@@ -19018,8 +19018,8 @@
         "comment": "",
         "meta": {
             "range": [
-                80933,
-                80961
+                80990,
+                81018
             ],
             "filename": "astronomy.js",
             "lineno": 1786,
@@ -19043,8 +19043,8 @@
         "comment": "",
         "meta": {
             "range": [
-                80971,
-                81024
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+                81081
             ],
             "filename": "astronomy.js",
             "lineno": 1789,
@@ -19067,8 +19067,8 @@
         "comment": "/**\n * @brief Ecliptic coordinates of a celestial body.\n *\n * The origin and date of the coordinate system may vary depending on the caller's usage.\n * In general, ecliptic coordinates are measured with respect to the mean plane of the Earth's\n * orbit around the Sun.\n * Includes Cartesian coordinates `(ex, ey, ez)` measured in\n * <a href=\"https://en.wikipedia.org/wiki/Astronomical_unit\">astronomical units</a> (AU)\n * and spherical coordinates `(elon, elat)` measured in degrees.\n *\n * @property {number} ex\n *      The Cartesian x-coordinate of the body in astronomical units (AU).\n *      The x-axis is within the ecliptic plane and is oriented in the direction of the\n *      <a href=\"https://en.wikipedia.org/wiki/Equinox_(celestial_coordinates)\">equinox</a>.\n *\n * @property {number} ey\n *      The Cartesian y-coordinate of the body in astronomical units (AU).\n *      The y-axis is within the ecliptic plane and is oriented 90 degrees\n *      counterclockwise from the equinox, as seen from above the Sun's north pole.\n *\n * @property {number} ez\n *      The Cartesian z-coordinate of the body in astronomical units (AU).\n *      The z-axis is oriented perpendicular to the ecliptic plane,\n *      along the direction of the Sun's north pole.\n *\n * @property {number} elat\n *      The ecliptic latitude of the body in degrees.\n *      This is the angle north or south of the ecliptic plane.\n *      The value is in the range [-90, +90].\n *      Positive values are north and negative values are south.\n *\n * @property {number} elon\n *      The ecliptic longitude of the body in degrees.\n *      This is the angle measured counterclockwise around the ecliptic plane,\n *      as seen from above the Sun's north pole.\n *      This is the same direction that the Earth orbits around the Sun.\n *      The angle is measured starting at 0 from the equinox and increases\n *      up to 360 degrees.\n */",
         "meta": {
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-                83196
+                82988,
+                83253
             ],
             "filename": "astronomy.js",
             "lineno": 1829,
@@ -19151,8 +19151,8 @@
         "comment": "",
         "meta": {
             "range": [
-                82963,
-                83194
+                83020,
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             ],
             "filename": "astronomy.js",
             "lineno": 1830,
@@ -19184,8 +19184,8 @@
         "comment": "/**\n * @brief Ecliptic coordinates of a celestial body.\n *\n * The origin and date of the coordinate system may vary depending on the caller's usage.\n * In general, ecliptic coordinates are measured with respect to the mean plane of the Earth's\n * orbit around the Sun.\n * Includes Cartesian coordinates `(ex, ey, ez)` measured in\n * <a href=\"https://en.wikipedia.org/wiki/Astronomical_unit\">astronomical units</a> (AU)\n * and spherical coordinates `(elon, elat)` measured in degrees.\n *\n * @property {number} ex\n *      The Cartesian x-coordinate of the body in astronomical units (AU).\n *      The x-axis is within the ecliptic plane and is oriented in the direction of the\n *      <a href=\"https://en.wikipedia.org/wiki/Equinox_(celestial_coordinates)\">equinox</a>.\n *\n * @property {number} ey\n *      The Cartesian y-coordinate of the body in astronomical units (AU).\n *      The y-axis is within the ecliptic plane and is oriented 90 degrees\n *      counterclockwise from the equinox, as seen from above the Sun's north pole.\n *\n * @property {number} ez\n *      The Cartesian z-coordinate of the body in astronomical units (AU).\n *      The z-axis is oriented perpendicular to the ecliptic plane,\n *      along the direction of the Sun's north pole.\n *\n * @property {number} elat\n *      The ecliptic latitude of the body in degrees.\n *      This is the angle north or south of the ecliptic plane.\n *      The value is in the range [-90, +90].\n *      Positive values are north and negative values are south.\n *\n * @property {number} elon\n *      The ecliptic longitude of the body in degrees.\n *      This is the angle measured counterclockwise around the ecliptic plane,\n *      as seen from above the Sun's north pole.\n *      This is the same direction that the Earth orbits around the Sun.\n *      The angle is measured starting at 0 from the equinox and increases\n *      up to 360 degrees.\n */",
         "meta": {
             "range": [
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-                83196
+                82988,
+                83253
             ],
             "filename": "astronomy.js",
             "lineno": 1829,
@@ -19267,8 +19267,8 @@
         "comment": "",
         "meta": {
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-                83035
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             ],
             "filename": "astronomy.js",
             "lineno": 1831,
@@ -19292,8 +19292,8 @@
         "comment": "",
         "meta": {
             "range": [
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-                83071
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             ],
             "filename": "astronomy.js",
             "lineno": 1832,
@@ -19317,8 +19317,8 @@
         "comment": "",
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             "filename": "astronomy.js",
             "lineno": 1833,
@@ -19342,8 +19342,8 @@
         "comment": "",
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             "filename": "astronomy.js",
             "lineno": 1834,
@@ -19367,8 +19367,8 @@
         "comment": "",
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-                83187
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             ],
             "filename": "astronomy.js",
             "lineno": 1835,
@@ -19392,8 +19392,8 @@
         "comment": "",
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             ],
             "filename": "astronomy.js",
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@@ -19416,8 +19416,8 @@
         "comment": "",
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             "range": [
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-                83833
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             ],
             "filename": "astronomy.js",
             "lineno": 1839,
@@ -19448,8 +19448,8 @@
         "comment": "",
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-                83329
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             ],
             "filename": "astronomy.js",
             "lineno": 1840,
@@ -19473,8 +19473,8 @@
         "comment": "",
         "meta": {
             "range": [
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-                83383
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             ],
             "filename": "astronomy.js",
             "lineno": 1841,
@@ -19498,8 +19498,8 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
             "lineno": 1846,
@@ -19521,8 +19521,8 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
             "lineno": 1846,
@@ -19544,8 +19544,8 @@
         "comment": "",
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             "filename": "astronomy.js",
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@@ -19567,8 +19567,8 @@
         "comment": "",
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             "range": [
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             ],
             "filename": "astronomy.js",
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@@ -19590,8 +19590,8 @@
         "comment": "",
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-                83594
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             ],
             "filename": "astronomy.js",
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@@ -19613,8 +19613,8 @@
         "comment": "",
         "meta": {
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             "filename": "astronomy.js",
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@@ -19636,8 +19636,8 @@
         "comment": "",
         "meta": {
             "range": [
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-                83672
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             ],
             "filename": "astronomy.js",
             "lineno": 1849,
@@ -19661,8 +19661,8 @@
         "comment": "",
         "meta": {
             "range": [
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-                83708
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             ],
             "filename": "astronomy.js",
             "lineno": 1851,
@@ -19687,8 +19687,8 @@
         "comment": "",
         "meta": {
             "range": [
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-                83777
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             ],
             "filename": "astronomy.js",
             "lineno": 1853,
@@ -19712,8 +19712,8 @@
         "comment": "",
         "meta": {
             "range": [
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-                84326
+                83891,
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             ],
             "filename": "astronomy.js",
             "lineno": 1856,
@@ -19753,8 +19753,8 @@
         "comment": "",
         "meta": {
             "range": [
-                83873,
-                83895
+                83930,
+                83952
             ],
             "filename": "astronomy.js",
             "lineno": 1857,
@@ -19778,8 +19778,8 @@
         "comment": "",
         "meta": {
             "range": [
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-                83930
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+                83987
             ],
             "filename": "astronomy.js",
             "lineno": 1858,
@@ -19803,8 +19803,8 @@
         "comment": "",
         "meta": {
             "range": [
-                83942,
-                83965
+                83999,
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             ],
             "filename": "astronomy.js",
             "lineno": 1859,
@@ -19828,8 +19828,8 @@
         "comment": "",
         "meta": {
             "range": [
-                83977,
-                83988
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+                84045
             ],
             "filename": "astronomy.js",
             "lineno": 1860,
@@ -19853,8 +19853,8 @@
         "comment": "",
         "meta": {
             "range": [
-                84000,
-                84011
+                84057,
+                84068
             ],
             "filename": "astronomy.js",
             "lineno": 1861,
@@ -19878,8 +19878,8 @@
         "comment": "",
         "meta": {
             "range": [
-                84023,
-                84029
+                84080,
+                84086
             ],
             "filename": "astronomy.js",
             "lineno": 1862,
@@ -19903,8 +19903,8 @@
         "comment": "",
         "meta": {
             "range": [
-                84041,
-                84053
+                84098,
+                84110
             ],
             "filename": "astronomy.js",
             "lineno": 1863,
@@ -19928,8 +19928,8 @@
         "comment": "",
         "meta": {
             "range": [
-                84065,
-                84076
+                84122,
+                84133
             ],
             "filename": "astronomy.js",
             "lineno": 1864,
@@ -19953,8 +19953,8 @@
         "comment": "",
         "meta": {
             "range": [
-                84088,
-                84094
+                84145,
+                84151
             ],
             "filename": "astronomy.js",
             "lineno": 1865,
@@ -19978,8 +19978,8 @@
         "comment": "",
         "meta": {
             "range": [
-                84106,
-                84112
+                84163,
+                84169
             ],
             "filename": "astronomy.js",
             "lineno": 1866,
@@ -20003,8 +20003,8 @@
         "comment": "",
         "meta": {
             "range": [
-                84124,
-                84130
+                84181,
+                84187
             ],
             "filename": "astronomy.js",
             "lineno": 1867,
@@ -20028,8 +20028,8 @@
         "comment": "",
         "meta": {
             "range": [
-                84142,
-                84148
+                84199,
+                84205
             ],
             "filename": "astronomy.js",
             "lineno": 1868,
@@ -20053,8 +20053,8 @@
         "comment": "/**\n * @brief Converts equatorial coordinates to horizontal coordinates.\n *\n * Given a date and time, a geographic location of an observer on the Earth, and\n * equatorial coordinates (right ascension and declination) of a celestial body,\n * returns horizontal coordinates (azimuth and altitude angles) for that body\n * as seen by that observer. Allows optional correction for atmospheric refraction.\n *\n * @param {FlexibleDateTime} date\n *      The date and time for which to find horizontal coordinates.\n *\n * @param {Observer} observer\n *      The location of the observer for which to find horizontal coordinates.\n *\n * @param {number} ra\n *      Right ascension in sidereal hours of the celestial object,\n *      referred to the mean equinox of date for the J2000 epoch.\n *\n * @param {number} dec\n *      Declination in degrees of the celestial object,\n *      referred to the mean equator of date for the J2000 epoch.\n *      Positive values are north of the celestial equator and negative values are south.\n *\n * @param {string} refraction\n *      If omitted or has a false-like value (false, null, undefined, etc.)\n *      the calculations are performed without any correction for atmospheric\n *      refraction. If the value is the string `\"normal\"`,\n *      uses the recommended refraction correction based on Meeus \"Astronomical Algorithms\"\n *      with a linear taper more than 1 degree below the horizon. The linear\n *      taper causes the refraction to linearly approach 0 as the altitude of the\n *      body approaches the nadir (-90 degrees).\n *      If the value is the string `\"jplhor\"`, uses a JPL Horizons\n *      compatible formula. This is the same algorithm as `\"normal\"`,\n *      only without linear tapering; this can result in physically impossible\n *      altitudes of less than -90 degrees, which may cause problems for some applications.\n *      (The `\"jplhor\"` option was created for unit testing against data\n *      generated by JPL Horizons, and is otherwise not recommended for use.)\n *\n * @returns {HorizontalCoordinates}\n */",
         "meta": {
             "range": [
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-                88918
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+                90957
             ],
             "filename": "astronomy.js",
             "lineno": 1915,
@@ -20180,8 +20180,8 @@
         "comment": "",
         "meta": {
             "range": [
-                86484,
-                86505
+                86541,
+                86562
             ],
             "filename": "astronomy.js",
             "lineno": 1917,
@@ -20205,8 +20205,8 @@
         "comment": "",
         "meta": {
             "range": [
-                86592,
-                86638
+                86649,
+                86695
             ],
             "filename": "astronomy.js",
             "lineno": 1921,
@@ -20230,8 +20230,8 @@
         "comment": "",
         "meta": {
             "range": [
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-                86696
+                86707,
+                86753
             ],
             "filename": "astronomy.js",
             "lineno": 1922,
@@ -20255,8 +20255,8 @@
         "comment": "",
         "meta": {
             "range": [
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-                86755
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+                86812
             ],
             "filename": "astronomy.js",
             "lineno": 1923,
@@ -20280,8 +20280,8 @@
         "comment": "",
         "meta": {
             "range": [
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-                86814
+                86824,
+                86871
             ],
             "filename": "astronomy.js",
             "lineno": 1924,
@@ -20305,8 +20305,8 @@
         "comment": "",
         "meta": {
             "range": [
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-                86857
+                86883,
+                86914
             ],
             "filename": "astronomy.js",
             "lineno": 1925,
@@ -20330,8 +20330,8 @@
         "comment": "",
         "meta": {
             "range": [
-                86869,
-                86900
+                86926,
+                86957
             ],
             "filename": "astronomy.js",
             "lineno": 1926,
@@ -20355,8 +20355,8 @@
         "comment": "",
         "meta": {
             "range": [
-                86912,
-                86947
+                86969,
+                87004
             ],
             "filename": "astronomy.js",
             "lineno": 1927,
@@ -20380,8 +20380,8 @@
         "comment": "",
         "meta": {
             "range": [
-                86959,
-                86994
+                87016,
+                87051
             ],
             "filename": "astronomy.js",
             "lineno": 1928,
@@ -20405,11 +20405,11 @@
         "comment": "",
         "meta": {
             "range": [
-                87004,
-                87052
+                87802,
+                87850
             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
                 "id": "astnode100010315",
@@ -20430,11 +20430,11 @@
         "comment": "",
         "meta": {
             "range": [
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-                87112
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             ],
             "filename": "astronomy.js",
-            "lineno": 1930,
+            "lineno": 1943,
             "columnno": 8,
             "code": {
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@@ -20455,11 +20455,11 @@
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         "meta": {
             "range": [
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-                87148
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
                 "id": "astnode100010339",
@@ -20480,11 +20480,11 @@
         "comment": "",
         "meta": {
             "range": [
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-                87198
+                88343,
+                88381
             ],
             "filename": "astronomy.js",
-            "lineno": 1932,
+            "lineno": 1950,
             "columnno": 10,
             "code": {
                 "id": "astnode100010347",
@@ -20505,11 +20505,11 @@
         "comment": "",
         "meta": {
             "range": [
-                87208,
-                87234
+                88391,
+                88417
             ],
             "filename": "astronomy.js",
-            "lineno": 1933,
+            "lineno": 1951,
             "columnno": 8,
             "code": {
                 "id": "astnode100010356",
@@ -20530,11 +20530,11 @@
         "comment": "",
         "meta": {
             "range": [
-                87244,
-                87270
+                88427,
+                88453
             ],
             "filename": "astronomy.js",
-            "lineno": 1934,
+            "lineno": 1952,
             "columnno": 8,
             "code": {
                 "id": "astnode100010363",
@@ -20555,11 +20555,11 @@
         "comment": "",
         "meta": {
             "range": [
-                87280,
-                87306
+                88463,
+                88489
             ],
             "filename": "astronomy.js",
-            "lineno": 1935,
+            "lineno": 1953,
             "columnno": 8,
             "code": {
                 "id": "astnode100010370",
@@ -20580,11 +20580,11 @@
         "comment": "",
         "meta": {
             "range": [
-                87316,
