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Fixed #126 - Added support for lunar libration.
There is now a Libration function in all 4 supported languages. The returned structure contains libration angles in ecliptic latitude and ecliptic longitude, along with the Moon's ecliptic position and distance. Also included is the Moon's apparent angular diameter.
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Don Cross
@@ -461,6 +461,25 @@ and the velocities in AU/day.
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---
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<a name="LibrationInfo"></a>
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### class LibrationInfo
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**Lunar libration angles, returned by [`Libration`](#Libration).**
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Contains lunar libration angles and lunar position information
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for a given moment in time. See [`Libration`](#Libration) for more details.
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| Type | Attribute | Description |
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| --- | --- | --- |
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| `float` | `elat` | Sub-Earth libration ecliptic latitude angle, in degrees. |
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| `float` | `elon` | Sub-Earth libration ecliptic longitude angle, in degrees. |
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| `float` | `mlat` | Moon's geocentric ecliptic latitude. |
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| `float` | `mlon` | Moon's geocentric ecliptic longitude. |
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| `float` | `dist_km` | Distance between the centers of the Earth and Moon in kilometers. |
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| `float` | `diam_deg` | The apparent angular diameter of the Moon as seen from the center of the Earth. |
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---
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<a name="LocalSolarEclipseInfo"></a>
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### class LocalSolarEclipseInfo
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@@ -1485,6 +1504,31 @@ The positions and velocities of Jupiter's 4 largest moons.
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---
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<a name="Libration"></a>
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### Libration(time)
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**Calculates the Moon's libration angles at a given moment in time.**
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Libration is an observed back-and-forth wobble of the portion of the
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Moon visible from the Earth. It is caused by the imperfect tidal locking
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of the Moon's fixed rotation rate, compared to its variable angular speed
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of orbit around the Earth.
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This function calculates a pair of perpendicular libration angles,
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one representing rotation of the Moon in eclitpic longitude `elon`, the other
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in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
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This function also returns the geocentric position of the Moon
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expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
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distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
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and the apparent angular diameter of the Moon `diam_deg`.
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| Type | Parameter | Description |
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| --- | --- | --- |
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| [`Time`](#Time) | `time` | The date and time for which to calculate the Moon's libration angles. |
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### Returns: [`LibrationInfo`](#LibrationInfo)
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---
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<a name="MoonPhase"></a>
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### MoonPhase(time)
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@@ -8537,3 +8537,157 @@ def NextTransit(body, prevTransitTime):
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"""
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startTime = prevTransitTime.AddDays(100.0)
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return SearchTransit(body, startTime)
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class LibrationInfo:
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"""Lunar libration angles, returned by #Libration.
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Contains lunar libration angles and lunar position information
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for a given moment in time. See #Libration for more details.
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Attributes
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----------
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elat : float
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Sub-Earth libration ecliptic latitude angle, in degrees.
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elon : float
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Sub-Earth libration ecliptic longitude angle, in degrees.
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mlat : float
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Moon's geocentric ecliptic latitude.
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mlon : float
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Moon's geocentric ecliptic longitude.
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dist_km : float
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Distance between the centers of the Earth and Moon in kilometers.
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diam_deg : float
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The apparent angular diameter of the Moon as seen from the center of the Earth.
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"""
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def __init__(self, elat, elon, mlat, mlon, dist_km, diam_deg):
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self.elat = elat
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self.elon = elon
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self.mlat = mlat
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self.mlon = mlon
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self.dist_km = dist_km
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self.diam_deg = diam_deg
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def Libration(time):
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"""Calculates the Moon's libration angles at a given moment in time.
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Libration is an observed back-and-forth wobble of the portion of the
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Moon visible from the Earth. It is caused by the imperfect tidal locking
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of the Moon's fixed rotation rate, compared to its variable angular speed
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of orbit around the Earth.
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This function calculates a pair of perpendicular libration angles,
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one representing rotation of the Moon in eclitpic longitude `elon`, the other
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in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
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This function also returns the geocentric position of the Moon
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expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
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distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
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and the apparent angular diameter of the Moon `diam_deg`.
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Parameters
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----------
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time : Time
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The date and time for which to calculate the Moon's libration angles.
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Returns
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-------
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LibrationInfo
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"""
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t = time.tt / 36525.0
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t2 = t * t
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t3 = t2 * t
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t4 = t2 * t2
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moon = _CalcMoon(time)
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mlon = moon.geo_eclip_lon
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mlat = moon.geo_eclip_lat
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dist_km = moon.distance_au * KM_PER_AU
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diam_deg = 2.0 * math.degrees(math.atan(_MOON_MEAN_RADIUS_KM / math.sqrt(dist_km*dist_km - _MOON_MEAN_RADIUS_KM*_MOON_MEAN_RADIUS_KM)))
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# Inclination angle
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I = math.radians(1.54242)
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# Moon's argument of latitude in radians.
