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Python: Implemented GlobalSolarEclipse.

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This commit is contained in:
Don Cross
2020-06-04 19:01:39 -04:00
parent b6fbdf9119
commit 9187e3e966
4 changed files with 685 additions and 43 deletions
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source/python/astronomy.py
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@@ -6598,34 +6598,55 @@ class EclipseKind(enum.Enum):
Total = 4
class _EarthShadowInfo:
def __init__(self, time, u, r, k, p):
class _ShadowInfo:
def __init__(self, time, u, r, k, p, target, dir):
self.time = time
self.u = u # dot product of (heliocentric earth) and (geocentric moon): defines the shadow plane where the Moon is
self.r = r # km distance between center of Moon and the line passing through the centers of the Sun and Earth.
self.k = k # umbra radius in km, at the shadow plane
self.p = p # penumbra radius in km, at the shadow plane
self.target = target # vector from center of shadow-casting body to target location that might receive the shadow
self.dir = dir # vector from center of Sun to center of shadow-casting body
def _CalcShadow(body_radius_km, time, target, dir):
u = (dir.x*target.x + dir.y*target.y + dir.z*target.z) / (dir.x*dir.x + dir.y*dir.y + dir.z*dir.z)
dx = (u * dir.x) - target.x
dy = (u * dir.y) - target.y
dz = (u * dir.z) - target.z
r = _KM_PER_AU * math.sqrt(dx*dx + dy*dy + dz*dz)
k = +_SUN_RADIUS_KM - (1.0 + u)*(_SUN_RADIUS_KM - body_radius_km)
p = -_SUN_RADIUS_KM + (1.0 + u)*(_SUN_RADIUS_KM + body_radius_km)
return _ShadowInfo(time, u, r, k, p, target, dir)
def _EarthShadow(time):
e = _CalcEarth(time)
m = GeoMoon(time)
u = (e.x*m.x + e.y*m.y + e.z*m.z) / (e.x*e.x + e.y*e.y + e.z*e.z)
dx = (u * e.x) - m.x
dy = (u * e.y) - m.y
dz = (u * e.z) - m.z
r = _KM_PER_AU * math.sqrt(dx*dx + dy*dy + dz*dz)
k = +_SUN_RADIUS_KM - (1.0 + u)*(_SUN_RADIUS_KM - _EARTH_ECLIPSE_RADIUS_KM)
p = -_SUN_RADIUS_KM + (1.0 + u)*(_SUN_RADIUS_KM + _EARTH_ECLIPSE_RADIUS_KM)
return _EarthShadowInfo(time, u, r, k, p)
return _CalcShadow(_EARTH_ECLIPSE_RADIUS_KM, time, m, e)
def _EarthShadowSlope(context, time):
def _MoonShadow(time):
# This is a variation on the logic in _EarthShadow().
# Instead of a heliocentric Earth and a geocentric Moon,
# we want a heliocentric Moon and a lunacentric Earth.
h = _CalcEarth(time) # heliocentric Earth
m = GeoMoon(time) # geocentric Moon
# Calculate lunacentric Earth.
e = Vector(-m.x, -m.y, -m.z, m.t)
# Convert geocentric moon to heliocentric Moon.
m.x += h.x
m.y += h.y
m.z += h.z
return _CalcShadow(_MOON_MEAN_RADIUS_KM, time, e, m)
def _ShadowDistanceSlope(shadowfunc, time):
dt = 1.0 / 86400.0
t1 = time.AddDays(-dt)
t2 = time.AddDays(+dt)
shadow1 = _EarthShadow(t1)
shadow2 = _EarthShadow(t2)
shadow1 = shadowfunc(t1)
shadow2 = shadowfunc(t2)
return (shadow2.r - shadow1.r) / dt
@@ -6633,9 +6654,17 @@ def _PeakEarthShadow(search_center_time):
window = 0.03 # initial search window, in days, before/after given time
t1 = search_center_time.AddDays(-window)
t2 = search_center_time.AddDays(+window)
tx = Search(_EarthShadowSlope, None, t1, t2, 1.0)
tx = Search(_ShadowDistanceSlope, _EarthShadow, t1, t2, 1.0)
return _EarthShadow(tx)
def _PeakMoonShadow(search_center_time):
window = 0.03 # initial search window, in days, before/after given time
t1 = search_center_time.AddDays(-window)
t2 = search_center_time.AddDays(+window)
tx = Search(_ShadowDistanceSlope, _MoonShadow, t1, t2, 1.0)
return _MoonShadow(tx)
class _ShadowDiffContext:
def __init__(self, radius_limit, direction):
self.radius_limit = radius_limit
@@ -6688,6 +6717,148 @@ class LunarEclipseInfo:
self.sd_total = sd_total
class GlobalSolarEclipseInfo:
"""Reports the time and geographic location of the peak of a solar eclipse.