-                87357
+                88665,
+                88706
             ],
             "filename": "astronomy.js",
-            "lineno": 1936,
+            "lineno": 1957,
             "columnno": 8,
             "code": {
                 "id": "astnode100010377",
@@ -20605,11 +20605,11 @@
         "comment": "",
         "meta": {
             "range": [
-                87369,
-                87416
+                89013,
+                89060
             ],
             "filename": "astronomy.js",
-            "lineno": 1937,
+            "lineno": 1964,
             "columnno": 10,
             "code": {
                 "id": "astnode100010388",
@@ -20630,11 +20630,11 @@
         "comment": "",
         "meta": {
             "range": [
-                87428,
-                87475
+                89072,
+                89119
             ],
             "filename": "astronomy.js",
-            "lineno": 1938,
+            "lineno": 1965,
             "columnno": 10,
             "code": {
                 "id": "astnode100010414",
@@ -20655,11 +20655,11 @@
         "comment": "",
         "meta": {
             "range": [
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-                87534
+                89131,
+                89178
             ],
             "filename": "astronomy.js",
-            "lineno": 1939,
+            "lineno": 1966,
             "columnno": 10,
             "code": {
                 "id": "astnode100010440",
@@ -20680,11 +20680,11 @@
         "comment": "",
         "meta": {
             "range": [
-                87544,
-                87579
+                89269,
+                89304
             ],
             "filename": "astronomy.js",
-            "lineno": 1940,
+            "lineno": 1968,
             "columnno": 8,
             "code": {
                 "id": "astnode100010466",
@@ -20705,17 +20705,15 @@
         "comment": "",
         "meta": {
             "range": [
-                87589,
-                87595
+                89385,
+                89387
             ],
             "filename": "astronomy.js",
-            "lineno": 1941,
+            "lineno": 1970,
             "columnno": 8,
             "code": {
                 "id": "astnode100010480",
-                "name": "az",
-                "type": "Literal",
-                "value": 0
+                "name": "az"
             }
         },
         "undocumented": true,
@@ -20730,14 +20728,14 @@
         "comment": "",
         "meta": {
             "range": [
-                87625,
-                87659
+                89560,
+                89594
             ],
             "filename": "astronomy.js",
-            "lineno": 1943,
+            "lineno": 1974,
             "columnno": 8,
             "code": {
-                "id": "astnode100010489",
+                "id": "astnode100010488",
                 "name": "az",
                 "type": "BinaryExpression",
                 "funcscope": "Horizon",
@@ -20756,14 +20754,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                87702
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             ],
             "filename": "astronomy.js",
-            "lineno": 1945,
+            "lineno": 1976,
             "columnno": 12,
             "code": {
-                "id": "astnode100010505",
+                "id": "astnode100010504",
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                 "type": "Literal",
                 "funcscope": "Horizon",
@@ -20782,40 +20780,40 @@
         "comment": "",
         "meta": {
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-                87748
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             ],
             "filename": "astronomy.js",
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-            "columnno": 12,
-            "code": {
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-                "name": "az",
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-                "paramnames": []
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-        },
-        "undocumented": true,
-        "name": "az",
-        "longname": "Horizon~az",
-        "kind": "member",
-        "memberof": "Horizon",
-        "scope": "inner"
-    },
-    {
-        "comment": "",
-        "meta": {
-            "range": [
-                87764,
-                87799
-            ],
-            "filename": "astronomy.js",
-            "lineno": 1949,
+            "lineno": 1981,
             "columnno": 8,
             "code": {
-                "id": "astnode100010517",
+                "id": "astnode100010509",
+                "name": "az",
+                "type": "Literal",
+                "funcscope": "Horizon",
+                "value": 0,
+                "paramnames": []
+            }
+        },
+        "undocumented": true,
+        "name": "az",
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@@ -21410,14 +21382,14 @@
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@@ -21572,14 +21544,14 @@
         "comment": "/**\n * @brief Returns apparent geocentric true ecliptic coordinates of date for the Sun.\n *\n * This function is used for calculating the times of equinoxes and solstices.\n *\n * <i>Geocentric</i> means coordinates as the Sun would appear to a hypothetical observer\n * at the center of the Earth.\n * <i>Ecliptic coordinates of date</i> are measured along the plane of the Earth's mean\n * orbit around the Sun, using the\n * <a href=\"https://en.wikipedia.org/wiki/Equinox_(celestial_coordinates)\">equinox</a>\n * of the Earth as adjusted for precession and nutation of the Earth's\n * axis of rotation on the given date.\n *\n * @param {FlexibleDateTime} date\n *      The date and time at which to calculate the Sun's apparent location as seen from\n *      the center of the Earth.\n *\n * @returns {EclipticCoordinates}\n */",
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@@ -21859,14 +21831,14 @@
         "comment": "/**\n * @brief Calculates equatorial coordinates of a Solar System body at a given time.\n *\n * Returns topocentric equatorial coordinates (right ascension and declination)\n * in one of two different systems: J2000 or true-equator-of-date.\n * Allows optional correction for aberration.\n * Always corrects for light travel time (represents the object as seen by the observer\n * with light traveling to the Earth at finite speed, not where the object is right now).\n * <i>Topocentric</i> refers to a position as seen by an observer on the surface of the Earth.\n * This function corrects for\n * <a href=\"https://en.wikipedia.org/wiki/Parallax\">parallax</a>\n * of the object between a geocentric observer and a topocentric observer.\n * This is most significant for the Moon, because it is so close to the Earth.\n * However, it can have a small effect on the apparent positions of other bodies.\n *\n * @param {string} body\n *      The name of the body for which to find equatorial coordinates.\n *      Not allowed to be `\"Earth\"`.\n *\n * @param {FlexibleDateTime} date\n *      Specifies the date and time at which the body is to be observed.\n *\n * @param {Observer} observer\n *      The location on the Earth of the observer.\n *\n * @param {bool} ofdate\n *      Pass `true` to return equatorial coordinates of date,\n *      i.e. corrected for precession and nutation at the given date.\n *      This is needed to get correct horizontal coordinates when you call\n *      {@link Horizon}.\n *      Pass `false` to return equatorial coordinates in the J2000 system.\n *\n * @param {bool} aberration\n *      Pass `true` to correct for\n *      <a href=\"https://en.wikipedia.org/wiki/Aberration_of_light\">aberration</a>,\n *      or `false` to leave uncorrected.\n *\n * @returns {EquatorialCoordinates}\n *      The topocentric coordinates of the body as adjusted for the given observer.\n */",
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@@ -21960,14 +21932,14 @@
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@@ -30094,14 +30066,14 @@
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             "columnno": 8,
             "code": {
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                 "name": "lon",
                 "type": "Literal",
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             "code": {
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@@ -30146,14 +30118,14 @@
         "comment": "/**\n * @brief Searches for when the Sun reaches a given ecliptic longitude.\n *\n * Searches for the moment in time when the center of the Sun reaches a given apparent\n * ecliptic longitude, as seen from the center of the Earth, within a given range of dates.\n * This function can be used to determine equinoxes and solstices.\n * However, it is usually more convenient and efficient to call {@link Seasons}\n * to calculate equinoxes and solstices for a given calendar year.\n * `SearchSunLongitude` is more general in that it allows searching for arbitrary longitude values.\n *\n * @param {number} targetLon\n *      The desired ecliptic longitude of date in degrees.\n *      This may be any value in the range [0, 360), although certain\n *      values have conventional meanings:\n *\n *      When `targetLon` is 0, finds the March equinox,\n *      which is the moment spring begins in the northern hemisphere\n *      and the beginning of autumn in the southern hemisphere.\n *\n *      When `targetLon` is 180, finds the September equinox,\n *      which is the moment autumn begins in the northern hemisphere and\n *      spring begins in the southern hemisphere.\n *\n *      When `targetLon` is 90, finds the northern solstice, which is the\n *      moment summer begins in the northern hemisphere and winter\n *      begins in the southern hemisphere.\n *\n *      When `targetLon` is 270, finds the southern solstice, which is the\n *      moment winter begins in the northern hemisphere and summer\n *      begins in the southern hemisphere.\n *\n * @param {FlexibleDateTime} dateStart\n *      A date and time known to be earlier than the desired longitude event.\n *\n * @param {number} limitDays\n *      A floating point number of days, which when added to `dateStart`,\n *      yields a date and time known to be after the desired longitude event.\n *\n * @returns {AstroTime | null}\n *      The date and time when the Sun reaches the apparent ecliptic longitude `targetLon`\n *      within the range of times specified by `dateStart` and `limitDays`.\n *      If the Sun does not reach the target longitude within the specified time range, or the\n *      time range is excessively wide, the return value is `null`.\n *      To avoid a `null` return value, the caller must pick a time window around\n *      the event that is within a few days but not so small that the event might fall outside the window.\n */",
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             "columnno": 0,
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                 "name": "SearchSunLongitude",
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                 "name": "exports.SearchSunLongitude",
                 "type": "Identifier",
                 "value": "SearchSunLongitude",
@@ -30354,14 +30326,14 @@
         "comment": "/**\n * @brief Calculates the longitude separation between the Sun and the given body.\n *\n * Calculates the ecliptic longitude difference\n * between the given body and the Sun as seen from\n * the Earth at a given moment in time.\n * The returned value ranges [0, 360) degrees.\n * By definition, the Earth and the Sun are both in the plane of the ecliptic.\n * Ignores the height of the `body` above or below the ecliptic plane;\n * the resulting angle is measured around the ecliptic plane for the \"shadow\"\n * of the body onto that plane.\n *\n * Use {@link AngleFromSun} instead, if you wish to calculate the full angle\n * between the Sun and a body, instead of just their longitude difference.\n *\n * @param {string} body\n *      The name of a supported celestial body other than the Earth.\n *\n * @param {FlexibleDateTime} date\n *      The time at which the relative longitude is to be found.\n *\n * @returns {number}\n *      An angle in degrees in the range [0, 360).\n *      Values less than 180 indicate that the body is to the east\n *      of the Sun as seen from the Earth; that is, the body sets after\n *      the Sun does and is visible in the evening sky.\n *      Values greater than 180 indicate that the body is to the west of\n *      the Sun and is visible in the morning sky.\n */",
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             "columnno": 0,
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                 "name": "LongitudeFromSun",
                 "type": "FunctionDeclaration",
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             "columnno": 10,
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@@ -30549,14 +30521,14 @@
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             "columnno": 0,
             "code": {
-                "id": "astnode100015146",
+                "id": "astnode100015133",
                 "name": "exports.LongitudeFromSun",
                 "type": "Identifier",
                 "value": "LongitudeFromSun",
@@ -30573,14 +30545,14 @@
         "comment": "/**\n * @brief Calculates the angular separation between the Sun and the given body.\n *\n * Returns the full angle seen from\n * the Earth, between the given body and the Sun.\n * Unlike {@link LongitudeFromSun}, this function does not\n * project the body's \"shadow\" onto the ecliptic;\n * the angle is measured in 3D space around the plane that\n * contains the centers of the Earth, the Sun, and `body`.\n *\n * @param {string} body\n *      The name of a supported celestial body other than the Earth.\n *\n * @param {FlexibleDateTime} date\n *      The time at which the angle from the Sun is to be found.\n *\n * @returns {number}\n *      An angle in degrees in the range [0, 180].\n */",
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             "columnno": 0,
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                 "name": "AngleFromSun",
                 "type": "FunctionDeclaration",
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@@ -30716,14 +30688,14 @@
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             "columnno": 0,
             "code": {
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+                "id": "astnode100015175",
                 "name": "exports.AngleFromSun",
                 "type": "Identifier",
                 "value": "AngleFromSun",
@@ -30740,14 +30712,14 @@
         "comment": "/**\n * @brief Calculates heliocentric ecliptic longitude based on the J2000 equinox.\n *\n * @param {string} body\n *      The name of a celestial body other than the Sun.\n *\n * @param {FlexibleDateTime} date\n *      The date and time for which to calculate the ecliptic longitude.\n *\n * @returns {number}\n *      The ecliptic longitude angle of the body in degrees measured counterclockwise around the mean\n *      plane of the Earth's orbit, as seen from above the Sun's north pole.\n *      Ecliptic longitude starts at 0 at the J2000\n *      <a href=\"https://en.wikipedia.org/wiki/Equinox_(celestial_coordinates)\">equinox</a> and\n *      increases in the same direction the Earth orbits the Sun.\n *      The returned value is always in the range [0, 360).\n */",
         "meta": {
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             ],
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             "columnno": 0,
             "code": {
-                "id": "astnode100015193",
+                "id": "astnode100015180",
                 "name": "EclipticLongitude",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -30807,14 +30779,14 @@
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                 "name": "exports.EclipticLongitude",
                 "type": "Identifier",
                 "value": "EclipticLongitude",
@@ -30881,14 +30853,14 @@
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@@ -30918,14 +30890,14 @@
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@@ -31016,14 +30988,14 @@
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@@ -31068,14 +31040,14 @@
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@@ -32444,14 +32416,14 @@
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@@ -32469,14 +32441,14 @@
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                 "type": "Identifier",
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@@ -32494,14 +32466,14 @@
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             "columnno": 8,
             "code": {
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+                "id": "astnode100015653",
                 "name": "this.helio_dist",
                 "type": "Identifier",
                 "value": "helio_dist",
@@ -32519,14 +32491,14 @@
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+                "id": "astnode100015659",
                 "name": "this.geo_dist",
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                 "value": "geo_dist",
@@ -32544,14 +32516,14 @@
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+                "id": "astnode100015665",
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@@ -32569,14 +32541,14 @@
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@@ -32594,14 +32566,14 @@
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-                "id": "astnode100015690",
+                "id": "astnode100015677",
                 "name": "this.ring_tilt",
                 "type": "Identifier",
                 "value": "ring_tilt",
@@ -32619,14 +32591,14 @@
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@@ -32644,14 +32616,14 @@
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             "columnno": 0,
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+                "id": "astnode100015699",
                 "name": "exports.IlluminationInfo",
                 "type": "Identifier",
                 "value": "IlluminationInfo",
@@ -32668,14 +32640,14 @@
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             ],
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+                "id": "astnode100015704",
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                 "paramnames": [
@@ -32742,14 +32714,14 @@
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@@ -32767,14 +32739,14 @@
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             "columnno": 10,
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@@ -32792,14 +32764,14 @@
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             }
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@@ -32815,14 +32787,14 @@
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+                "id": "astnode100015735",
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@@ -32838,14 +32810,14 @@
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+                "id": "astnode100015738",
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@@ -32861,14 +32833,14 @@
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             ],
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+                "id": "astnode100015741",
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             }
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@@ -32884,14 +32856,14 @@
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+                "id": "astnode100015749",
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@@ -32910,14 +32882,14 @@
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@@ -32936,14 +32908,14 @@
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             ],
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             "columnno": 8,
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-                "id": "astnode100015789",
+                "id": "astnode100015776",
                 "name": "phase",
                 "type": "Literal",
                 "funcscope": "Illumination",
@@ -32962,14 +32934,14 @@
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@@ -32988,14 +32960,14 @@
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@@ -33014,14 +32986,14 @@
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@@ -33040,14 +33012,14 @@
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@@ -33066,14 +33038,14 @@
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+                "id": "astnode100015854",
                 "name": "phase",
                 "type": "CallExpression",
                 "funcscope": "Illumination",
@@ -33092,14 +33064,14 @@
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             ],
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             "columnno": 8,
             "code": {
-                "id": "astnode100015874",
+                "id": "astnode100015861",
                 "name": "geo_dist",