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f = math.radians(_NormalizeLongitude(93.2720950 + 483202.0175233*t - 0.0036539*t2 - t3/3526000 + t4/863310000))
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# Moon's ascending node's mean longitude in radians.
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omega = math.radians(_NormalizeLongitude(125.0445479 - 1934.1362891*t + 0.0020754*t2 + t3/467441 - t4/60616000))
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# Sun's mean anomaly.
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m = math.radians(_NormalizeLongitude(357.5291092 + 35999.0502909*t - 0.0001536*t2 + t3/24490000))
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# Moon's mean anomaly.
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mdash = math.radians(_NormalizeLongitude(134.9633964 + 477198.8675055*t + 0.0087414*t2 + t3/69699 - t4/14712000))
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# Moon's mean elongation.
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d = math.radians(_NormalizeLongitude(297.8501921 + 445267.1114034*t - 0.0018819*t2 + t3/545868 - t4/113065000))
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# Eccentricity of the Earth's orbit.
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e = 1.0 - 0.002516*t - 0.0000074*t2
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# Optical librations
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w = mlon - omega
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a = math.atan2(math.sin(w)*math.cos(mlat)*math.cos(I) - math.sin(mlat)*math.sin(I), math.cos(w)*math.cos(mlat))
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ldash = _LongitudeOffset(math.degrees(a - f))
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bdash = math.asin(-math.sin(w)*math.cos(mlat)*math.sin(I) - math.sin(mlat)*math.cos(I))
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# Physical librations
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k1 = math.radians(119.75 + 131.849*t)
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k2 = math.radians(72.56 + 20.186*t)
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rho = (
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-0.02752*math.cos(mdash) +
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-0.02245*math.sin(f) +
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+0.00684*math.cos(mdash - 2*f) +
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-0.00293*math.cos(2*f) +
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-0.00085*math.cos(2*f - 2*d) +
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-0.00054*math.cos(mdash - 2*d) +
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-0.00020*math.sin(mdash + f) +
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-0.00020*math.cos(mdash + 2*f) +
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-0.00020*math.cos(mdash - f) +
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+0.00014*math.cos(mdash + 2*f - 2*d)
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)
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sigma = (
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-0.02816*math.sin(mdash) +
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+0.02244*math.cos(f) +
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-0.00682*math.sin(mdash - 2*f) +
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-0.00279*math.sin(2*f) +
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-0.00083*math.sin(2*f - 2*d) +
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+0.00069*math.sin(mdash - 2*d) +
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+0.00040*math.cos(mdash + f) +
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-0.00025*math.sin(2*mdash) +
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-0.00023*math.sin(mdash + 2*f) +
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+0.00020*math.cos(mdash - f) +
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+0.00019*math.sin(mdash - f) +
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+0.00013*math.sin(mdash + 2*f - 2*d) +
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-0.00010*math.cos(mdash - 3*f)
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)
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tau = (
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+0.02520*e*math.sin(m) +
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+0.00473*math.sin(2*mdash - 2*f) +
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-0.00467*math.sin(mdash) +
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+0.00396*math.sin(k1) +
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+0.00276*math.sin(2*mdash - 2*d) +
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+0.00196*math.sin(omega) +
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-0.00183*math.cos(mdash - f) +
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+0.00115*math.sin(mdash - 2*d) +
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-0.00096*math.sin(mdash - d) +
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+0.00046*math.sin(2*f - 2*d) +
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-0.00039*math.sin(mdash - f) +
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-0.00032*math.sin(mdash - m - d) +
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+0.00027*math.sin(2*mdash - m - 2*d) +
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+0.00023*math.sin(k2) +
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-0.00014*math.sin(2*d) +
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+0.00014*math.cos(2*mdash - 2*f) +
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-0.00012*math.sin(mdash - 2*f) +
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-0.00012*math.sin(2*mdash) +
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+0.00011*math.sin(2*mdash - 2*m - 2*d)
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)
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ldash2 = -tau + (rho*math.cos(a) + sigma*math.sin(a))*math.tan(bdash)
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bdash = math.degrees(bdash)
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bdash2 = sigma*math.cos(a) - rho*math.sin(a)
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return LibrationInfo(bdash + bdash2, ldash + ldash2, mlat, mlon, dist_km, diam_deg)
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