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e47602f46b316142198556ab7bb00bad6b0b30ab
astronomy/source/python/astronomy.py
Don Cross e47602f46b Python: translation in progress.
2019-06-23 21:28:45 -04:00

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#!/usr/bin/env python3
import math
import datetime
_PI2 = 2.0 * math.pi
_EPOCH = datetime.datetime(2000, 1, 1, 12)
_T0 = 2451545.0
_MJD_BASIS = 2400000.5
_Y2000_IN_MJD = _T0 - _MJD_BASIS
_DEG2RAD = 0.017453292519943296
_RAD2DEG = 57.295779513082321
_ASEC360 = 1296000.0
_ASEC2RAD = 4.848136811095359935899141e-6
_ARC = 3600.0 * 180.0 / math.pi # arcseconds per radian
_C_AUDAY = 173.1446326846693 # speed of light in AU/day
_ERAD = 6378136.6 # mean earth radius in meters
_AU = 1.4959787069098932e+11 # astronomical unit in meters
_KM_PER_AU = 1.4959787069098932e+8
_ANGVEL = 7.2921150e-5
_SECONDS_PER_DAY = 24.0 * 3600.0
_SOLAR_DAYS_PER_SIDEREAL_DAY = 0.9972695717592592
_MEAN_SYNODIC_MONTH = 29.530588
_EARTH_ORBITAL_PERIOD = 365.256
_REFRACTION_NEAR_HORIZON = 34.0 / 60.0
_SUN_RADIUS_AU = 4.6505e-3
_MOON_RADIUS_AU = 1.15717e-5
_ASEC180 = 180.0 * 60.0 * 60.0
def _LongitudeOffset(diff):
offset = diff
while offset <= -180.0:
offset += 360.0
while offset > 180.0:
offset -= 360.0
return offset
def _NormalizeLongitude(lon):
while lon < 0.0:
lon += 360.0
while lon >= 360.0:
lon -= 360.0
return lon
def VectorLength(vector):
return math.sqrt(vector.x**2 + vector.y**2 + vector.z**2)
BODY_INVALID = -1
BODY_MERCURY = 0
BODY_VENUS = 1
BODY_EARTH = 2
BODY_MARS = 3
BODY_JUPITER = 4
BODY_SATURN = 5
BODY_URANUS = 6
BODY_NEPTUNE = 7
BODY_PLUTO = 8
BODY_SUN = 9
BODY_MOON = 10
BodyName = [
'Mercury',
'Venus',
'Earth',
'Mars',
'Jupiter',
'Saturn',
'Uranus',
'Neptune',
'Pluto',
'Sun',
'Moon',
]
def BodyCode(name):
return BodyName.index(name)
def _IsSuperiorPlanet(body):
return body in [BODY_MARS, BODY_JUPITER, BODY_SATURN, BODY_URANUS, BODY_NEPTUNE, BODY_PLUTO]
_PlanetOrbitalPeriod = [
87.969,
224.701,
_EARTH_ORBITAL_PERIOD,
686.980,
4332.589,
10759.22,
30685.4,
60189.0,
90560.0
]
class Error(Exception):
def __init__(self, message):
Exception.__init__(self, message)
class EarthNotAllowedError(Error):
def __init__(self):
Error.__init__(self, 'The Earth is not allowed as the body.')
class InvalidBodyError(Error):
def __init__(self):
Error.__init__(self, 'Invalid astronomical body.')
class BadVectorError(Error):
def __init__(self):
Error.__init__(self, 'Vector is too small to have a direction.')