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                 "value": ""
@@ -33117,14 +33089,14 @@
         "comment": "",
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+                "id": "astnode100015868",
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@@ -33142,14 +33114,14 @@
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+                "id": "astnode100015875",
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@@ -33165,14 +33137,14 @@
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+                "id": "astnode100015883",
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@@ -33191,14 +33163,14 @@
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+                "id": "astnode100015900",
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@@ -33217,14 +33189,14 @@
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@@ -33242,14 +33214,14 @@
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-                "id": "astnode100015936",
+                "id": "astnode100015923",
                 "name": "mag",
                 "type": "MemberExpression",
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@@ -33268,14 +33240,14 @@
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             "columnno": 8,
             "code": {
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+                "id": "astnode100015929",
                 "name": "ring_tilt",
                 "type": "MemberExpression",
                 "funcscope": "Illumination",
@@ -33294,14 +33266,14 @@
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             "range": [
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             ],
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             "columnno": 8,
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-                "id": "astnode100015949",
+                "id": "astnode100015936",
                 "name": "mag",
                 "type": "CallExpression",
                 "funcscope": "Illumination",
@@ -33320,14 +33292,14 @@
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             "range": [
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             ],
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             "columnno": 0,
             "code": {
-                "id": "astnode100015969",
+                "id": "astnode100015956",
                 "name": "exports.Illumination",
                 "type": "Identifier",
                 "value": "Illumination",
@@ -33344,14 +33316,14 @@
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             "range": [
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             ],
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             "columnno": 0,
             "code": {
-                "id": "astnode100015974",
+                "id": "astnode100015961",
                 "name": "SynodicPeriod",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -33376,14 +33348,14 @@
         "comment": "",
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             "columnno": 8,
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+                "id": "astnode100015978",
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                 "type": "MemberExpression",
                 "value": "Planet[undefined]"
@@ -33401,14 +33373,14 @@
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             "range": [
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+                148023
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             "columnno": 10,
             "code": {
-                "id": "astnode100016005",
+                "id": "astnode100015992",
                 "name": "Te",
                 "type": "MemberExpression",
                 "value": "Planet.Earth.OrbitalPeriod"
@@ -33426,14 +33398,14 @@
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             "range": [
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+                148060
             ],
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             "columnno": 10,
             "code": {
-                "id": "astnode100016013",
+                "id": "astnode100016000",
                 "name": "Tp",
                 "type": "MemberExpression",
                 "value": "planet.OrbitalPeriod"
@@ -33451,14 +33423,14 @@
         "comment": "",
         "meta": {
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             "columnno": 10,
             "code": {
-                "id": "astnode100016019",
+                "id": "astnode100016006",
                 "name": "synodicPeriod",
                 "type": "CallExpression",
                 "value": ""
@@ -33476,14 +33448,14 @@
         "comment": "/**\n * @brief Searches for when the Earth and a given body reach a relative ecliptic longitude separation.\n *\n * Searches for the date and time the relative ecliptic longitudes of\n * the specified body and the Earth, as seen from the Sun, reach a certain\n * difference. This function is useful for finding conjunctions and oppositions\n * of the planets. For the opposition of a superior planet (Mars, Jupiter, ..., Pluto),\n * or the inferior conjunction of an inferior planet (Mercury, Venus),\n * call with `targetRelLon` = 0. The 0 value indicates that both\n * planets are on the same ecliptic longitude line, ignoring the other planet's\n * distance above or below the plane of the Earth's orbit.\n * For superior conjunctions, call with `targetRelLon` = 180.\n * This means the Earth and the other planet are on opposite sides of the Sun.\n *\n * @param {string} body\n *      The name of a planet other than the Earth.\n *\n * @param {number} targetRelLon\n *      The desired angular difference in degrees between the ecliptic longitudes\n *      of `body` and the Earth. Must be in the range (-180, +180].\n *\n * @param {FlexibleDateTime} startDate\n *      The date and time after which to find the next occurrence of the\n *      body and the Earth reaching the desired relative longitude.\n *\n * @returns {AstroTime}\n *      The time when the Earth and the body next reach the specified relative longitudes.\n */",
         "meta": {
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             ],
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             "columnno": 0,
             "code": {
-                "id": "astnode100016034",
+                "id": "astnode100016021",
                 "name": "SearchRelativeLongitude",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -33561,14 +33533,14 @@
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             "columnno": 10,
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+                "id": "astnode100016032",
                 "name": "planet",
                 "type": "MemberExpression",
                 "value": "Planet[undefined]"
@@ -33586,14 +33558,14 @@
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             "columnno": 10,
             "code": {
-                "id": "astnode100016065",
+                "id": "astnode100016052",
                 "name": "direction",
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         "comment": "/**\n * @brief Determines the moon's phase expressed as an ecliptic longitude.\n *\n * @param {FlexibleDateTime} date\n *      The date and time for which to calculate the moon's phase.\n *\n * @returns {number}\n *      A value in the range [0, 360) indicating the difference\n *      in ecliptic longitude between the center of the Sun and the\n *      center of the Moon, as seen from the center of the Earth.\n *      Certain longitude values have conventional meanings:\n *\n * * 0 = new moon\n * * 90 = first quarter\n * * 180 = full moon\n * * 270 = third quarter\n */",
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         "comment": "/**\n * @brief Searches for the date and time that the Moon reaches a specified phase.\n *\n * Lunar phases are defined in terms of geocentric ecliptic longitudes\n * with respect to the Sun.  When the Moon and the Sun have the same ecliptic\n * longitude, that is defined as a new moon. When the two ecliptic longitudes\n * are 180 degrees apart, that is defined as a full moon.\n * To enumerate quarter lunar phases, it is simpler to call\n * {@link SearchMoonQuarter} once, followed by repeatedly calling\n * {@link NextMoonQuarter}. `SearchMoonPhase` is only\n * necessary for finding other lunar phases than the usual quarter phases.\n *\n * @param {number} targetLon\n *      The difference in geocentric ecliptic longitude between the Sun and Moon\n *      that specifies the lunar phase being sought. This can be any value\n *      in the range [0, 360). Here are some helpful examples:\n *      0 = new moon,\n *      90 = first quarter,\n *      180 = full moon,\n *      270 = third quarter.\n *\n * @param {FlexibleDateTime} dateStart\n *      The beginning of the window of time in which to search.\n *\n * @param {number} limitDays\n *      The floating point number of days after `dateStart`\n *      that limits the window of time in which to search.\n *\n * @returns {AstroTime | null}\n *      If the specified lunar phase occurs after `dateStart`\n *      and before `limitDays` days after `dateStart`,\n *      this function returns the date and time of the first such occurrence.\n *      Otherwise, it returns `null`.\n */",
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@@ -34488,14 +34460,14 @@
         "comment": "/**\n * @brief A quarter lunar phase, along with when it occurs.\n *\n * @property {number} quarter\n *      An integer as follows:\n *      0 = new moon,\n *      1 = first quarter,\n *      2 = full moon,\n *      3 = third quarter.\n *\n * @property {AstroTime} time\n *      The date and time of the quarter lunar phase.\n */",
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         "comment": "/**\n * @brief A quarter lunar phase, along with when it occurs.\n *\n * @property {number} quarter\n *      An integer as follows:\n *      0 = new moon,\n *      1 = first quarter,\n *      2 = full moon,\n *      3 = third quarter.\n *\n * @property {AstroTime} time\n *      The date and time of the quarter lunar phase.\n */",
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                 "name": "exports.MoonQuarter",
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@@ -34699,14 +34671,14 @@
         "comment": "/**\n * @brief Finds the first quarter lunar phase after the specified date and time.\n *\n * The quarter lunar phases are: new moon, first quarter, full moon, and third quarter.\n * To enumerate quarter lunar phases, call `SearchMoonQuarter` once,\n * then pass its return value to {@link NextMoonQuarter} to find the next\n * `MoonQuarter`. Keep calling `NextMoonQuarter` in a loop,\n * passing the previous return value as the argument to the next call.\n *\n * @param {FlexibleDateTime} dateStart\n *      The date and time after which to find the first quarter lunar phase.\n *\n * @returns {MoonQuarter}\n */",
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                 "name": "exports.HourAngleEvent",
                 "type": "Identifier",
                 "value": "HourAngleEvent",
@@ -36125,14 +36097,14 @@
         "comment": "/**\n * @brief Finds when a body will reach a given hour angle.\n *\n * Finds the next time the given body is seen to reach the specified\n * <a href=\"https://en.wikipedia.org/wiki/Hour_angle\">hour angle</a>\n * by the given observer.\n * Providing `hourAngle` = 0 finds the next maximum altitude event (culmination).\n * Providing `hourAngle` = 12 finds the next minimum altitude event.\n * Note that, especially close to the Earth's poles, a body as seen on a given day\n * may always be above the horizon or always below the horizon, so the caller cannot\n * assume that a culminating object is visible nor that an object is below the horizon\n * at its minimum altitude.\n *\n * @param {string} body\n *      The name of a celestial body other than the Earth.\n *\n * @param {Observer} observer\n *      Specifies the geographic coordinates and elevation above sea level of the observer.\n *\n * @param {number} hourAngle\n *      The hour angle expressed in\n *      <a href=\"https://en.wikipedia.org/wiki/Sidereal_time\">sidereal</a>\n *      hours for which the caller seeks to find the body attain.\n *      The value must be in the range [0, 24).\n *      The hour angle represents the number of sidereal hours that have\n *      elapsed since the most recent time the body crossed the observer's local\n *      <a href=\"https://en.wikipedia.org/wiki/Meridian_(astronomy)\">meridian</a>.\n *      This specifying `hourAngle` = 0 finds the moment in time\n *      the body reaches the highest angular altitude in a given sidereal day.\n *\n * @param {FlexibleDateTime} dateStart\n *      The date and time after which the desired hour angle crossing event\n *      is to be found.\n *\n * @returns {HourAngleEvent}\n */",
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@@ -36216,14 +36188,14 @@
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@@ -36241,14 +36213,14 @@
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                 "funcscope": "SearchHourAngle",
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                 "name": "exports.SearchHourAngle",
                 "type": "Identifier",
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@@ -36519,14 +36491,14 @@
         "comment": "/**\n * @brief When the seasons change for a given calendar year.\n *\n * Represents the dates and times of the two solstices\n * and the two equinoxes in a given calendar year.\n * These four events define the changing of the seasons on the Earth.\n *\n * @property {AstroTime} mar_equinox\n *      The date and time of the March equinox in the given calendar year.\n *      This is the moment in March that the plane of the Earth's equator passes\n *      through the center of the Sun; thus the Sun's declination\n *      changes from a negative number to a positive number.\n *      The March equinox defines\n *      the beginning of spring in the northern hemisphere and\n *      the beginning of autumn in the southern hemisphere.\n *\n * @property {AstroTime} jun_solstice\n *      The date and time of the June solstice in the given calendar year.\n *      This is the moment in June that the Sun reaches its most positive\n *      declination value.\n *      At this moment the Earth's north pole is most tilted most toward the Sun.\n *      The June solstice defines\n *      the beginning of summer in the northern hemisphere and\n *      the beginning of winter in the southern hemisphere.\n *\n * @property {AstroTime} sep_equinox\n *      The date and time of the September equinox in the given calendar year.\n *      This is the moment in September that the plane of the Earth's equator passes\n *      through the center of the Sun; thus the Sun's declination\n *      changes from a positive number to a negative number.\n *      The September equinox defines\n *      the beginning of autumn in the northern hemisphere and\n *      the beginning of spring in the southern hemisphere.\n *\n * @property {AstroTime} dec_solstice\n *      The date and time of the December solstice in the given calendar year.\n *      This is the moment in December that the Sun reaches its most negative\n *      declination value.\n *      At this moment the Earth's south pole is tilted most toward the Sun.\n *      The December solstice defines\n *      the beginning of winter in the northern hemisphere and\n *      the beginning of summer in the southern hemisphere.\n */",
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@@ -36625,14 +36597,14 @@
         "comment": "/**\n * @brief When the seasons change for a given calendar year.\n *\n * Represents the dates and times of the two solstices\n * and the two equinoxes in a given calendar year.\n * These four events define the changing of the seasons on the Earth.\n *\n * @property {AstroTime} mar_equinox\n *      The date and time of the March equinox in the given calendar year.\n *      This is the moment in March that the plane of the Earth's equator passes\n *      through the center of the Sun; thus the Sun's declination\n *      changes from a negative number to a positive number.\n *      The March equinox defines\n *      the beginning of spring in the northern hemisphere and\n *      the beginning of autumn in the southern hemisphere.\n *\n * @property {AstroTime} jun_solstice\n *      The date and time of the June solstice in the given calendar year.\n *      This is the moment in June that the Sun reaches its most positive\n *      declination value.\n *      At this moment the Earth's north pole is most tilted most toward the Sun.\n *      The June solstice defines\n *      the beginning of summer in the northern hemisphere and\n *      the beginning of winter in the southern hemisphere.\n *\n * @property {AstroTime} sep_equinox\n *      The date and time of the September equinox in the given calendar year.\n *      This is the moment in September that the plane of the Earth's equator passes\n *      through the center of the Sun; thus the Sun's declination\n *      changes from a positive number to a negative number.\n *      The September equinox defines\n *      the beginning of autumn in the northern hemisphere and\n *      the beginning of spring in the southern hemisphere.\n *\n * @property {AstroTime} dec_solstice\n *      The date and time of the December solstice in the given calendar year.\n *      This is the moment in December that the Sun reaches its most negative\n *      declination value.\n *      At this moment the Earth's south pole is tilted most toward the Sun.\n *      The December solstice defines\n *      the beginning of winter in the northern hemisphere and\n *      the beginning of summer in the southern hemisphere.\n */",
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@@ -36698,14 +36670,14 @@
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                 "name": "this.mar_equinox",
                 "type": "Identifier",
                 "value": "mar_equinox",
@@ -36723,14 +36695,14 @@
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                 "name": "this.jun_solstice",
                 "type": "Identifier",
                 "value": "jun_solstice",
@@ -36748,14 +36720,14 @@
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                 "type": "Identifier",
                 "value": "sep_equinox",
@@ -36773,14 +36745,14 @@
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                 "type": "Identifier",
                 "value": "dec_solstice",
@@ -36798,14 +36770,14 @@
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                 "name": "exports.SeasonInfo",
                 "type": "Identifier",
                 "value": "SeasonInfo",
@@ -36822,14 +36794,14 @@
         "comment": "/**\n * @brief Finds the equinoxes and solstices for a given calendar year.\n *\n * @param {number | AstroTime} year\n *      The integer value or `AstroTime` object that specifies\n *      the UTC calendar year for which to find equinoxes and solstices.\n *\n * @returns {SeasonInfo}\n */",
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             "columnno": 0,
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-                "id": "astnode100017016",
+                "id": "astnode100017003",
                 "name": "Seasons",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -36883,14 +36855,14 @@
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@@ -36916,14 +36888,14 @@
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@@ -36941,14 +36913,14 @@
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@@ -36966,14 +36938,14 @@
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                 "name": "year",
                 "type": "CallExpression",
                 "funcscope": "Seasons",
@@ -36992,14 +36964,14 @@
         "comment": "",
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             "columnno": 8,
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@@ -37017,14 +36989,14 @@
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@@ -37042,14 +37014,14 @@
         "comment": "",
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@@ -37067,14 +37039,14 @@
         "comment": "",
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@@ -37092,14 +37064,14 @@
         "comment": "",
         "meta": {
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             "columnno": 0,
             "code": {
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                 "name": "exports.Seasons",
                 "type": "Identifier",
                 "value": "Seasons",
@@ -37116,14 +37088,14 @@