Returned by #SearchGlobalSolarEclipse or #NextGlobalSolarEclipse
to report information about a solar eclipse event.
Field `peak` holds the date and time of the peak of the eclipse, defined as
the instant when the axis of the Moon's shadow cone passes closest to the Earth's center.
The eclipse is classified as partial, annular, or total, depending on the
maximum amount of the Sun's disc obscured, as seen at the peak location
on the surface of the Earth.
The `kind` field thus holds `EclipseKind.Partial`, `EclipseKind.Annular`, or `EclipseKind.Total`.
A total eclipse is when the peak observer sees the Sun completely blocked by the Moon.
An annular eclipse is like a total eclipse, but the Moon is too far from the Earth's surface
to completely block the Sun; instead, the Sun takes on a ring-shaped appearance.
A partial eclipse is when the Moon blocks part of the Sun's disc, but nobody on the Earth
observes either a total or annular eclipse.
If `kind` is `EclipseKind.Total` or `EclipseKind.Annular`, the `latitude` and `longitude`
fields give the geographic coordinates of the center of the Moon's shadow projected
onto the daytime side of the Earth at the instant of the eclipse's peak.
If `kind` has any other value, `latitude` and `longitude` are undefined and should
not be used.
"""
def __init__(self, kind, peak, distance, latitude, longitude):
self.kind = kind
self.peak = peak
self.distance = distance
self.latitude = latitude
self.longitude = longitude
def _EclipseKindFromUmbra(k):
# The umbra radius tells us what kind of eclipse the observer sees.
# If the umbra radius is positive, this is a total eclipse. Otherwise, it's annular.
# HACK: I added a tiny bias (14 meters) to match Espenak test data.
if k > 0.014:
return EclipseKind.Total
return EclipseKind.Annular
def _GeoidIntersect(shadow):
#astro_global_solar_eclipse_t eclipse;
#astro_rotation_t rot, inv;
#astro_vector_t v, e, o;
#shadow_t surface;
#double A, B, C, radic, u, R;
#double px, py, pz, proj;
#double gast;
kind = EclipseKind.Partial
peak = shadow.time
distance = shadow.r
latitude = longitude = math.nan
# We want to calculate the intersection of the shadow axis with the Earth's geoid.
# First we must convert EQJ (equator of J2000) coordinates to EQD (equator of date)
# coordinates that are perfectly aligned with the Earth's equator at this
# moment in time.
rot = Rotation_EQJ_EQD(shadow.time)
v = RotateVector(rot, shadow.dir) # shadow-axis vector in equator-of-date coordinates
e = RotateVector(rot, shadow.target) # lunacentric Earth in equator-of-date coordinates
# Convert all distances from AU to km.
# But dilate the z-coordinates so that the Earth becomes a perfect sphere.
# Then find the intersection of the vector with the sphere.
# See p 184 in Montenbruck & Pfleger's "Astronomy on the Personal Computer", second edition.
v.x *= _KM_PER_AU
v.y *= _KM_PER_AU
v.z *= _KM_PER_AU / _EARTH_FLATTENING
e.x *= _KM_PER_AU
e.y *= _KM_PER_AU
e.z *= _KM_PER_AU / _EARTH_FLATTENING
# Solve the quadratic equation that finds whether and where
# the shadow axis intersects with the Earth in the dilated coordinate system.
R = _EARTH_EQUATORIAL_RADIUS_KM
A = v.x*v.x + v.y*v.y + v.z*v.z
B = -2.0 * (v.x*e.x + v.y*e.y + v.z*e.z)
C = (e.x*e.x + e.y*e.y + e.z*e.z) - R*R
radic = B*B - 4*A*C
if radic > 0.0:
# Calculate the closer of the two intersection points.
# This will be on the day side of the Earth.
u = (-B - math.sqrt(radic)) / (2 * A)
# Convert lunacentric dilated coordinates to geocentric coordinates.
px = u*v.x - e.x
py = u*v.y - e.y
pz = (u*v.z - e.z) * _EARTH_FLATTENING
# Convert cartesian coordinates into geodetic latitude/longitude.
proj = math.sqrt(px*px + py*py) * (_EARTH_FLATTENING * _EARTH_FLATTENING)
if proj == 0.0:
if pz > 0.0:
latitude = +90.0
else:
latitude = -90.0
else:
latitude = math.degrees(math.atan(pz / proj))
# Adjust longitude for Earth's rotation at the given UT.
gast = _sidereal_time(peak)
longitude = math.fmod(math.degrees(math.atan2(py, px)) - (15*gast), 360.0)
if longitude <= -180.0:
longitude += 360.0
elif longitude > +180.0:
longitude -= 360.0
# We want to determine whether the observer sees a total eclipse or an annular eclipse.
# We need to perform a series of vector calculations...
# Calculate the inverse rotation matrix, so we can convert EQD to EQJ.
inv = InverseRotation(rot)
# Put the EQD geocentric coordinates of the observer into the vector 'o'.
# Also convert back from kilometers to astronomical units.
o = Vector(px / _KM_PER_AU, py / _KM_PER_AU, pz / _KM_PER_AU, shadow.time)
# Rotate the observer's geocentric EQD back to the EQJ system.
o = RotateVector(inv, o)
# Convert geocentric vector to lunacentric vector.
o.x += shadow.target.x
o.y += shadow.target.y
o.z += shadow.target.z
# Recalculate the shadow using a vector from the Moon's center toward the observer.
surface = _CalcShadow(_MOON_POLAR_RADIUS_KM, shadow.time, o, shadow.dir)
# If we did everything right, the shadow distance should be very close to zero.
# That's because we already determined the observer 'o' is on the shadow axis!
if surface.r > 1.0e-9 or surface.r < 0.0:
raise Error('Unexpected shadow distance from geoid intersection = {}'.format(surface.r))
kind = _EclipseKindFromUmbra(surface.k)
return GlobalSolarEclipseInfo(kind, peak, distance, latitude, longitude)
def _ShadowSemiDurationMinutes(center_time, radius_limit, window_minutes):
# Search backwards and forwards from the center time until shadow axis distance crosses radius limit.
window = window_minutes / (24.0 * 60.0)
@@ -6780,4 +6951,73 @@ def NextLunarEclipse(prevEclipseTime):
LunarEclipseInfo
"""
startTime = prevEclipseTime.AddDays(10.0)
return SearchLunarEclipse(startTime)
return SearchLunarEclipse(startTime)
def SearchGlobalSolarEclipse(startTime):
"""Searches for a solar eclipse visible anywhere on the Earth's surface.
This function finds the first solar eclipse that occurs after `startTime`.
A solar eclipse found may be partial, annular, or total.
See #GlobalSolarEclipseInfo for more information.
To find a series of solar eclipses, call this function once,
then keep calling #NextGlobalSolarEclipse as many times as desired,
passing in the `peak` value returned from the previous call.
Parameters
----------
startTime : Time
The date and time for starting the search for a solar eclipse.
Returns
-------
GlobalSolarEclipseInfo
"""
PruneLatitude = 1.8 # Moon's ecliptic latitude beyond which eclipse is impossible
# Iterate through consecutive new moons until we find a solar eclipse visible somewhere on Earth.
nmtime = startTime
for nmcount in range(12):
# Search for the next new moon. Any eclipse will be near it.
newmoon = SearchMoonPhase(0.0, nmtime, 40.0)
if newmoon is None:
raise Error('Cannot find new moon')
# Pruning: if the new moon's ecliptic latitude is too large, a solar eclipse is not possible.
mp = _CalcMoon(newmoon)
if math.degrees(abs(mp.geo_eclip_lat)) < PruneLatitude:
# Search near the new moon for the time when the center of the Earth
# is closest to the line passing through the centers of the Sun and Moon.
shadow = _PeakMoonShadow(newmoon)
if shadow.r < shadow.p + _EARTH_MEAN_RADIUS_KM:
# This is at least a partial solar eclipse visible somewhere on Earth.
# Try to find an intersection between the shadow axis and the Earth's oblate geoid.
return _GeoidIntersect(shadow)
# We didn't find an eclipse on this new moon, so search for the next one.
nmtime = newmoon.AddDays(10.0)
# Safety valve to prevent infinite loop.
# This should never happen, because at least 2 solar eclipses happen per year.
raise Error('Failed to find solar eclipse within 12 full moons.')
def NextGlobalSolarEclipse(prevEclipseTime):
"""Searches for the next global solar eclipse in a series.
After using #SearchGlobalSolarEclipse to find the first solar eclipse
in a series, you can call this function to find the next consecutive solar eclipse.
Pass in the `peak` value from the #GlobalSolarEclipseInfo returned by the
previous call to `SearchGlobalSolarEclipse` or `NextGlobalSolarEclipse`
to find the next solar eclipse.
Parameters
----------
prevEclipseTime : Time
A date and time near a new moon. Solar eclipse search will start at the next new moon.
Returns
-------
GlobalSolarEclipseInfo
"""
startTime = prevEclipseTime.AddDays(10.0)
return SearchGlobalSolarEclipse(startTime)