def _SynodicPeriod(body):
if body == BODY_EARTH:
raise EarthNotAllowedError()
if body < 0 or body >= len(_PlanetOrbitalPeriod):
raise InvalidBodyError()
if body == BODY_MOON:
return _MEAN_SYNODIC_MONTH
return abs(_EARTH_ORBITAL_PERIOD / (_EARTH_ORBITAL_PERIOD/_PlanetOrbitalPeriod[body] - 1.0))
def _AngleBetween(a, b):
r = VectorLength(a) * VectorLength(b)
if r < 1.0e-8:
return BadVectorError()
dot = (a.x*b.x + a.y*b.y + a.z*b.z) / r
if dot <= -1.0:
return 180.0
if dot >= +1.0:
return 0.0
return _RAD2DEG * math.acos(dot)
class _delta_t_entry_t:
def __init__(self, mjd, dt):
self.mjd = mjd
self.dt = dt
_DT = [
_delta_t_entry_t(-72638.0, 38),
_delta_t_entry_t(-65333.0, 26),
_delta_t_entry_t(-58028.0, 21),
_delta_t_entry_t(-50724.0, 21.1),
_delta_t_entry_t(-43419.0, 13.5),
_delta_t_entry_t(-39766.0, 13.7),
_delta_t_entry_t(-36114.0, 14.8),
_delta_t_entry_t(-32461.0, 15.7),
_delta_t_entry_t(-28809.0, 15.6),
_delta_t_entry_t(-25156.0, 13.3),
_delta_t_entry_t(-21504.0, 12.6),
_delta_t_entry_t(-17852.0, 11.2),
_delta_t_entry_t(-14200.0, 11.13),
_delta_t_entry_t(-10547.0, 7.95),
_delta_t_entry_t(-6895.0, 6.22),
_delta_t_entry_t(-3242.0, 6.55),
_delta_t_entry_t(-1416.0, 7.26),
_delta_t_entry_t(410.0, 7.35),
_delta_t_entry_t(2237.0, 5.92),
_delta_t_entry_t(4063.0, 1.04),
_delta_t_entry_t(5889.0, -3.19),
_delta_t_entry_t(7715.0, -5.36),
_delta_t_entry_t(9542.0, -5.74),
_delta_t_entry_t(11368.0, -5.86),
_delta_t_entry_t(13194.0, -6.41),
_delta_t_entry_t(15020.0, -2.70),
_delta_t_entry_t(16846.0, 3.92),
_delta_t_entry_t(18672.0, 10.38),
_delta_t_entry_t(20498.0, 17.19),
_delta_t_entry_t(22324.0, 21.41),
_delta_t_entry_t(24151.0, 23.63),
_delta_t_entry_t(25977.0, 24.02),
_delta_t_entry_t(27803.0, 23.91),
_delta_t_entry_t(29629.0, 24.35),
_delta_t_entry_t(31456.0, 26.76),
_delta_t_entry_t(33282.0, 29.15),
_delta_t_entry_t(35108.0, 31.07),
_delta_t_entry_t(36934.0, 33.150),
_delta_t_entry_t(38761.0, 35.738),
_delta_t_entry_t(40587.0, 40.182),
_delta_t_entry_t(42413.0, 45.477),
_delta_t_entry_t(44239.0, 50.540),
_delta_t_entry_t(44605.0, 51.3808),
_delta_t_entry_t(44970.0, 52.1668),
_delta_t_entry_t(45335.0, 52.9565),
_delta_t_entry_t(45700.0, 53.7882),
_delta_t_entry_t(46066.0, 54.3427),
_delta_t_entry_t(46431.0, 54.8712),
_delta_t_entry_t(46796.0, 55.3222),
_delta_t_entry_t(47161.0, 55.8197),
_delta_t_entry_t(47527.0, 56.3000),
_delta_t_entry_t(47892.0, 56.8553),
_delta_t_entry_t(48257.0, 57.5653),
_delta_t_entry_t(48622.0, 58.3092),
_delta_t_entry_t(48988.0, 59.1218),
_delta_t_entry_t(49353.0, 59.9845),
_delta_t_entry_t(49718.0, 60.7853),
_delta_t_entry_t(50083.0, 61.6287),
_delta_t_entry_t(50449.0, 62.2950),
_delta_t_entry_t(50814.0, 62.9659),
_delta_t_entry_t(51179.0, 63.4673),
_delta_t_entry_t(51544.0, 63.8285),
_delta_t_entry_t(51910.0, 64.0908),
_delta_t_entry_t(52275.0, 64.2998),
_delta_t_entry_t(52640.0, 64.4734),
_delta_t_entry_t(53005.0, 64.5736),
_delta_t_entry_t(53371.0, 64.6876),
_delta_t_entry_t(53736.0, 64.8452),
_delta_t_entry_t(54101.0, 65.1464),
_delta_t_entry_t(54466.0, 65.4573),
_delta_t_entry_t(54832.0, 65.7768),
_delta_t_entry_t(55197.0, 66.0699),
_delta_t_entry_t(55562.0, 66.3246),
_delta_t_entry_t(55927.0, 66.6030),
_delta_t_entry_t(56293.0, 66.9069),
_delta_t_entry_t(56658.0, 67.2810),
_delta_t_entry_t(57023.0, 67.6439),
_delta_t_entry_t(57388.0, 68.1024),
_delta_t_entry_t(57754.0, 68.5927),
_delta_t_entry_t(58119.0, 68.9676),
_delta_t_entry_t(58484.0, 69.2201),
_delta_t_entry_t(58849.0, 69.87),
_delta_t_entry_t(59214.0, 70.39),
_delta_t_entry_t(59580.0, 70.91),
_delta_t_entry_t(59945.0, 71.40),
_delta_t_entry_t(60310.0, 71.88),
_delta_t_entry_t(60675.0, 72.36),
_delta_t_entry_t(61041.0, 72.83),
_delta_t_entry_t(61406.0, 73.32),
_delta_t_entry_t(61680.0, 73.66)
]
def _DeltaT(mjd):
if mjd <= _DT[0].mjd:
return _DT[0].dt
if mjd >= _DT[-1].mjd:
return _DT[-1].dt
# Do a binary search to find the pair of indexes this mjd lies between.
lo = 0
hi = len(_DT) - 2 # Make sure there is always an array element after the one we are looking at.
while True:
if lo > hi:
# This should never happen unless there is a bug in the binary search.
raise Error('Could not find delta-t value.')
c = (lo + hi) // 2
if mjd < _DT[c].mjd:
hi = c-1
elif mjd > _DT[c+1].mjd:
lo = c+1
else:
frac = (mjd - _DT[c].mjd) / (_DT[c+1].mjd - _DT[c].mjd)
return _DT[c].dt + frac*(_DT[c+1].dt - _DT[c].dt)
def _TerrestrialTime(ut):
return ut + _DeltaT(ut + _Y2000_IN_MJD) / 86400.0
class Time:
def __init__(self, ut):
self.ut = ut
self.tt = _TerrestrialTime(ut)
@staticmethod
def Make(year, month, day, hour, minute, second):
micro = round((second % 1) * 1000000)
second = math.floor(second - micro/1000000)
d = datetime.datetime(year, month, day, hour, minute, second, micro)
ut = (d - _EPOCH).total_seconds() / 86400
return Time(ut)
@staticmethod
def Now():
ut = (datetime.datetime.utcnow() - _EPOCH).total_seconds() / 86400.0
return Time(ut)
def AddDays(self, days):
return Time(self.ut + days)
def __str__(self):
millis = round(self.ut * 86400000.0)
n = _EPOCH + datetime.timedelta(milliseconds=millis)
return '{:04d}-{:02d}-{:02d}T{:02d}:{:02d}:{:02d}.{:03d}Z'.format(n.year, n.month, n.day, n.hour, n.minute, n.second, math.floor(n.microsecond / 1000))
def Utc(self):
return _EPOCH + datetime.timedelta(days=self.ut)
class Observer:
def __init__(self, latitude, longitude, height=0):
self.latitude = latitude
self.longitude = longitude
self.height = height
_nals_t = [
[ 0, 0, 0, 0, 1],
[ 0, 0, 2, -2, 2],
[ 0, 0, 2, 0, 2],
[ 0, 0, 0, 0, 2],
[ 0, 1, 0, 0, 0],
[ 0, 1, 2, -2, 2],
[ 1, 0, 0, 0, 0],
[ 0, 0, 2, 0, 1],
[ 1, 0, 2, 0, 2],
[ 0, -1, 2, -2, 2],
[ 0, 0, 2, -2, 1],
[-1, 0, 2, 0, 2],
[-1, 0, 0, 2, 0],
[ 1, 0, 0, 0, 1],
[-1, 0, 0, 0, 1],
[-1, 0, 2, 2, 2],
[ 1, 0, 2, 0, 1],
[-2, 0, 2, 0, 1],
[ 0, 0, 0, 2, 0],
[ 0, 0, 2, 2, 2],
[ 0, -2, 2, -2, 2],
[-2, 0, 0, 2, 0],
[ 2, 0, 2, 0, 2],
[ 1, 0, 2, -2, 2],
[-1, 0, 2, 0, 1],
[ 2, 0, 0, 0, 0],
[ 0, 0, 2, 0, 0],
[ 0, 1, 0, 0, 1],
[-1, 0, 0, 2, 1],
[ 0, 2, 2, -2, 2],
[ 0, 0, -2, 2, 0],
[ 1, 0, 0, -2, 1],
[ 0, -1, 0, 0, 1],
[-1, 0, 2, 2, 1],
[ 0, 2, 0, 0, 0],
[ 1, 0, 2, 2, 2],
[-2, 0, 2, 0, 0],
[ 0, 1, 2, 0, 2],