         "comment": "/**\n * @brief The viewing conditions of a body relative to the Sun.\n *\n * Represents the angular separation of a body from the Sun as seen from the Earth\n * and the relative ecliptic longitudes between that body and the Earth as seen from the Sun.\n *\n * @property {AstroTime} time\n *      The date and time of the observation.\n *\n * @property {string}  visibility\n *      Either `\"morning\"` or `\"evening\"`,\n *      indicating when the body is most easily seen.\n *\n * @property {number}  elongation\n *      The angle in degrees, as seen from the center of the Earth,\n *      of the apparent separation between the body and the Sun.\n *      This angle is measured in 3D space and is not projected onto the ecliptic plane.\n *      When `elongation` is less than a few degrees, the body is very\n *      difficult to see from the Earth because it is lost in the Sun's glare.\n *      The elongation is always in the range [0, 180].\n *\n * @property {number}  ecliptic_separation\n *      The absolute value of the difference between the body's ecliptic longitude\n *      and the Sun's ecliptic longitude, both as seen from the center of the Earth.\n *      This angle measures around the plane of the Earth's orbit (the ecliptic),\n *      and ignores how far above or below that plane the body is.\n *      The ecliptic separation is measured in degrees and is always in the range [0, 180].\n *\n * @see {@link Elongation}\n */",
         "meta": {
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             "columnno": 0,
             "code": {
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                 "name": "ElongationEvent",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -37193,14 +37165,14 @@
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         "meta": {
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             "columnno": 4,
             "code": {
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                 "name": "ElongationEvent",
                 "type": "MethodDefinition",
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@@ -37225,14 +37197,14 @@
         "comment": "/**\n * @brief The viewing conditions of a body relative to the Sun.\n *\n * Represents the angular separation of a body from the Sun as seen from the Earth\n * and the relative ecliptic longitudes between that body and the Earth as seen from the Sun.\n *\n * @property {AstroTime} time\n *      The date and time of the observation.\n *\n * @property {string}  visibility\n *      Either `\"morning\"` or `\"evening\"`,\n *      indicating when the body is most easily seen.\n *\n * @property {number}  elongation\n *      The angle in degrees, as seen from the center of the Earth,\n *      of the apparent separation between the body and the Sun.\n *      This angle is measured in 3D space and is not projected onto the ecliptic plane.\n *      When `elongation` is less than a few degrees, the body is very\n *      difficult to see from the Earth because it is lost in the Sun's glare.\n *      The elongation is always in the range [0, 180].\n *\n * @property {number}  ecliptic_separation\n *      The absolute value of the difference between the body's ecliptic longitude\n *      and the Sun's ecliptic longitude, both as seen from the center of the Earth.\n *      This angle measures around the plane of the Earth's orbit (the ecliptic),\n *      and ignores how far above or below that plane the body is.\n *      The ecliptic separation is measured in degrees and is always in the range [0, 180].\n *\n * @see {@link Elongation}\n */",
         "meta": {
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             "columnno": 0,
             "code": {
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+                "id": "astnode100017127",
                 "name": "ElongationEvent",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -37301,14 +37273,14 @@
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         "meta": {
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             "columnno": 8,
             "code": {
-                "id": "astnode100017152",
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                 "name": "this.time",
                 "type": "Identifier",
                 "value": "time",
@@ -37326,14 +37298,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                170668
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100017158",
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                 "name": "this.visibility",
                 "type": "Identifier",
                 "value": "visibility",
@@ -37351,14 +37323,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                170706
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100017164",
+                "id": "astnode100017151",
                 "name": "this.elongation",
                 "type": "Identifier",
                 "value": "elongation",
@@ -37376,14 +37348,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                170762
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100017170",
+                "id": "astnode100017157",
                 "name": "this.ecliptic_separation",
                 "type": "Identifier",
                 "value": "ecliptic_separation",
@@ -37401,14 +37373,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                170813
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             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100017176",
+                "id": "astnode100017163",
                 "name": "exports.ElongationEvent",
                 "type": "Identifier",
                 "value": "ElongationEvent",
@@ -37425,14 +37397,14 @@
         "comment": "/**\n * @brief Calculates the viewing conditions of a body relative to the Sun.\n *\n * Calculates angular separation of a body from the Sun as seen from the Earth\n * and the relative ecliptic longitudes between that body and the Earth as seen from the Sun.\n * See the return type {@link ElongationEvent} for details.\n *\n * This function is helpful for determining how easy\n * it is to view a planet away from the Sun's glare on a given date.\n * It also determines whether the object is visible in the morning or evening;\n * this is more important the smaller the elongation is.\n * It is also used to determine how far a planet is from opposition, conjunction, or quadrature.\n *\n * @param {string} body\n *      The name of the observed body. Not allowed to be `\"Earth\"`.\n *\n * @returns {ElongationEvent}\n */",
         "meta": {
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             ],
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             "columnno": 0,
             "code": {
-                "id": "astnode100017181",
+                "id": "astnode100017168",
                 "name": "Elongation",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -37484,14 +37456,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
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                 "name": "time",
                 "type": "CallExpression",
                 "value": ""
@@ -37509,14 +37481,14 @@
         "comment": "",
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             "range": [
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             ],
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             "columnno": 8,
             "code": {
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                 "name": "lon",
                 "type": "CallExpression",
                 "value": ""
@@ -37534,14 +37506,14 @@
         "comment": "",
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             "range": [
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             "columnno": 8,
             "code": {
-                "id": "astnode100017200",
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                 "name": "vis"
             }
         },
@@ -37557,14 +37529,14 @@
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         "meta": {
             "range": [
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             "columnno": 8,
             "code": {
-                "id": "astnode100017208",
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                 "name": "vis",
                 "type": "Literal",
                 "funcscope": "Elongation",
@@ -37583,14 +37555,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
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                 "name": "lon",
                 "type": "BinaryExpression",
                 "funcscope": "Elongation",
@@ -37609,14 +37581,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100017219",
+                "id": "astnode100017206",
                 "name": "vis",
                 "type": "Literal",
                 "funcscope": "Elongation",
@@ -37635,14 +37607,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
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             "columnno": 8,
             "code": {
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                 "type": "CallExpression",
                 "value": ""
@@ -37660,14 +37632,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100017237",
+                "id": "astnode100017224",
                 "name": "exports.Elongation",
                 "type": "Identifier",
                 "value": "Elongation",
@@ -37684,14 +37656,14 @@
         "comment": "/**\n * @brief Finds the next time Mercury or Venus reaches maximum elongation.\n *\n * Searches for the next maximum elongation event for Mercury or Venus\n * that occurs after the given start date. Calling with other values\n * of `body` will result in an exception.\n * Maximum elongation occurs when the body has the greatest\n * angular separation from the Sun, as seen from the Earth.\n * Returns an `ElongationEvent` object containing the date and time of the next\n * maximum elongation, the elongation in degrees, and whether\n * the body is visible in the morning or evening.\n *\n * @param {string} body     Either `\"Mercury\"` or `\"Venus\"`.\n * @param {FlexibleDateTime} startDate  The date and time after which to search for the next maximum elongation event.\n *\n * @returns {ElongationEvent}\n */",
         "meta": {
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             ],
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             "columnno": 0,
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-                "id": "astnode100017242",
+                "id": "astnode100017229",
                 "name": "SearchMaxElongation",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -37766,14 +37738,14 @@
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             "columnno": 10,
             "code": {
-                "id": "astnode100017248",
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                 "name": "dt",
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@@ -37791,14 +37763,14 @@
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             "columnno": 4,
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+                "id": "astnode100017238",
                 "name": "neg_slope",
                 "type": "FunctionDeclaration",
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@@ -37825,14 +37797,14 @@
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@@ -37850,14 +37822,14 @@
         "comment": "",
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             "range": [
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             ],
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             "columnno": 14,
             "code": {
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@@ -37875,14 +37847,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
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             "columnno": 12,
             "code": {
-                "id": "astnode100017278",
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                 "name": "e1",
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                 "value": ""
@@ -37900,14 +37872,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
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             "columnno": 12,
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@@ -37925,14 +37897,14 @@
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             ],
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             "columnno": 12,
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@@ -37950,14 +37922,14 @@
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             "columnno": 8,
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                 "name": "startTime",
                 "type": "CallExpression",
                 "value": ""
@@ -37975,14 +37947,14 @@
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             "columnno": 10,
             "code": {
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                 "name": "table",
                 "type": "ObjectExpression",
                 "value": "{\"Mercury\":\"\",\"Venus\":\"\"}"
@@ -38000,14 +37972,14 @@
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             "columnno": 8,
             "code": {
-                "id": "astnode100017311",
+                "id": "astnode100017298",
                 "name": "Mercury",
                 "type": "ObjectExpression",
                 "value": "{\"s1\":50,\"s2\":85}"
@@ -38024,14 +37996,14 @@
         "comment": "",
         "meta": {
             "range": [
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+                "id": "astnode100017300",
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@@ -38048,14 +38020,14 @@
         "comment": "",
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@@ -38072,14 +38044,14 @@
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             "columnno": 8,
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-                "id": "astnode100017317",
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                 "name": "Venus",
                 "type": "ObjectExpression",
                 "value": "{\"s1\":40,\"s2\":50}"
@@ -38096,14 +38068,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                "id": "astnode100017319",
+                "id": "astnode100017306",
                 "name": "s1",
                 "type": "Literal",
                 "value": 40
@@ -38120,14 +38092,14 @@
         "comment": "",
         "meta": {
             "range": [
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+                "id": "astnode100017308",
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@@ -38144,14 +38116,14 @@
         "comment": "",
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             "columnno": 10,
             "code": {
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+                "id": "astnode100017311",
                 "name": "planet",
                 "type": "MemberExpression",
                 "value": "table[undefined]"
@@ -38169,14 +38141,14 @@
         "comment": "",
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@@ -38194,14 +38166,14 @@
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@@ -38219,14 +38191,14 @@
         "comment": "",
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                 "value": ""
@@ -38244,14 +38216,14 @@
         "comment": "",
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@@ -38269,14 +38241,14 @@
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@@ -38292,14 +38264,14 @@
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             "columnno": 21,
             "code": {
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+                "id": "astnode100017356",
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@@ -38315,14 +38287,14 @@
         "comment": "",
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             "range": [
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             "columnno": 30,
             "code": {
-                "id": "astnode100017371",
+                "id": "astnode100017358",
                 "name": "adjust_days"
             }
         },
@@ -38338,14 +38310,14 @@
         "comment": "",
         "meta": {
             "range": [
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             "columnno": 12,
             "code": {
-                "id": "astnode100017389",
+                "id": "astnode100017376",
                 "name": "adjust_days",
                 "type": "Literal",
                 "funcscope": "SearchMaxElongation",
@@ -38364,14 +38336,14 @@
         "comment": "",
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             "range": [
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@@ -42804,14 +42776,14 @@
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@@ -43302,14 +43274,14 @@
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@@ -43494,14 +43466,14 @@
         "comment": "/**\n * @brief Converts Cartesian coordinates to spherical coordinates.\n *\n * Given a Cartesian vector, returns latitude, longitude, and distance.\n *\n * @param {Vector} vector\n *      Cartesian vector to be converted to spherical coordinates.\n *\n * @returns {Spherical}\n *      Spherical coordinates that are equivalent to the given vector.\n */",
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@@ -43910,14 +43882,14 @@
         "comment": "/**\n * @brief Converts Cartesian coordinates to horizontal coordinates.\n *\n * Given a horizontal Cartesian vector, returns horizontal azimuth and altitude.\n *\n * *IMPORTANT:* This function differs from {@link SphereFromVector} in two ways:\n * - `SphereFromVector` returns a `lon` value that represents azimuth defined counterclockwise\n *   from north (e.g., west = +90), but this function represents a clockwise rotation\n *   (e.g., east = +90). The difference is because `SphereFromVector` is intended\n *   to preserve the vector \"right-hand rule\", while this function defines azimuth in a more\n *   traditional way as used in navigation and cartography.\n * - This function optionally corrects for atmospheric refraction, while `SphereFromVector` does not.\n *\n * The returned object contains the azimuth in `lon`.\n * It is measured in degrees clockwise from north: east = +90 degrees, west = +270 degrees.\n *\n * The altitude is stored in `lat`.\n *\n * The distance to the observed object is stored in `dist`,\n * and is expressed in astronomical units (AU).\n *\n * @param {Vector} vector\n *      Cartesian vector to be converted to horizontal coordinates.\n *\n * @param {string} refraction\n *      `\"normal\"`: correct altitude for atmospheric refraction (recommended).\n *      `\"jplhor\"`: for JPL Horizons compatibility testing only; not recommended for normal use.\n *      `null`: no atmospheric refraction correction is performed.\n *\n * @returns {Spherical}\n */",
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         "comment": "/**\n * @brief Given apparent angular horizontal coordinates in `sphere`, calculate horizontal vector.\n *\n * @param {Spherical} sphere\n *      A structure that contains apparent horizontal coordinates:\n *      `lat` holds the refracted azimuth angle,\n *      `lon` holds the azimuth in degrees clockwise from north,\n *      and `dist` holds the distance from the observer to the object in AU.\n *\n * @param {AstroTime} time\n *      The date and time of the observation. This is needed because the returned\n *      vector object requires a valid time value when passed to certain other functions.\n *\n * @param {string} refraction\n *      `\"normal\"`: correct altitude for atmospheric refraction (recommended).\n *      `\"jplhor\"`: for JPL Horizons compatibility testing only; not recommended for normal use.\n *      `null`: no atmospheric refraction correction is performed.\n *\n * @returns {Vector}\n *      A vector in the horizontal system: `x` = north, `y` = west, and `z` = zenith (up).\n */",
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@@ -44255,14 +44227,14 @@
         "comment": "/**\n * @brief Calculates the amount of \"lift\" to an altitude angle caused by atmospheric refraction.\n *\n * Given an altitude angle and a refraction option, calculates\n * the amount of \"lift\" caused by atmospheric refraction.\n * This is the number of degrees higher in the sky an object appears\n * due to the lensing of the Earth's atmosphere.\n *\n * @param {string} refraction\n *      `\"normal\"`: correct altitude for atmospheric refraction (recommended).\n *      `\"jplhor\"`: for JPL Horizons compatibility testing only; not recommended for normal use.\n *      `null`: no atmospheric refraction correction is performed.\n *\n * @param {number} altitude\n *      An altitude angle in a horizontal coordinate system. Must be a value between -90 and +90.\n *\n * @returns {number}\n *      The angular adjustment in degrees to be added to the altitude angle to correct for atmospheric lensing.\n */",
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100019921",
+                "id": "astnode100019908",
                 "name": "refr",
                 "type": "Literal",
                 "funcscope": "Refraction",
@@ -44474,14 +44446,14 @@
         "comment": "",
         "meta": {
             "range": [
-                207297,
-                207328
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+                209367
             ],
             "filename": "astronomy.js",
-            "lineno": 4733,
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             "columnno": 0,
             "code": {
-                "id": "astnode100019927",
+                "id": "astnode100019914",
                 "name": "exports.Refraction",
                 "type": "Identifier",
                 "value": "Refraction",
@@ -44498,14 +44470,14 @@
         "comment": "/**\n * @brief Calculates the inverse of an atmospheric refraction angle.\n *\n * Given an observed altitude angle that includes atmospheric refraction,\n * calculate the negative angular correction to obtain the unrefracted\n * altitude. This is useful for cases where observed horizontal\n * coordinates are to be converted to another orientation system,\n * but refraction first must be removed from the observed position.\n *\n * @param {string} refraction\n *      `\"normal\"`: correct altitude for atmospheric refraction (recommended).\n *      `\"jplhor\"`: for JPL Horizons compatibility testing only; not recommended for normal use.\n *      `null`: no atmospheric refraction correction is performed.\n *\n * @param {number} bent_altitude\n *      The apparent altitude that includes atmospheric refraction.\n *\n * @returns {number}\n *      The angular adjustment in degrees to be added to the\n *      altitude angle to correct for atmospheric lensing.\n *      This will be less than or equal to zero.\n */",
         "meta": {
             "range": [
-                208326,
-                208927
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+                210966
             ],
             "filename": "astronomy.js",
-            "lineno": 4756,
+            "lineno": 4788,
             "columnno": 0,
             "code": {
-                "id": "astnode100019932",
+                "id": "astnode100019919",
                 "name": "InverseRefraction",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -44565,14 +44537,14 @@
         "comment": "",
         "meta": {
             "range": [
-                208612,
-                208676
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+                210715
             ],
             "filename": "astronomy.js",
-            "lineno": 4761,
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             "columnno": 8,
             "code": {
-                "id": "astnode100019951",
+                "id": "astnode100019938",
                 "name": "altitude",
                 "type": "BinaryExpression",
                 "value": ""
@@ -44590,14 +44562,14 @@
         "comment": "",
         "meta": {
             "range": [
-                208741,
-                208809
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+                210848
             ],
             "filename": "astronomy.js",
-            "lineno": 4764,
+            "lineno": 4796,
             "columnno": 12,
             "code": {
-                "id": "astnode100019962",
+                "id": "astnode100019949",
                 "name": "diff",
                 "type": "BinaryExpression",
                 "value": ""
@@ -44615,14 +44587,14 @@
         "comment": "",
         "meta": {
             "range": [
-                208902,
-                208918
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+                210957
             ],
             "filename": "astronomy.js",
-            "lineno": 4767,
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             "columnno": 8,
             "code": {
-                "id": "astnode100019985",
+                "id": "astnode100019972",
                 "name": "altitude",
                 "type": "Identifier",
                 "funcscope": "InverseRefraction",
@@ -44641,14 +44613,14 @@
         "comment": "",
         "meta": {
             "range": [
-                208928,
-                208973
+                210967,
+                211012
             ],
             "filename": "astronomy.js",
-            "lineno": 4770,
+            "lineno": 4802,
             "columnno": 0,
             "code": {
-                "id": "astnode100019989",
+                "id": "astnode100019976",
                 "name": "exports.InverseRefraction",
                 "type": "Identifier",
                 "value": "InverseRefraction",
@@ -44665,14 +44637,14 @@
         "comment": "/**\n * @brief Applies a rotation to a vector, yielding a rotated vector.\n *\n * This function transforms a vector in one orientation to a vector\n * in another orientation.\n *\n * @param {RotationMatrix} rotation\n *      A rotation matrix that specifies how the orientation of the vector is to be changed.\n *\n * @param {Vector} vector\n *      The vector whose orientation is to be changed.\n *\n * @returns {Vector}\n *      A vector in the orientation specified by `rotation`.\n */",
         "meta": {
             "range": [
-                209451,
-                209812
+                211490,
+                211851
             ],
             "filename": "astronomy.js",
-            "lineno": 4786,
+            "lineno": 4818,
             "columnno": 0,
             "code": {
-                "id": "astnode100019994",
+                "id": "astnode100019981",
                 "name": "RotateVector",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -44728,14 +44700,14 @@
         "comment": "",
         "meta": {
             "range": [
-                209813,
-                209848
+                211852,
+                211887
             ],
             "filename": "astronomy.js",
-            "lineno": 4789,
+            "lineno": 4821,
             "columnno": 0,
             "code": {
-                "id": "astnode100020111",
+                "id": "astnode100020098",
                 "name": "exports.RotateVector",
                 "type": "Identifier",
                 "value": "RotateVector",
@@ -44752,14 +44724,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from equatorial J2000 (EQJ) to ecliptic J2000 (ECL).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: EQJ = equatorial system, using equator at J2000 epoch.\n * Target: ECL = ecliptic system, using equator at J2000 epoch.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts EQJ to ECL.\n */",
         "meta": {
             "range": [
-                210291,
-                210601
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+                212640
             ],
             "filename": "astronomy.js",
-            "lineno": 4801,
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             "columnno": 0,
             "code": {
-                "id": "astnode100020116",
+                "id": "astnode100020103",
                 "name": "Rotation_EQJ_ECL",
                 "type": "FunctionDeclaration",
                 "paramnames": []
@@ -44797,14 +44769,14 @@
         "comment": "",
         "meta": {
             "range": [
-                210414,
-                210436
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             ],
             "filename": "astronomy.js",
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             "columnno": 10,
             "code": {
-                "id": "astnode100020120",
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                 "type": "Literal",
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@@ -44822,14 +44794,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 10,
             "code": {
-                "id": "astnode100020124",
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                 "type": "Literal",
                 "value": 0.3977769691083922
@@ -44847,14 +44819,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100020148",
+                "id": "astnode100020135",
                 "name": "exports.Rotation_EQJ_ECL",
                 "type": "Identifier",
                 "value": "Rotation_EQJ_ECL",
@@ -44871,14 +44843,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from ecliptic J2000 (ECL) to equatorial J2000 (EQJ).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: ECL = ecliptic system, using equator at J2000 epoch.\n * Target: EQJ = equatorial system, using equator at J2000 epoch.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts ECL to EQJ.\n */",
         "meta": {
             "range": [
-                211088,
-                211398
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+                213437
             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100020153",
+                "id": "astnode100020140",
                 "name": "Rotation_ECL_EQJ",
                 "type": "FunctionDeclaration",
                 "paramnames": []
@@ -44916,14 +44888,14 @@
         "comment": "",
         "meta": {
             "range": [
-                211211,
-                211233
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+                213272
             ],
             "filename": "astronomy.js",
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             "columnno": 10,
             "code": {
-                "id": "astnode100020157",
+                "id": "astnode100020144",
                 "name": "c",
                 "type": "Literal",
                 "value": 0.9174821430670688
@@ -44941,14 +44913,14 @@
         "comment": "",
         "meta": {
             "range": [
-                211259,
-                211281
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+                213320
             ],
             "filename": "astronomy.js",
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             "columnno": 10,
             "code": {
-                "id": "astnode100020161",
+                "id": "astnode100020148",
                 "name": "s",
                 "type": "Literal",
                 "value": 0.3977769691083922
@@ -44966,14 +44938,14 @@
         "comment": "",
         "meta": {
             "range": [
-                211399,
-                211442
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+                213481
             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100020185",
+                "id": "astnode100020172",
                 "name": "exports.Rotation_ECL_EQJ",
                 "type": "Identifier",
                 "value": "Rotation_ECL_EQJ",
@@ -44990,14 +44962,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from equatorial J2000 (EQJ) to equatorial of-date (EQD).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: EQJ = equatorial system, using equator at J2000 epoch.\n * Target: EQD = equatorial system, using equator of the specified date/time.\n *\n * @param {AstroTime} time\n *      The date and time at which the Earth's equator defines the target orientation.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts EQJ to EQD at `time`.\n */",
         "meta": {
             "range": [
-                212030,
-                212190
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+                214229
             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100020190",
+                "id": "astnode100020177",
                 "name": "Rotation_EQJ_EQD",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -45047,14 +45019,14 @@
         "comment": "",
         "meta": {
             "range": [
-                212074,
-                212109
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+                214148
             ],
             "filename": "astronomy.js",
-            "lineno": 4849,
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             "columnno": 10,
             "code": {
-                "id": "astnode100020195",
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                 "name": "prec",
                 "type": "CallExpression",
                 "value": ""
@@ -45072,14 +45044,14 @@
         "comment": "",
         "meta": {
             "range": [
-                212121,
-                212148
+                214160,
+                214187
             ],
             "filename": "astronomy.js",
-            "lineno": 4850,
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             "columnno": 10,
             "code": {
-                "id": "astnode100020204",
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                 "name": "nut",
                 "type": "CallExpression",
                 "value": ""
@@ -45097,14 +45069,14 @@
         "comment": "",
         "meta": {
             "range": [
-                212191,
-                212234
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+                214273
             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100020216",
+                "id": "astnode100020203",
                 "name": "exports.Rotation_EQJ_EQD",
                 "type": "Identifier",
                 "value": "Rotation_EQJ_EQD",
@@ -45121,14 +45093,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from equatorial of-date (EQD) to equatorial J2000 (EQJ).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: EQD = equatorial system, using equator of the specified date/time.\n * Target: EQJ = equatorial system, using equator at J2000 epoch.\n *\n * @param {AstroTime} time\n *      The date and time at which the Earth's equator defines the source orientation.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts EQD at `time` to EQJ.\n */",
         "meta": {
             "range": [
-                212822,
-                212982
+                214861,
+                215021
             ],
             "filename": "astronomy.js",
-            "lineno": 4868,
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             "columnno": 0,
             "code": {
-                "id": "astnode100020221",
+                "id": "astnode100020208",
                 "name": "Rotation_EQD_EQJ",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -45178,14 +45150,14 @@
         "comment": "",
         "meta": {
             "range": [
-                212866,
-                212893
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+                214932
             ],
             "filename": "astronomy.js",
-            "lineno": 4869,
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             "columnno": 10,
             "code": {
-                "id": "astnode100020226",
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                 "type": "CallExpression",
                 "value": ""
@@ -45203,14 +45175,14 @@
         "comment": "",
         "meta": {
             "range": [
-                212905,
-                212940
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+                214979
             ],
             "filename": "astronomy.js",
-            "lineno": 4870,
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             "columnno": 10,
             "code": {
-                "id": "astnode100020233",
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                 "type": "CallExpression",
                 "value": ""
@@ -45228,14 +45200,14 @@
         "comment": "",
         "meta": {
             "range": [
-                212983,
-                213026
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+                215065
             ],
             "filename": "astronomy.js",
-            "lineno": 4873,
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             "columnno": 0,
             "code": {
-                "id": "astnode100020247",
+                "id": "astnode100020234",
                 "name": "exports.Rotation_EQD_EQJ",
                 "type": "Identifier",
                 "value": "Rotation_EQD_EQJ",
@@ -45252,14 +45224,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from equatorial of-date (EQD) to horizontal (HOR).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: EQD = equatorial system, using equator of the specified date/time.\n * Target: HOR = horizontal system.\n *\n * Use `HorizonFromVector` to convert the return value\n * to a traditional altitude/azimuth pair.\n *\n * @param {AstroTime} time\n *      The date and time at which the Earth's equator applies.\n *\n * @param {Observer} observer\n *      A location near the Earth's mean sea level that defines the observer's horizon.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts EQD to HOR at `time` and for `observer`.\n *      The components of the horizontal vector are:\n *      x = north, y = west, z = zenith (straight up from the observer).\n *      These components are chosen so that the \"right-hand rule\" works for the vector\n *      and so that north represents the direction where azimuth = 0.\n */",
         "meta": {
             "range": [
-                214079,
-                214815
+                216118,
+                216854
             ],
             "filename": "astronomy.js",
-            "lineno": 4898,
+            "lineno": 4930,
             "columnno": 0,
             "code": {
-                "id": "astnode100020252",
+                "id": "astnode100020239",
                 "name": "Rotation_EQD_HOR",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -45328,14 +45300,14 @@
         "comment": "",
         "meta": {
             "range": [
-                214133,
-                214179
+                216172,
+                216218
             ],
             "filename": "astronomy.js",
-            "lineno": 4899,
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             "columnno": 10,
             "code": {
-                "id": "astnode100020258",
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                 "name": "sinlat",
                 "type": "CallExpression",
                 "value": ""
@@ -45353,14 +45325,14 @@
         "comment": "",
         "meta": {
             "range": [
-                214191,
-                214237
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+                216276
             ],
             "filename": "astronomy.js",
-            "lineno": 4900,
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             "columnno": 10,
             "code": {
-                "id": "astnode100020270",
+                "id": "astnode100020257",
                 "name": "coslat",
                 "type": "CallExpression",
                 "value": ""
@@ -45378,14 +45350,14 @@
         "comment": "",
         "meta": {
             "range": [
-                214249,
-                214296
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+                216335
             ],
             "filename": "astronomy.js",
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             "columnno": 10,
             "code": {
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+                "id": "astnode100020269",
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                 "type": "CallExpression",
                 "value": ""
@@ -45403,14 +45375,14 @@
         "comment": "",
         "meta": {
             "range": [
-                214308,
-                214355
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+                216394
             ],
             "filename": "astronomy.js",
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             "columnno": 10,
             "code": {
-                "id": "astnode100020294",
+                "id": "astnode100020281",
                 "name": "coslon",
                 "type": "CallExpression",
                 "value": ""
@@ -45428,14 +45400,14 @@
         "comment": "",
         "meta": {
             "range": [
-                214367,
-                214415
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+                216454
             ],
             "filename": "astronomy.js",
-            "lineno": 4903,
+            "lineno": 4935,
             "columnno": 10,
             "code": {
-                "id": "astnode100020306",
+                "id": "astnode100020293",
                 "name": "uze",
                 "type": "ArrayExpression",
                 "value": "[\"\",\"\",\"sinlat\"]"
@@ -45453,14 +45425,14 @@
         "comment": "",
         "meta": {
             "range": [
-                214427,
-                214477
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+                216516
             ],
             "filename": "astronomy.js",
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             "columnno": 10,
             "code": {
-                "id": "astnode100020317",
+                "id": "astnode100020304",
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                 "type": "ArrayExpression",
                 "value": "[\"\",\"\",\"coslat\"]"
@@ -45478,14 +45450,14 @@
         "comment": "",
         "meta": {
             "range": [
-                214489,