[ 0, 0, 2, 2, 1],
[ 0, -1, 2, 0, 2],
[ 0, 0, 0, 2, 1],
[ 1, 0, 2, -2, 1],
[ 2, 0, 2, -2, 2],
[-2, 0, 0, 2, 1],
[ 2, 0, 2, 0, 1],
[ 0, -1, 2, -2, 1],
[ 0, 0, 0, -2, 1],
[-1, -1, 0, 2, 0],
[ 2, 0, 0, -2, 1],
[ 1, 0, 0, 2, 0],
[ 0, 1, 2, -2, 1],
[ 1, -1, 0, 0, 0],
[-2, 0, 2, 0, 2],
[ 3, 0, 2, 0, 2],
[ 0, -1, 0, 2, 0],
[ 1, -1, 2, 0, 2],
[ 0, 0, 0, 1, 0],
[-1, -1, 2, 2, 2],
[-1, 0, 2, 0, 0],
[ 0, -1, 2, 2, 2],
[-2, 0, 0, 0, 1],
[ 1, 1, 2, 0, 2],
[ 2, 0, 0, 0, 1],
[-1, 1, 0, 1, 0],
[ 1, 1, 0, 0, 0],
[ 1, 0, 2, 0, 0],
[-1, 0, 2, -2, 1],
[ 1, 0, 0, 0, 2],
[-1, 0, 0, 1, 0],
[ 0, 0, 2, 1, 2],
[-1, 0, 2, 4, 2],
[-1, 1, 0, 1, 1],
[ 0, -2, 2, -2, 1],
[ 1, 0, 2, 2, 1],
[-2, 0, 2, 2, 2],
[-1, 0, 0, 0, 2],
[ 1, 1, 2, -2, 2]
]
_cls_t = [
[-172064161.0, -174666.0, 33386.0, 92052331.0, 9086.0, 15377.0],
[ -13170906.0, -1675.0, -13696.0, 5730336.0, -3015.0, -4587.0],
[ -2276413.0, -234.0, 2796.0, 978459.0, -485.0, 1374.0],
[ 2074554.0, 207.0, -698.0, -897492.0, 470.0, -291.0],
[ 1475877.0, -3633.0, 11817.0, 73871.0, -184.0, -1924.0],
[ -516821.0, 1226.0, -524.0, 224386.0, -677.0, -174.0],
[ 711159.0, 73.0, -872.0, -6750.0, 0.0, 358.0],
[ -387298.0, -367.0, 380.0, 200728.0, 18.0, 318.0],
[ -301461.0, -36.0, 816.0, 129025.0, -63.0, 367.0],
[ 215829.0, -494.0, 111.0, -95929.0, 299.0, 132.0],
[ 128227.0, 137.0, 181.0, -68982.0, -9.0, 39.0],
[ 123457.0, 11.0, 19.0, -53311.0, 32.0, -4.0],
[ 156994.0, 10.0, -168.0, -1235.0, 0.0, 82.0],
[ 63110.0, 63.0, 27.0, -33228.0, 0.0, -9.0],
[ -57976.0, -63.0, -189.0, 31429.0, 0.0, -75.0],
[ -59641.0, -11.0, 149.0, 25543.0, -11.0, 66.0],
[ -51613.0, -42.0, 129.0, 26366.0, 0.0, 78.0],
[ 45893.0, 50.0, 31.0, -24236.0, -10.0, 20.0],
[ 63384.0, 11.0, -150.0, -1220.0, 0.0, 29.0],
[ -38571.0, -1.0, 158.0, 16452.0, -11.0, 68.0],
[ 32481.0, 0.0, 0.0, -13870.0, 0.0, 0.0],
[ -47722.0, 0.0, -18.0, 477.0, 0.0, -25.0],
[ -31046.0, -1.0, 131.0, 13238.0, -11.0, 59.0],
[ 28593.0, 0.0, -1.0, -12338.0, 10.0, -3.0],
[ 20441.0, 21.0, 10.0, -10758.0, 0.0, -3.0],
[ 29243.0, 0.0, -74.0, -609.0, 0.0, 13.0],
[ 25887.0, 0.0, -66.0, -550.0, 0.0, 11.0],
[ -14053.0, -25.0, 79.0, 8551.0, -2.0, -45.0],
[ 15164.0, 10.0, 11.0, -8001.0, 0.0, -1.0],
[ -15794.0, 72.0, -16.0, 6850.0, -42.0, -5.0],
[ 21783.0, 0.0, 13.0, -167.0, 0.0, 13.0],
[ -12873.0, -10.0, -37.0, 6953.0, 0.0, -14.0],