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             ],
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             "columnno": 10,
             "code": {
-                "id": "astnode100020330",
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                 "name": "uwe",
                 "type": "ArrayExpression",
                 "value": "[\"sinlon\",\"-coslon\",0]"
@@ -45503,14 +45475,14 @@
         "comment": "",
         "meta": {
             "range": [
-                214527,
-                214565
+                216566,
+                216604
             ],
             "filename": "astronomy.js",
-            "lineno": 4906,
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             "columnno": 10,
             "code": {
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+                "id": "astnode100020325",
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                 "type": "BinaryExpression",
                 "value": ""
@@ -45528,14 +45500,14 @@
         "comment": "",
         "meta": {
             "range": [
-                214577,
-                214603
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+                216642
             ],
             "filename": "astronomy.js",
-            "lineno": 4907,
+            "lineno": 4939,
             "columnno": 10,
             "code": {
-                "id": "astnode100020347",
+                "id": "astnode100020334",
                 "name": "uz",
                 "type": "CallExpression",
                 "value": ""
@@ -45553,14 +45525,14 @@
         "comment": "",
         "meta": {
             "range": [
-                214615,
-                214641
+                216654,
+                216680
             ],
             "filename": "astronomy.js",
-            "lineno": 4908,
+            "lineno": 4940,
             "columnno": 10,
             "code": {
-                "id": "astnode100020354",
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                 "name": "un",
                 "type": "CallExpression",
                 "value": ""
@@ -45578,14 +45550,14 @@
         "comment": "",
         "meta": {
             "range": [
-                214653,
-                214679
+                216692,
+                216718
             ],
             "filename": "astronomy.js",
-            "lineno": 4909,
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             "columnno": 10,
             "code": {
-                "id": "astnode100020361",
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                 "type": "CallExpression",
                 "value": ""
@@ -45603,14 +45575,14 @@
         "comment": "",
         "meta": {
             "range": [
-                214816,
-                214859
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+                216898
             ],
             "filename": "astronomy.js",
-            "lineno": 4916,
+            "lineno": 4948,
             "columnno": 0,
             "code": {
-                "id": "astnode100020402",
+                "id": "astnode100020389",
                 "name": "exports.Rotation_EQD_HOR",
                 "type": "Identifier",
                 "value": "Rotation_EQD_HOR",
@@ -45627,14 +45599,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from horizontal (HOR) to equatorial of-date (EQD).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: HOR = horizontal system (x=North, y=West, z=Zenith).\n * Target: EQD = equatorial system, using equator of the specified date/time.\n *\n * @param {AstroTime} time\n *      The date and time at which the Earth's equator applies.\n *\n * @param {Observer} observer\n *      A location near the Earth's mean sea level that defines the observer's horizon.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts HOR to EQD at `time` and for `observer`.\n */",
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@@ -45742,14 +45714,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from horizontal (HOR) to J2000 equatorial (EQJ).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: HOR = horizontal system (x=North, y=West, z=Zenith).\n * Target: EQJ = equatorial system, using equator at the J2000 epoch.\n *\n * @param {AstroTime} time\n *      The date and time of the observation.\n *\n * @param {Observer} observer\n *      A location near the Earth's mean sea level that defines the observer's horizon.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts HOR to EQD at `time` and for `observer`.\n */",
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@@ -45883,14 +45855,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from equatorial J2000 (EQJ) to horizontal (HOR).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: EQJ = equatorial system, using the equator at the J2000 epoch.\n * Target: HOR = horizontal system.\n *\n * Use {@link HorizonFromVector} to convert the return value\n * to a traditional altitude/azimuth pair.\n *\n * @param time\n *      The date and time of the desired horizontal orientation.\n *\n * @param observer\n *      A location near the Earth's mean sea level that defines the observer's horizon.\n *\n * @return\n *      A rotation matrix that converts EQJ to HOR at `time` and for `observer`.\n *      The components of the horizontal vector are:\n *      x = north, y = west, z = zenith (straight up from the observer).\n *      These components are chosen so that the \"right-hand rule\" works for the vector\n *      and so that north represents the direction where azimuth = 0.\n */",
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@@ -45934,14 +45906,14 @@
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@@ -45983,14 +45955,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from equatorial of-date (EQD) to ecliptic J2000 (ECL).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: EQD = equatorial system, using equator of date.\n * Target: ECL = ecliptic system, using equator at J2000 epoch.\n *\n * @param {AstroTime} time\n *      The date and time of the source equator.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts EQD to ECL.\n */",
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             ],
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             "columnno": 0,
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             "columnno": 10,
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@@ -46114,14 +46086,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from ecliptic J2000 (ECL) to equatorial of-date (EQD).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: ECL = ecliptic system, using equator at J2000 epoch.\n * Target: EQD = equatorial system, using equator of date.\n *\n * @param {AstroTime} time\n *      The date and time of the desired equator.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts ECL to EQD.\n */",
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                 "type": "Identifier",
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@@ -46219,14 +46191,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from ecliptic J2000 (ECL) to horizontal (HOR).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: ECL = ecliptic system, using equator at J2000 epoch.\n * Target: HOR = horizontal system.\n *\n * Use {@link HorizonFromVector} to convert the return value\n * to a traditional altitude/azimuth pair.\n *\n * @param {AstroTime} time\n *      The date and time of the desired horizontal orientation.\n *\n * @param {Observer} observer\n *      A location near the Earth's mean sea level that defines the observer's horizon.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts ECL to HOR at `time` and for `observer`.\n *      The components of the horizontal vector are:\n *      x = north, y = west, z = zenith (straight up from the observer).\n *      These components are chosen so that the \"right-hand rule\" works for the vector\n *      and so that north represents the direction where azimuth = 0.\n */",
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@@ -46360,14 +46332,14 @@
         "comment": "/**\n * @brief Calculates a rotation matrix from horizontal (HOR) to ecliptic J2000 (ECL).\n *\n * This is one of the family of functions that returns a rotation matrix\n * for converting from one orientation to another.\n * Source: HOR = horizontal system.\n * Target: ECL = ecliptic system, using equator at J2000 epoch.\n *\n * @param {AstroTime} time\n *      The date and time of the horizontal observation.\n *\n * @param {Observer} observer\n *      The location of the horizontal observer.\n *\n * @returns {RotationMatrix}\n *      A rotation matrix that converts HOR to ECL.\n */",
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             ],
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             "columnno": 0,
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@@ -46426,14 +46398,14 @@
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@@ -46451,14 +46423,14 @@
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@@ -46523,14 +46495,14 @@
         "comment": "",
         "meta": {
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             "filename": "astronomy.js",
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@@ -46545,14 +46517,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 4,
             "code": {
-                "id": "astnode100022801",
+                "id": "astnode100022788",
                 "name": "Epoch2000"
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@@ -46567,14 +46539,14 @@
         "comment": "/**\n * @brief Reports the constellation that a given celestial point lies within.\n *\n * @property {string} symbol\n *      3-character mnemonic symbol for the constellation, e.g. \"Ori\".\n *\n * @property {string} name\n *      Full name of constellation, e.g. \"Orion\".\n *\n * @property {number} ra1875\n *      Right ascension expressed in B1875 coordinates.\n *\n * @property {number} dec1875\n *      Declination expressed in B1875 coordinates.\n */",
         "meta": {
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-                "id": "astnode100022803",
+                "id": "astnode100022790",
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                 "type": "ClassDeclaration",
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@@ -46641,14 +46613,14 @@
         "comment": "",
         "meta": {
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             "columnno": 4,
             "code": {
-                "id": "astnode100022806",
+                "id": "astnode100022793",
                 "name": "ConstellationInfo",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -46673,14 +46645,14 @@
         "comment": "/**\n * @brief Reports the constellation that a given celestial point lies within.\n *\n * @property {string} symbol\n *      3-character mnemonic symbol for the constellation, e.g. \"Ori\".\n *\n * @property {string} name\n *      Full name of constellation, e.g. \"Orion\".\n *\n * @property {number} ra1875\n *      Right ascension expressed in B1875 coordinates.\n *\n * @property {number} dec1875\n *      Declination expressed in B1875 coordinates.\n */",
         "meta": {
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+                "id": "astnode100022790",
                 "name": "ConstellationInfo",
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@@ -46746,14 +46718,14 @@
         "comment": "",
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             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100022815",
+                "id": "astnode100022802",
                 "name": "this.symbol",
                 "type": "Identifier",
                 "value": "symbol",
@@ -46771,14 +46743,14 @@
         "comment": "",
         "meta": {
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100022821",
+                "id": "astnode100022808",
                 "name": "this.name",
                 "type": "Identifier",
                 "value": "name",
@@ -46796,14 +46768,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100022827",
+                "id": "astnode100022814",
                 "name": "this.ra1875",
                 "type": "Identifier",
                 "value": "ra1875",
@@ -46821,14 +46793,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100022833",
+                "id": "astnode100022820",
                 "name": "this.dec1875",
                 "type": "Identifier",
                 "value": "dec1875",
@@ -46846,14 +46818,14 @@
         "comment": "",
         "meta": {
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             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100022839",
+                "id": "astnode100022826",
                 "name": "exports.ConstellationInfo",
                 "type": "Identifier",
                 "value": "ConstellationInfo",
@@ -46870,14 +46842,14 @@
         "comment": "/**\n * @brief Determines the constellation that contains the given point in the sky.\n *\n * Given J2000 equatorial (EQJ) coordinates of a point in the sky,\n * determines the constellation that contains that point.\n *\n * @param {number} ra\n *      The right ascension (RA) of a point in the sky, using the J2000 equatorial system.\n *\n * @param {number} dec\n *      The declination (DEC) of a point in the sky, using the J2000 equatorial system.\n *\n * @returns {ConstellationInfo}\n *      An object that contains the 3-letter abbreviation and full name\n *      of the constellation that contains the given (ra,dec), along with\n *      the converted B1875 (ra,dec) for that point.\n */",
         "meta": {
             "range": [
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+                244112
             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100022844",
+                "id": "astnode100022831",
                 "name": "Constellation",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -46949,14 +46921,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 4,
             "code": {
-                "id": "astnode100022871",
+                "id": "astnode100022858",
                 "name": "ra",
                 "type": "Literal",
                 "funcscope": "Constellation",
@@ -46975,14 +46947,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100022880",
+                "id": "astnode100022867",
                 "name": "ra",
                 "type": "Literal",
                 "funcscope": "Constellation",
@@ -47001,14 +46973,14 @@
         "comment": "",
         "meta": {
             "range": [
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+                243039
             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100022888",
+                "id": "astnode100022875",
                 "name": "ConstelRot",
                 "type": "CallExpression",
                 "funcscope": "Constellation",
@@ -47027,14 +46999,14 @@
         "comment": "",
         "meta": {
             "range": [
-                241010,
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             ],
             "filename": "astronomy.js",
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+            "lineno": 6074,
             "columnno": 8,
             "code": {
-                "id": "astnode100022897",
+                "id": "astnode100022884",
                 "name": "Epoch2000",
                 "type": "NewExpression",
                 "funcscope": "Constellation",
@@ -47053,14 +47025,14 @@
         "comment": "",
         "meta": {
             "range": [
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+                243192
             ],
             "filename": "astronomy.js",
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             "columnno": 10,
             "code": {
-                "id": "astnode100022903",
+                "id": "astnode100022890",
                 "name": "equ2000",
                 "type": "NewExpression",
                 "value": ""
@@ -47078,14 +47050,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 10,
             "code": {
-                "id": "astnode100022911",
+                "id": "astnode100022898",
                 "name": "vec2000",
                 "type": "CallExpression",
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@@ -47103,14 +47075,14 @@
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             "columnno": 0,
             "code": {
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@@ -47350,14 +47322,14 @@
         "comment": "/**\n * @brief Returns information about a lunar eclipse.\n *\n * Returned by {@link SearchLunarEclipse} or {@link NextLunarEclipse}\n * to report information about a lunar eclipse event.\n * When a lunar eclipse is found, it is classified as penumbral, partial, or total.\n * Penumbral eclipses are difficult to observe, because the moon is only slightly dimmed\n * by the Earth's penumbra; no part of the Moon touches the Earth's umbra.\n * Partial eclipses occur when part, but not all, of the Moon touches the Earth's umbra.\n * Total eclipses occur when the entire Moon passes into the Earth's umbra.\n *\n * The `kind` field thus holds one of the strings `\"penumbral\"`, `\"partial\"`,\n * or `\"total\"`, depending on the kind of lunar eclipse found.\n *\n * Field `peak` holds the date and time of the peak of the eclipse, when it is at its peak.\n *\n * Fields `sd_penum`, `sd_partial`, and `sd_total` hold the semi-duration of each phase\n * of the eclipse, which is half of the amount of time the eclipse spends in each\n * phase (expressed in minutes), or 0 if the eclipse never reaches that phase.\n * By converting from minutes to days, and subtracting/adding with `peak`, the caller\n * may determine the date and time of the beginning/end of each eclipse phase.\n *\n * @property {string} kind\n *      The type of lunar eclipse found.\n *\n * @property {AstroTime} peak\n *      The time of the eclipse at its peak.\n *\n * @property {number} sd_penum\n *      The semi-duration of the penumbral phase in minutes.\n *\n * @property {number} sd_partial\n *      The semi-duration of the penumbral phase in minutes, or 0.0 if none.\n *\n * @property {number} sd_total\n *      The semi-duration of the penumbral phase in minutes, or 0.0 if none.\n *\n */",
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             "columnno": 0,
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                 "paramnames": [
@@ -47434,14 +47406,14 @@
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             "columnno": 4,
             "code": {
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                 "name": "LunarEclipseInfo",
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@@ -47467,14 +47439,14 @@
         "comment": "/**\n * @brief Returns information about a lunar eclipse.\n *\n * Returned by {@link SearchLunarEclipse} or {@link NextLunarEclipse}\n * to report information about a lunar eclipse event.\n * When a lunar eclipse is found, it is classified as penumbral, partial, or total.\n * Penumbral eclipses are difficult to observe, because the moon is only slightly dimmed\n * by the Earth's penumbra; no part of the Moon touches the Earth's umbra.\n * Partial eclipses occur when part, but not all, of the Moon touches the Earth's umbra.\n * Total eclipses occur when the entire Moon passes into the Earth's umbra.\n *\n * The `kind` field thus holds one of the strings `\"penumbral\"`, `\"partial\"`,\n * or `\"total\"`, depending on the kind of lunar eclipse found.\n *\n * Field `peak` holds the date and time of the peak of the eclipse, when it is at its peak.\n *\n * Fields `sd_penum`, `sd_partial`, and `sd_total` hold the semi-duration of each phase\n * of the eclipse, which is half of the amount of time the eclipse spends in each\n * phase (expressed in minutes), or 0 if the eclipse never reaches that phase.\n * By converting from minutes to days, and subtracting/adding with `peak`, the caller\n * may determine the date and time of the beginning/end of each eclipse phase.\n *\n * @property {string} kind\n *      The type of lunar eclipse found.\n *\n * @property {AstroTime} peak\n *      The time of the eclipse at its peak.\n *\n * @property {number} sd_penum\n *      The semi-duration of the penumbral phase in minutes.\n *\n * @property {number} sd_partial\n *      The semi-duration of the penumbral phase in minutes, or 0.0 if none.\n *\n * @property {number} sd_total\n *      The semi-duration of the penumbral phase in minutes, or 0.0 if none.\n *\n */",
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             "columnno": 8,
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             "columnno": 8,
             "code": {
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                 "name": "this.sd_penum",
                 "type": "Identifier",
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         "comment": "",
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                 "name": "exports.LunarEclipseInfo",
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@@ -47699,14 +47671,14 @@