[ -12654.0, 11.0, 63.0, 6415.0, 0.0, 26.0],
[ -10204.0, 0.0, 25.0, 5222.0, 0.0, 15.0],
[ 16707.0, -85.0, -10.0, 168.0, -1.0, 10.0],
[ -7691.0, 0.0, 44.0, 3268.0, 0.0, 19.0],
[ -11024.0, 0.0, -14.0, 104.0, 0.0, 2.0],
[ 7566.0, -21.0, -11.0, -3250.0, 0.0, -5.0],
[ -6637.0, -11.0, 25.0, 3353.0, 0.0, 14.0],
[ -7141.0, 21.0, 8.0, 3070.0, 0.0, 4.0],
[ -6302.0, -11.0, 2.0, 3272.0, 0.0, 4.0],
[ 5800.0, 10.0, 2.0, -3045.0, 0.0, -1.0],
[ 6443.0, 0.0, -7.0, -2768.0, 0.0, -4.0],
[ -5774.0, -11.0, -15.0, 3041.0, 0.0, -5.0],
[ -5350.0, 0.0, 21.0, 2695.0, 0.0, 12.0],
[ -4752.0, -11.0, -3.0, 2719.0, 0.0, -3.0],
[ -4940.0, -11.0, -21.0, 2720.0, 0.0, -9.0],
[ 7350.0, 0.0, -8.0, -51.0, 0.0, 4.0],
[ 4065.0, 0.0, 6.0, -2206.0, 0.0, 1.0],
[ 6579.0, 0.0, -24.0, -199.0, 0.0, 2.0],
[ 3579.0, 0.0, 5.0, -1900.0, 0.0, 1.0],
[ 4725.0, 0.0, -6.0, -41.0, 0.0, 3.0],
[ -3075.0, 0.0, -2.0, 1313.0, 0.0, -1.0],
[ -2904.0, 0.0, 15.0, 1233.0, 0.0, 7.0],
[ 4348.0, 0.0, -10.0, -81.0, 0.0, 2.0],
[ -2878.0, 0.0, 8.0, 1232.0, 0.0, 4.0],
[ -4230.0, 0.0, 5.0, -20.0, 0.0, -2.0],
[ -2819.0, 0.0, 7.0, 1207.0, 0.0, 3.0],
[ -4056.0, 0.0, 5.0, 40.0, 0.0, -2.0],
[ -2647.0, 0.0, 11.0, 1129.0, 0.0, 5.0],
[ -2294.0, 0.0, -10.0, 1266.0, 0.0, -4.0],
[ 2481.0, 0.0, -7.0, -1062.0, 0.0, -3.0],
[ 2179.0, 0.0, -2.0, -1129.0, 0.0, -2.0],
[ 3276.0, 0.0, 1.0, -9.0, 0.0, 0.0],
[ -3389.0, 0.0, 5.0, 35.0, 0.0, -2.0],
[ 3339.0, 0.0, -13.0, -107.0, 0.0, 1.0],
[ -1987.0, 0.0, -6.0, 1073.0, 0.0, -2.0],
[ -1981.0, 0.0, 0.0, 854.0, 0.0, 0.0],
[ 4026.0, 0.0, -353.0, -553.0, 0.0, -139.0],
[ 1660.0, 0.0, -5.0, -710.0, 0.0, -2.0],
[ -1521.0, 0.0, 9.0, 647.0, 0.0, 4.0],
[ 1314.0, 0.0, 0.0, -700.0, 0.0, 0.0],
[ -1283.0, 0.0, 0.0, 672.0, 0.0, 0.0],
[ -1331.0, 0.0, 8.0, 663.0, 0.0, 4.0],
[ 1383.0, 0.0, -2.0, -594.0, 0.0, -2.0],
[ 1405.0, 0.0, 4.0, -610.0, 0.0, 2.0],
[ 1290.0, 0.0, 0.0, -556.0, 0.0, 0.0]
]
class _iau2000b:
def __init__(self, time):
t = time.tt / 36525
el = ((485868.249036 + t * 1717915923.2178) % ASEC360) * ASEC2RAD
elp = ((1287104.79305 + t * 129596581.0481) % ASEC360) * ASEC2RAD
f = ((335779.526232 + t * 1739527262.8478) % ASEC360) * ASEC2RAD
d = ((1072260.70369 + t * 1602961601.2090) % ASEC360) * ASEC2RAD
om = ((450160.398036 - t * 6962890.5431) % ASEC360) * ASEC2RAD
dp = 0
de = 0
i = 76