         "comment": "/**\n * @ignore\n *\n * @brief Represents the relative alignment of the Earth and another body, and their respective shadows.\n *\n * This is an internal data structure used to assist calculation of\n * lunar eclipses, solar eclipses, and transits of Mercury and Venus.\n *\n * Definitions:\n *\n * casting body = A body that casts a shadow of interest, possibly striking another body.\n *\n * receiving body = A body on which the shadow of another body might land.\n *\n * shadow axis = The line passing through the center of the Sun and the center of the casting body.\n *\n * shadow plane = The plane passing through the center of a receiving body,\n * and perpendicular to the shadow axis.\n *\n * @property {AstroTime} time\n *      The time associated with the shadow calculation.\n *\n * @property {number} u\n *      The distance [au] between the center of the casting body and the shadow plane.\n *\n * @property {number} r\n *      The distance [km] between center of receiving body and the shadow axis.\n *\n * @property {number} k\n *      The umbra radius [km] at the shadow plane.\n *\n * @property {number} p\n *      The penumbra radius [km] at the shadow plane.\n *\n * @property {Vector} target\n *      The location in space where we are interested in determining how close a shadow falls.\n *      For example, when calculating lunar eclipses, `target` would be the center of the Moon\n *      expressed in geocentric coordinates. Then we can evaluate how far the center of the Earth's\n *      shadow cone approaches the center of the Moon.\n *      The vector components are expressed in [au].\n *\n * @property {Vector} dir\n *      The direction in space that the shadow points away from the center of a shadow-casting body.\n *      This vector lies on the shadow axis and points away from the Sun.\n *      In other words: the direction light from the Sun would be traveling,\n *      except that the center of a body (Earth, Moon, Mercury, or Venus) is blocking it.\n *      The distance units do not matter, because the vector will be normalized.\n */",
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@@ -47804,14 +47776,14 @@
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@@ -47839,14 +47811,14 @@
         "comment": "/**\n * @ignore\n *\n * @brief Represents the relative alignment of the Earth and another body, and their respective shadows.\n *\n * This is an internal data structure used to assist calculation of\n * lunar eclipses, solar eclipses, and transits of Mercury and Venus.\n *\n * Definitions:\n *\n * casting body = A body that casts a shadow of interest, possibly striking another body.\n *\n * receiving body = A body on which the shadow of another body might land.\n *\n * shadow axis = The line passing through the center of the Sun and the center of the casting body.\n *\n * shadow plane = The plane passing through the center of a receiving body,\n * and perpendicular to the shadow axis.\n *\n * @property {AstroTime} time\n *      The time associated with the shadow calculation.\n *\n * @property {number} u\n *      The distance [au] between the center of the casting body and the shadow plane.\n *\n * @property {number} r\n *      The distance [km] between center of receiving body and the shadow axis.\n *\n * @property {number} k\n *      The umbra radius [km] at the shadow plane.\n *\n * @property {number} p\n *      The penumbra radius [km] at the shadow plane.\n *\n * @property {Vector} target\n *      The location in space where we are interested in determining how close a shadow falls.\n *      For example, when calculating lunar eclipses, `target` would be the center of the Moon\n *      expressed in geocentric coordinates. Then we can evaluate how far the center of the Earth's\n *      shadow cone approaches the center of the Moon.\n *      The vector components are expressed in [au].\n *\n * @property {Vector} dir\n *      The direction in space that the shadow points away from the center of a shadow-casting body.\n *      This vector lies on the shadow axis and points away from the Sun.\n *      In other words: the direction light from the Sun would be traveling,\n *      except that the center of a body (Earth, Moon, Mercury, or Venus) is blocking it.\n *      The distance units do not matter, because the vector will be normalized.\n */",
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@@ -47968,14 +47940,14 @@
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@@ -47993,14 +47965,14 @@
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@@ -48093,14 +48065,14 @@
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@@ -48118,14 +48090,14 @@
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@@ -48156,14 +48128,14 @@
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@@ -48181,14 +48153,14 @@
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@@ -48206,14 +48178,14 @@
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@@ -48231,14 +48203,14 @@
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@@ -48256,14 +48228,14 @@
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         "comment": "/**\n    @brief Reports the time and geographic location of the peak of a solar eclipse.\n\n    Returned by {@link SearchGlobalSolarEclipse} or {@link NextGlobalSolarEclipse}\n    to report information about a solar eclipse event.\n\n    Field `peak` holds the date and time of the peak of the eclipse, defined as\n    the instant when the axis of the Moon's shadow cone passes closest to the Earth's center.\n\n    The eclipse is classified as partial, annular, or total, depending on the\n    maximum amount of the Sun's disc obscured, as seen at the peak location\n    on the surface of the Earth.\n\n    The `kind` field thus holds one of the strings `\"partial\"`, `\"annular\"`, or `\"total\"`.\n    A total eclipse is when the peak observer sees the Sun completely blocked by the Moon.\n    An annular eclipse is like a total eclipse, but the Moon is too far from the Earth's surface\n    to completely block the Sun; instead, the Sun takes on a ring-shaped appearance.\n    A partial eclipse is when the Moon blocks part of the Sun's disc, but nobody on the Earth\n    observes either a total or annular eclipse.\n\n    If `kind` is `\"total\"` or `\"annular\"`, the `latitude` and `longitude`\n    fields give the geographic coordinates of the center of the Moon's shadow projected\n    onto the daytime side of the Earth at the instant of the eclipse's peak.\n    If `kind` has any other value, `latitude` and `longitude` are undefined and should\n    not be used.\n\n    @property {string} kind\n        One of the following string values: `\"partial\"`, `\"annular\"`, `\"total\"`.\n\n    @property {AstroTime} peak\n        The date and time of the peak of the eclipse, defined as the instant\n        when the axis of the Moon's shadow cone passes closest to the Earth's center.\n\n    @property {number} distance\n        The distance in kilometers between the axis of the Moon's shadow cone\n        and the center of the Earth at the time indicated by `peak`.\n\n    @property {number | undefined} latitude\n        If `kind` holds `\"total\"`, the geographic latitude in degrees\n        where the center of the Moon's shadow falls on the Earth at the\n        time indicated by `peak`; otherwise, `latitude` holds `undefined`.\n\n    @property {number | undefined} longitude\n        If `kind` holds `\"total\"`, the geographic longitude in degrees\n        where the center of the Moon's shadow falls on the Earth at the\n        time indicated by `peak`; otherwise, `longitude` holds `undefined`.\n*/",
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@@ -51811,14 +51783,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                261925
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
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                 "type": "MemberExpression",
                 "funcscope": "GeoidIntersect",
@@ -51837,14 +51809,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                261957
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
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                 "name": "o.z",
                 "type": "MemberExpression",
                 "funcscope": "GeoidIntersect",
@@ -51863,14 +51835,14 @@
         "comment": "",
         "meta": {
             "range": [
-                262066,
-                262136
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             ],
             "filename": "astronomy.js",
-            "lineno": 6492,
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             "columnno": 14,
             "code": {
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                 "value": ""
@@ -51888,14 +51860,14 @@
         "comment": "",
         "meta": {
             "range": [
-                262473,
-                262511
+                264512,
+                264550
             ],
             "filename": "astronomy.js",
-            "lineno": 6498,
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             "columnno": 8,
             "code": {
-                "id": "astnode100024629",
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                 "name": "kind",
                 "type": "CallExpression",
                 "funcscope": "GeoidIntersect",
@@ -51914,14 +51886,14 @@
         "comment": "/**\n * @brief Searches for the next lunar eclipse in a series.\n *\n * After using {@link SearchLunarEclipse} to find the first lunar eclipse\n * in a series, you can call this function to find the next consecutive lunar eclipse.\n * Pass in the `center` value from the {@link LunarEclipseInfo} returned by the\n * previous call to `SearchLunarEclipse` or `NextLunarEclipse`\n * to find the next lunar eclipse.\n *\n * @param {AstroTime} prevEclipseTime\n *      A date and time near a full moon. Lunar eclipse search will start at the next full moon.\n *\n * @returns {LunarEclipseInfo}\n */",
         "meta": {
             "range": [
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-                263323
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+                265362
             ],
             "filename": "astronomy.js",
-            "lineno": 6516,
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             "columnno": 0,
             "code": {
-                "id": "astnode100024644",
+                "id": "astnode100024631",
                 "name": "NextLunarEclipse",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -51969,14 +51941,14 @@
         "comment": "",
         "meta": {
             "range": [
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-                263278
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+                265317
             ],
             "filename": "astronomy.js",
-            "lineno": 6517,
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             "columnno": 10,
             "code": {
-                "id": "astnode100024649",
+                "id": "astnode100024636",
                 "name": "startTime",
                 "type": "CallExpression",
                 "value": ""
@@ -51994,14 +51966,14 @@
         "comment": "",
         "meta": {
             "range": [
-                263324,
-                263367
+                265363,
+                265406
             ],
             "filename": "astronomy.js",
-            "lineno": 6520,
+            "lineno": 6552,
             "columnno": 0,
             "code": {
-                "id": "astnode100024661",
+                "id": "astnode100024648",
                 "name": "exports.NextLunarEclipse",
                 "type": "Identifier",
                 "value": "NextLunarEclipse",
@@ -52018,14 +51990,14 @@
         "comment": "/**\n * @brief Searches for a solar eclipse visible anywhere on the Earth's surface.\n *\n * This function finds the first solar eclipse that occurs after `startTime`.\n * A solar eclipse may be partial, annular, or total.\n * See {@link GlobalSolarEclipseInfo} for more information.\n * To find a series of solar eclipses, call this function once,\n * then keep calling {@link NextGlobalSolarEclipse} as many times as desired,\n * passing in the `peak` value returned from the previous call.\n *\n * @param {AstroTime} startTime\n *      The date and time for starting the search for a solar eclipse.\n *\n * @returns {GlobalSolarEclipseInfo}\n */",
         "meta": {
             "range": [
-                264004,
-                265621
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+                267660
             ],
             "filename": "astronomy.js",
-            "lineno": 6536,
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             "columnno": 0,
             "code": {
-                "id": "astnode100024666",
+                "id": "astnode100024653",
                 "name": "SearchGlobalSolarEclipse",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -52078,14 +52050,14 @@
         "comment": "",
         "meta": {
             "range": [
-                264061,
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             ],
             "filename": "astronomy.js",
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             "columnno": 10,
             "code": {
-                "id": "astnode100024671",
+                "id": "astnode100024658",
                 "name": "PruneLatitude",
                 "type": "Literal",
                 "value": 1.8
@@ -52103,14 +52075,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
-            "lineno": 6539,
+            "lineno": 6571,
             "columnno": 8,
             "code": {
-                "id": "astnode100024675",
+                "id": "astnode100024662",
                 "name": "nmtime",
                 "type": "Identifier",
                 "value": "startTime"
@@ -52128,14 +52100,14 @@
         "comment": "",
         "meta": {
             "range": [
-                264284,
-                264291
+                266323,
+                266330
             ],
             "filename": "astronomy.js",
-            "lineno": 6540,
+            "lineno": 6572,
             "columnno": 8,
             "code": {
-                "id": "astnode100024679",
+                "id": "astnode100024666",
                 "name": "nmcount"
             }
         },
@@ -52151,14 +52123,14 @@
         "comment": "",
         "meta": {
             "range": [
-                264302,
-                264313
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             ],
             "filename": "astronomy.js",
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             "columnno": 9,
             "code": {
-                "id": "astnode100024682",
+                "id": "astnode100024669",
                 "name": "nmcount",
                 "type": "Literal",
                 "funcscope": "SearchGlobalSolarEclipse",
@@ -52177,14 +52149,14 @@
         "comment": "",
         "meta": {
             "range": [
-                264426,
-                264470
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             ],
             "filename": "astronomy.js",
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             "columnno": 14,
             "code": {
-                "id": "astnode100024692",
+                "id": "astnode100024679",
                 "name": "newmoon",
                 "type": "CallExpression",
                 "value": ""
@@ -52202,14 +52174,14 @@
         "comment": "",
         "meta": {
             "range": [
-                264653,
-                264701
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+                266740
             ],
             "filename": "astronomy.js",
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             "columnno": 14,
             "code": {
-                "id": "astnode100024705",
+                "id": "astnode100024692",
                 "name": "eclip_lat",
                 "type": "CallExpression",
                 "value": ""
@@ -52227,14 +52199,14 @@
         "comment": "",
         "meta": {
             "range": [
-                264941,
-                264973
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+                267012
             ],
             "filename": "astronomy.js",
-            "lineno": 6551,
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             "columnno": 18,
             "code": {
-                "id": "astnode100024720",
+                "id": "astnode100024707",
                 "name": "shadow",
                 "type": "CallExpression",
                 "value": ""
@@ -52252,14 +52224,14 @@
         "comment": "",
         "meta": {
             "range": [
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             ],
             "filename": "astronomy.js",
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             "columnno": 8,
             "code": {
-                "id": "astnode100024741",
+                "id": "astnode100024728",
                 "name": "nmtime",
                 "type": "CallExpression",
                 "funcscope": "SearchGlobalSolarEclipse",
@@ -52278,14 +52250,14 @@
         "comment": "",
         "meta": {
             "range": [
-                265622,
-                265681
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+                267720
             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100024751",
+                "id": "astnode100024738",
                 "name": "exports.SearchGlobalSolarEclipse",
                 "type": "Identifier",
                 "value": "SearchGlobalSolarEclipse",
@@ -52302,14 +52274,14 @@
         "comment": "/**\n * @brief Searches for the next global solar eclipse in a series.\n *\n * After using {@link SearchGlobalSolarEclipse} to find the first solar eclipse\n * in a series, you can call this function to find the next consecutive solar eclipse.\n * Pass in the `peak` value from the {@link GlobalSolarEclipseInfo} returned by the\n * previous call to `SearchGlobalSolarEclipse` or `NextGlobalSolarEclipse`\n * to find the next solar eclipse.\n *\n * @param {AstroTime} prevEclipseTime\n *      A date and time near a new moon. Solar eclipse search will start at the next new moon.\n *\n * @returns {GlobalSolarEclipseInfo}\n */",
         "meta": {
             "range": [
-                266297,
-                266450
+                268336,
+                268489
             ],
             "filename": "astronomy.js",
-            "lineno": 6580,
+            "lineno": 6612,
             "columnno": 0,
             "code": {
-                "id": "astnode100024756",
+                "id": "astnode100024743",
                 "name": "NextGlobalSolarEclipse",
                 "type": "FunctionDeclaration",
                 "paramnames": [
@@ -52357,14 +52329,14 @@
         "comment": "",
         "meta": {
             "range": [
-                266358,
-                266399
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+                268438
             ],
             "filename": "astronomy.js",
-            "lineno": 6581,
+            "lineno": 6613,
             "columnno": 10,
             "code": {
-                "id": "astnode100024761",
+                "id": "astnode100024748",
                 "name": "startTime",
                 "type": "CallExpression",
                 "value": ""
@@ -52382,14 +52354,14 @@
         "comment": "",
         "meta": {
             "range": [
-                266451,
-                266506
+                268490,
+                268545
             ],
             "filename": "astronomy.js",
-            "lineno": 6584,
+            "lineno": 6616,
             "columnno": 0,
             "code": {
-                "id": "astnode100024773",
+                "id": "astnode100024760",
                 "name": "exports.NextGlobalSolarEclipse",
                 "type": "Identifier",
                 "value": "NextGlobalSolarEclipse",
@@ -52406,14 +52378,14 @@
         "comment": "/**\n * @brief Holds a time and the observed altitude of the Sun at that time.\n *\n * When reporting a solar eclipse observed at a specific location on the Earth\n * (a \"local\" solar eclipse), a series of events occur. In addition\n * to the time of each event, it is important to know the altitude of the Sun,\n * because each event may be invisible to the observer if the Sun is below\n * the horizon (i.e. it at night).\n *\n * If `altitude` is negative, the event is theoretical only; it would be\n * visible if the Earth were transparent, but the observer cannot actually see it.\n * If `altitude` is positive but less than a few degrees, visibility will be impaired by\n * atmospheric interference (sunrise or sunset conditions).\n *\n * @property {AstroTime} time\n *      The date and time of the event.\n *\n * @property {number} altitude\n *      The angular altitude of the center of the Sun above/below the horizon, at `time`,\n *      corrected for atmospheric refraction and expressed in degrees.\n */",