while i >= 0:
arg = (_nals_t[i][0]*el + _nals_t[i][1]*elp + _nals_t[i][2]*f + _nals_t[i][3]*d + _nals_t[i][4]*om) % _PI2
sarg = math.sin(arg)
carg = math.cos(arg)
dp += (_cls_t[i][0] + _cls_t[i][1] * t)*sarg + _cls_t[i][2]*carg
de += (_cls_t[i][3] + _cls_t[i][4] * t)*carg + _cls_t[i][5]*sarg
i -= 1
self.dpsi = -0.000135 + (dp * 1.0e-7)
self.deps = +0.000388 + (de * 1.0e-7)
def _mean_obliq(tt):
t = tt / 36525
asec = (
(((( - 0.0000000434 * t
- 0.000000576 ) * t
+ 0.00200340 ) * t
- 0.0001831 ) * t
- 46.836769 ) * t + 84381.406
)
return asec / 3600.0
class _e_tilt:
def __init__(self, time):
e = _iau2000b(time)
self.dpsi = e.dpsi
self.deps = e.deps
self.mobl = _mean_obliq(time.tt)
self.tobl = self.mobl + (e.deps / 3600.0)
self.tt = time.tt
self.ee = e.dpsi * math.cos(self.mobl * _DEG2RAD) / 15.0
def _ecl2equ_vec(time, ecl, equ):
obl = _mean_obliq(time.tt) * _DEG2RAD
cos_obl = math.cos(obl)
sin_obl = math.sin(obl)
return [
ecl[0],
ecl[1]*cos_obl - ecl[2]*sin_obl,
ecl[1]*sin_obl + ecl[2]*cos_obl
]
def _precession(tt1, pos1, tt2):
eps0 = 84381.406
if tt1 != 0 and tt2 != 0:
raise Error('One of (tt1, tt2) must be zero.')
t = (tt2 - tt1) / 36525
if tt2 == 0:
t = -t
psia = (((((- 0.0000000951 * t
+ 0.000132851 ) * t
- 0.00114045 ) * t
- 1.0790069 ) * t
+ 5038.481507 ) * t)
omegaa = (((((+ 0.0000003337 * t
- 0.000000467 ) * t
- 0.00772503 ) * t
+ 0.0512623 ) * t
- 0.025754 ) * t + eps0)
chia = (((((- 0.0000000560 * t
+ 0.000170663 ) * t
- 0.00121197 ) * t
- 2.3814292 ) * t
+ 10.556403 ) * t)
eps0 *= _ASEC2RAD
psia *= _ASEC2RAD
omegaa *= _ASEC2RAD
chia *= _ASEC2RAD
sa = math.sin(eps0)
ca = math.cos(eps0)
sb = math.sin(-psia)
cb = math.cos(-psia)
sc = math.sin(-omegaa)
cc = math.cos(-omegaa)
sd = math.sin(chia)
cd = math.cos(chia)
xx = cd * cb - sb * sd * cc
yx = cd * sb * ca + sd * cc * cb * ca - sa * sd * sc
zx = cd * sb * sa + sd * cc * cb * sa + ca * sd * sc
xy = -sd * cb - sb * cd * cc
yy = -sd * sb * ca + cd * cc * cb * ca - sa * cd * sc
zy = -sd * sb * sa + cd * cc * cb * sa + ca * cd * sc
xz = sb * sc
yz = -sc * cb * ca - sa * cc
zz = -sc * cb * sa + cc * ca
if tt2 == 0.0:
# Perform rotation from other epoch to J2000.0.
return [
xx * pos1[0] + xy * pos1[1] + xz * pos1[2],
yx * pos1[0] + yy * pos1[1] + yz * pos1[2],
zx * pos1[0] + zy * pos1[1] + zz * pos1[2]
]