         "meta": {
             "range": [
-                267505,
-                267627
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+                269666
             ],
             "filename": "astronomy.js",
-            "lineno": 6606,
+            "lineno": 6638,
             "columnno": 0,
             "code": {
-                "id": "astnode100024778",
+                "id": "astnode100024765",
                 "name": "EclipseEvent",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -52460,14 +52432,14 @@
         "comment": "",
         "meta": {
             "range": [
-                267530,
-                267625
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+                269664
             ],
             "filename": "astronomy.js",
-            "lineno": 6607,
+            "lineno": 6639,
             "columnno": 4,
             "code": {
-                "id": "astnode100024781",
+                "id": "astnode100024768",
                 "name": "EclipseEvent",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -52490,14 +52462,14 @@
         "comment": "/**\n * @brief Holds a time and the observed altitude of the Sun at that time.\n *\n * When reporting a solar eclipse observed at a specific location on the Earth\n * (a \"local\" solar eclipse), a series of events occur. In addition\n * to the time of each event, it is important to know the altitude of the Sun,\n * because each event may be invisible to the observer if the Sun is below\n * the horizon (i.e. it at night).\n *\n * If `altitude` is negative, the event is theoretical only; it would be\n * visible if the Earth were transparent, but the observer cannot actually see it.\n * If `altitude` is positive but less than a few degrees, visibility will be impaired by\n * atmospheric interference (sunrise or sunset conditions).\n *\n * @property {AstroTime} time\n *      The date and time of the event.\n *\n * @property {number} altitude\n *      The angular altitude of the center of the Sun above/below the horizon, at `time`,\n *      corrected for atmospheric refraction and expressed in degrees.\n */",
         "meta": {
             "range": [
-                267505,
-                267627
+                269544,
+                269666
             ],
             "filename": "astronomy.js",
-            "lineno": 6606,
+            "lineno": 6638,
             "columnno": 0,
             "code": {
-                "id": "astnode100024778",
+                "id": "astnode100024765",
                 "name": "EclipseEvent",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -52543,14 +52515,14 @@
         "comment": "",
         "meta": {
             "range": [
-                267568,
-                267584
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+                269623
             ],
             "filename": "astronomy.js",
-            "lineno": 6608,
+            "lineno": 6640,
             "columnno": 8,
             "code": {
-                "id": "astnode100024788",
+                "id": "astnode100024775",
                 "name": "this.time",
                 "type": "Identifier",
                 "value": "time",
@@ -52568,14 +52540,14 @@
         "comment": "",
         "meta": {
             "range": [
-                267594,
-                267618
+                269633,
+                269657
             ],
             "filename": "astronomy.js",
-            "lineno": 6609,
+            "lineno": 6641,
             "columnno": 8,
             "code": {
-                "id": "astnode100024794",
+                "id": "astnode100024781",
                 "name": "this.altitude",
                 "type": "Identifier",
                 "value": "altitude",
@@ -52593,14 +52565,14 @@
         "comment": "",
         "meta": {
             "range": [
-                267628,
-                267663
+                269667,
+                269702
             ],
             "filename": "astronomy.js",
-            "lineno": 6612,
+            "lineno": 6644,
             "columnno": 0,
             "code": {
-                "id": "astnode100024800",
+                "id": "astnode100024787",
                 "name": "exports.EclipseEvent",
                 "type": "Identifier",
                 "value": "EclipseEvent",
@@ -52617,14 +52589,14 @@
         "comment": "/**\n * @brief Information about a solar eclipse as seen by an observer at a given time and geographic location.\n *\n * Returned by {@link SearchLocalSolarEclipse} or {@link NextLocalSolarEclipse}\n * to report information about a solar eclipse as seen at a given geographic location.\n *\n * When a solar eclipse is found, it is classified by setting `kind`\n * to `\"partial\"`, `\"annular\"`, or `\"total\"`.\n * A partial solar eclipse is when the Moon does not line up directly enough with the Sun\n * to completely block the Sun's light from reaching the observer.\n * An annular eclipse occurs when the Moon's disc is completely visible against the Sun\n * but the Moon is too far away to completely block the Sun's light; this leaves the\n * Sun with a ring-like appearance.\n * A total eclipse occurs when the Moon is close enough to the Earth and aligned with the\n * Sun just right to completely block all sunlight from reaching the observer.\n *\n * There are 5 \"event\" fields, each of which contains a time and a solar altitude.\n * Field `peak` holds the date and time of the center of the eclipse, when it is at its peak.\n * The fields `partial_begin` and `partial_end` are always set, and indicate when\n * the eclipse begins/ends. If the eclipse reaches totality or becomes annular,\n * `total_begin` and `total_end` indicate when the total/annular phase begins/ends.\n * When an event field is valid, the caller must also check its `altitude` field to\n * see whether the Sun is above the horizon at the time indicated by the `time` field.\n * See {@link EclipseEvent} for more information.\n *\n * @property {string} kind\n *      The type of solar eclipse found: `\"partial\"`, `\"annular\"`, or `\"total\"`.\n *\n * @property {EclipseEvent} partial_begin\n *      The time and Sun altitude at the beginning of the eclipse.\n *\n * @property {EclipseEvent | undefined} total_begin\n *      If this is an annular or a total eclipse, the time and Sun altitude when annular/total phase begins; otherwise undefined.\n *\n * @property {EclipseEvent} peak\n *      The time and Sun altitude when the eclipse reaches its peak.\n *\n * @property {EclipseEvent | undefined} total_end\n *      If this is an annular or a total eclipse, the time and Sun altitude when annular/total phase ends; otherwise undefined.\n *\n * @property {EclipseEvent} partial_end\n *      The time and Sun altitude at the end of the eclipse.\n */",
         "meta": {
             "range": [
-                270049,
-                270380
+                272088,
+                272419
             ],
             "filename": "astronomy.js",
-            "lineno": 6656,
+            "lineno": 6688,
             "columnno": 0,
             "code": {
-                "id": "astnode100024805",
+                "id": "astnode100024792",
                 "name": "LocalSolarEclipseInfo",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -52713,14 +52685,14 @@
         "comment": "",
         "meta": {
             "range": [
-                270083,
-                270378
+                272122,
+                272417
             ],
             "filename": "astronomy.js",
-            "lineno": 6657,
+            "lineno": 6689,
             "columnno": 4,
             "code": {
-                "id": "astnode100024808",
+                "id": "astnode100024795",
                 "name": "LocalSolarEclipseInfo",
                 "type": "MethodDefinition",
                 "paramnames": [
@@ -52747,14 +52719,14 @@
         "comment": "/**\n * @brief Information about a solar eclipse as seen by an observer at a given time and geographic location.\n *\n * Returned by {@link SearchLocalSolarEclipse} or {@link NextLocalSolarEclipse}\n * to report information about a solar eclipse as seen at a given geographic location.\n *\n * When a solar eclipse is found, it is classified by setting `kind`\n * to `\"partial\"`, `\"annular\"`, or `\"total\"`.\n * A partial solar eclipse is when the Moon does not line up directly enough with the Sun\n * to completely block the Sun's light from reaching the observer.\n * An annular eclipse occurs when the Moon's disc is completely visible against the Sun\n * but the Moon is too far away to completely block the Sun's light; this leaves the\n * Sun with a ring-like appearance.\n * A total eclipse occurs when the Moon is close enough to the Earth and aligned with the\n * Sun just right to completely block all sunlight from reaching the observer.\n *\n * There are 5 \"event\" fields, each of which contains a time and a solar altitude.\n * Field `peak` holds the date and time of the center of the eclipse, when it is at its peak.\n * The fields `partial_begin` and `partial_end` are always set, and indicate when\n * the eclipse begins/ends. If the eclipse reaches totality or becomes annular,\n * `total_begin` and `total_end` indicate when the total/annular phase begins/ends.\n * When an event field is valid, the caller must also check its `altitude` field to\n * see whether the Sun is above the horizon at the time indicated by the `time` field.\n * See {@link EclipseEvent} for more information.\n *\n * @property {string} kind\n *      The type of solar eclipse found: `\"partial\"`, `\"annular\"`, or `\"total\"`.\n *\n * @property {EclipseEvent} partial_begin\n *      The time and Sun altitude at the beginning of the eclipse.\n *\n * @property {EclipseEvent | undefined} total_begin\n *      If this is an annular or a total eclipse, the time and Sun altitude when annular/total phase begins; otherwise undefined.\n *\n * @property {EclipseEvent} peak\n *      The time and Sun altitude when the eclipse reaches its peak.\n *\n * @property {EclipseEvent | undefined} total_end\n *      If this is an annular or a total eclipse, the time and Sun altitude when annular/total phase ends; otherwise undefined.\n *\n * @property {EclipseEvent} partial_end\n *      The time and Sun altitude at the end of the eclipse.\n */",
         "meta": {
             "range": [
-                270049,
-                270380
+                272088,
+                272419
             ],
             "filename": "astronomy.js",
-            "lineno": 6656,
+            "lineno": 6688,
             "columnno": 0,
             "code": {
-                "id": "astnode100024805",
+                "id": "astnode100024792",
                 "name": "LocalSolarEclipseInfo",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -52842,14 +52814,14 @@
         "comment": "",
         "meta": {
             "range": [
-                270169,
-                270185
+                272208,
+                272224
             ],
             "filename": "astronomy.js",
-            "lineno": 6658,
+            "lineno": 6690,
             "columnno": 8,
             "code": {
-                "id": "astnode100024819",
+                "id": "astnode100024806",
                 "name": "this.kind",
                 "type": "Identifier",
                 "value": "kind",
@@ -52867,14 +52839,14 @@
         "comment": "",
         "meta": {
             "range": [
-                270195,
-                270229
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+                272268
             ],
             "filename": "astronomy.js",
-            "lineno": 6659,
+            "lineno": 6691,
             "columnno": 8,
             "code": {
-                "id": "astnode100024825",
+                "id": "astnode100024812",
                 "name": "this.partial_begin",
                 "type": "Identifier",
                 "value": "partial_begin",
@@ -52892,14 +52864,14 @@
         "comment": "",
         "meta": {
             "range": [
-                270239,
-                270269
+                272278,
+                272308
             ],
             "filename": "astronomy.js",
-            "lineno": 6660,
+            "lineno": 6692,
             "columnno": 8,
             "code": {
-                "id": "astnode100024831",
+                "id": "astnode100024818",
                 "name": "this.total_begin",
                 "type": "Identifier",
                 "value": "total_begin",
@@ -52917,14 +52889,14 @@
         "comment": "",
         "meta": {
             "range": [
-                270279,
-                270295
+                272318,
+                272334
             ],
             "filename": "astronomy.js",
-            "lineno": 6661,
+            "lineno": 6693,
             "columnno": 8,
             "code": {
-                "id": "astnode100024837",
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         "comment": "/**\n * @brief Information about a transit of Mercury or Venus, as seen from the Earth.\n *\n * Returned by {@link SearchTransit} or {@link NextTransit} to report\n * information about a transit of Mercury or Venus.\n * A transit is when Mercury or Venus passes between the Sun and Earth so that\n * the other planet is seen in silhouette against the Sun.\n *\n * The calculations are performed from the point of view of a geocentric observer.\n *\n * @property {AstroTime} start\n *      The date and time at the beginning of the transit.\n *      This is the moment the planet first becomes visible against the Sun in its background.\n *\n * @property {AstroTime} peak\n *      When the planet is most aligned with the Sun, as seen from the Earth.\n *\n * @property {AstroTime} finish\n *      The date and time at the end of the transit.\n *      This is the moment the planet is last seen against the Sun in its background.\n *\n * @property {number} separation\n *      The minimum angular separation, in arcminutes, between the centers of the Sun and the planet.\n *      This angle pertains to the time stored in `peak`.\n */",
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             "columnno": 0,
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                 "paramnames": [
@@ -54215,14 +54187,14 @@
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             "columnno": 4,
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                 "name": "TransitInfo",
                 "type": "MethodDefinition",
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@@ -54247,14 +54219,14 @@
         "comment": "/**\n * @brief Information about a transit of Mercury or Venus, as seen from the Earth.\n *\n * Returned by {@link SearchTransit} or {@link NextTransit} to report\n * information about a transit of Mercury or Venus.\n * A transit is when Mercury or Venus passes between the Sun and Earth so that\n * the other planet is seen in silhouette against the Sun.\n *\n * The calculations are performed from the point of view of a geocentric observer.\n *\n * @property {AstroTime} start\n *      The date and time at the beginning of the transit.\n *      This is the moment the planet first becomes visible against the Sun in its background.\n *\n * @property {AstroTime} peak\n *      When the planet is most aligned with the Sun, as seen from the Earth.\n *\n * @property {AstroTime} finish\n *      The date and time at the end of the transit.\n *      This is the moment the planet is last seen against the Sun in its background.\n *\n * @property {number} separation\n *      The minimum angular separation, in arcminutes, between the centers of the Sun and the planet.\n *      This angle pertains to the time stored in `peak`.\n */",
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             "columnno": 0,
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                 "name": "TransitInfo",
                 "type": "ClassDeclaration",
                 "paramnames": [
@@ -54320,14 +54292,14 @@
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             "columnno": 8,
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                 "name": "this.peak",
                 "type": "Identifier",
                 "value": "peak",
@@ -54370,14 +54342,14 @@
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             "columnno": 8,
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                 "name": "this.finish",
                 "type": "Identifier",
                 "value": "finish",
@@ -54395,14 +54367,14 @@
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         "meta": {
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             "columnno": 8,
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                 "type": "Identifier",
                 "value": "separation",
@@ -54420,14 +54392,14 @@
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             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
-                "id": "astnode100025305",
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                 "name": "exports.TransitInfo",
                 "type": "Identifier",
                 "value": "TransitInfo",
@@ -54444,14 +54416,14 @@
         "comment": "",
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             ],
             "filename": "astronomy.js",
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             "columnno": 0,
             "code": {
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                 "name": "PlanetShadowBoundary",
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@@ -54476,14 +54448,14 @@
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             "columnno": 0,
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                 "name": "PlanetTransitBoundary",
                 "type": "FunctionDeclaration",
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@@ -54535,14 +54507,14 @@
         "comment": "",
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             "filename": "astronomy.js",
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             "columnno": 10,
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                 "name": "tx",
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@@ -54560,14 +54532,14 @@
         "comment": "/**\n * @brief Searches for the first transit of Mercury or Venus after a given date.\n *\n * Finds the first transit of Mercury or Venus after a specified date.\n * A transit is when an inferior planet passes between the Sun and the Earth\n * so that the silhouette of the planet is visible against the Sun in the background.\n * To continue the search, pass the `finish` time in the returned structure to\n * {@link NextTransit}.\n *\n * @param {string} body\n *      The planet whose transit is to be found. Must be `\"Mercury\"` or `\"Venus\"`.\n *\n * @param {AstroTime} startTime\n *      The date and time for starting the search for a transit.\n *\n * @returns {TransitInfo}\n */",
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             "columnno": 0,
             "code": {
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                 "name": "SearchTransit",
                 "type": "FunctionDeclaration",
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@@ -54636,14 +54608,14 @@
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                 "name": "threshold_angle",
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             "code": {
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@@ -54735,14 +54707,14 @@
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                 "name": "search_time",
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@@ -54786,14 +54758,14 @@
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@@ -54936,14 +54908,14 @@
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                 "type": "Identifier",
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@@ -55036,14 +55008,14 @@
         "comment": "/**\n * @brief Searches for the next transit of Mercury or Venus in a series.\n *\n * After calling {@link SearchTransit} to find a transit of Mercury or Venus,\n * this function finds the next transit after that.\n * Keep calling this function as many times as you want to keep finding more transits.\n *\n * @param {string} body\n *      The planet whose transit is to be found. Must be `\"Mercury\"` or `\"Venus\"`.\n *\n * @param {AstroTime} prevTransitTime\n *      A date and time near the previous transit.\n *\n * @returns {TransitInfo}\n */",
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             "columnno": 0,
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@@ -55101,14 +55073,14 @@
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@@ -55126,14 +55098,14 @@
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             "columnno": 0,
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                 "name": "exports.NextTransit",
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