# Perform rotation from J2000.0 to other epoch.
return [
xx * pos1[0] + yx * pos1[1] + zx * pos1[2],
xy * pos1[0] + yy * pos1[1] + zy * pos1[2],
xz * pos1[0] + yz * pos1[1] + zz * pos1[2]
]
class Equatorial:
def __init__(self, ra, dec, dist):
self.ra = ra
self.dec = dec
self.dist = dist
def _vector2radec(pos):
xyproj = pos[0]*pos[0] + pos[1]*pos[1]
dist = math.sqrt(xyproj + pos[2]*pos[2])
if xyproj == 0.0:
if pos[2] == 0.0:
# Indeterminate coordinates: pos vector has zero length.
raise Error('Cannot convert vector to polar coordinates')
ra = 0.0
if pos[2] < 0.0:
dec = -90.0
else:
dec = +90.0
else:
ra = math.atan2(pos[1], pos[0]) / (_DEG2RAD * 15)
if ra < 0:
ra += 24
dec = _RAD2DEG * math.atan2(pos[2], math.sqrt(xyproj))
return Equatorial(ra, dec, dist)
def _nutation(time, direction, inpos):
tilt = _e_tilt(time)
oblm = tilt.mobl * _DEG2RAD
oblt = tilt.tobl * _DEG2RAD
psi = tilt.dpsi * _ASEC2RAD
cobm = math.cos(oblm)
sobm = math.sin(oblm)
cobt = math.cos(oblt)
sobt = math.sin(oblt)
cpsi = math.cos(psi)
spsi = math.sin(psi)
xx = cpsi
yx = -spsi * cobm
zx = -spsi * sobm
xy = spsi * cobt
yy = cpsi * cobm * cobt + sobm * sobt
zy = cpsi * sobm * cobt - cobm * sobt
xz = spsi * sobt
yz = cpsi * cobm * sobt - sobm * cobt
zz = cpsi * sobm * sobt + cobm * cobt
if direction == 0:
# forward rotation
return [
xx * inpos[0] + yx * inpos[1] + zx * inpos[2],
xy * inpos[0] + yy * inpos[1] + zy * inpos[2],
xz * inpos[0] + yz * inpos[1] + zz * inpos[2]
]
# inverse rotation
return [
xx * inpos[0] + xy * inpos[1] + xz * inpos[2],
yx * inpos[0] + yy * inpos[1] + yz * inpos[2],
zx * inpos[0] + zy * inpos[1] + zz * inpos[2]
]
def _era(time): # Earth Rotation Angle
thet1 = 0.7790572732640 + 0.00273781191135448 * time.ut
thet3 = time.ut % 1.0
theta = 360.0 * ((thet1 + thet3) % 1.0)
if theta < 0.0:
theta += 360.0
return theta
def _sidereal_time(time):
t = time.tt / 36525.0
eqeq = 15.0 * _e_tilt(time).ee # Replace with eqeq=0 to get GMST instead of GAST (if we ever need it)
theta = _era(time)
st = (eqeq + 0.014506 +
(((( - 0.0000000368 * t
- 0.000029956 ) * t
- 0.00000044 ) * t
+ 1.3915817 ) * t
+ 4612.156534 ) * t)
gst = ((st/3600.0 + theta) % 360.0) / 15.0
if gst < 0.0:
gst += 24.0
return gst
def _terra(observer, st):
erad_km = _ERAD / 1000.0
df = 1.0 - 0.003352819697896 # flattening of the Earth
df2 = df * df
phi = observer.latitude * _DEG2RAD
sinphi = math.sin(phi)
cosphi = math.cos(phi)
c = 1.0 / math.sqrt(cosphi*cosphi + df2*sinphi*sinphi)
s = df2 * c
ht_km = observer.height / 1000.0
ach = erad_km*c + ht_km
ash = erad_km*s + ht_km
stlocl = (15.0*st + observer.longitude) * _DEG2RAD
sinst = math.sin(stlocl)
cosst = math.cos(stlocl)
return [
ach * cosphi * cosst / _KM_PER_AU,
ach * cosphi * sinst / _KM_PER_AU,
ash * sinphi / _KM_PER_AU
]
def _geo_pos(time, observer):
gast = _sidereal_time(time)
pos1 = _terra(observer, gast)
pos2 = _nutation(time, -1, pos1)
outpos = _precession(time.tt, pos2, 0.0)
return outpos
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