def calc_horizontal(self, date, longitude, latitude):
h = GCMath.putIn360(
GCEarthData.star_time(date) - self.rektaszension + longitude)
self.azimuth = GCMath.rad2deg(
math.atan2(
GCMath.sinDeg(h),
GCMath.cosDeg(h) * GCMath.sinDeg(latitude) -
GCMath.tanDeg(self.declination) * GCMath.cosDeg(latitude)))
self.elevation = GCMath.rad2deg(
math.asin(
GCMath.sinDeg(latitude) * GCMath.sinDeg(self.declination) +
GCMath.cosDeg(latitude) * GCMath.cosDeg(self.declination) *
GCMath.cosDeg(h)))
def star_time(date):
jd = date
t = (jd - 2451545.0) / 36525.0
delta_phi, epsilon = calc_epsilon_phi(date)
return GCMath.putIn360(280.46061837 + 360.98564736629 * (jd - 2451545.0) +
t * t * (0.000387933 - t / 38710000) +
delta_phi * GCMath.cosDeg(epsilon))
def equatorialToHorizontalCoords(eqc, obs, date):
hc = GCCoords.GCHorizontalCoords()
h = GCMath.putIn360(
star_time(date) - eqc.rightAscension + obs.longitude_deg)
hc.azimut = GCMath.rad2deg(
math.atan2(
GCMath.sinDeg(h),
GCMath.cosDeg(h) * GCMath.sinDeg(obs.latitude_deg) -
GCMath.tanDeg(eqc.declination) * GCMath.cosDeg(obs.latitude_deg)))
hc.elevation = GCMath.rad2deg(
math.asin(
GCMath.sinDeg(obs.latitude_deg) * GCMath.sinDeg(eqc.declination) +
GCMath.cosDeg(obs.latitude_deg) * GCMath.cosDeg(eqc.declination) *
GCMath.cosDeg(h)))
return hc
def eclipticalToEquatorialCoords(ecc, date):
eqc = GCCoords.GCEquatorialCoords()
epsilon = 0.0
delta_phi = 0.0
alpha = delta = 0.0
delta_phi, epsilon = calc_epsilon_phi(date)
ecc.longitude = GCMath.putIn360(ecc.longitude + delta_phi)
eqc.rightAscension = GCMath.arcTan2Deg(
GCMath.sinDeg(ecc.longitude) * GCMath.cosDeg(epsilon) -
GCMath.tanDeg(ecc.latitude) * GCMath.sinDeg(epsilon),
GCMath.cosDeg(ecc.longitude))
eqc.declination = GCMath.arcSinDeg(
GCMath.sinDeg(ecc.latitude) * GCMath.cosDeg(epsilon) +
GCMath.cosDeg(ecc.latitude) * GCMath.sinDeg(epsilon) *
GCMath.sinDeg(ecc.longitude))
return eqc, ecc
def correct_position(self, jdate, latitude, longitude, height):
b_a = 0.99664719
u = GCMath.arcTanDeg(b_a * b_a * GCMath.tanDeg(latitude))
rho_sin = b_a * GCMath.sinDeg(u) + height / 6378140.0 * GCMath.sinDeg(
latitude)
rho_cos = GCMath.cosDeg(
u) + height / 6378140.0 * GCMath.cosDeg(latitude)
self.parallax = GCMath.arcSinDeg(
GCMath.sinDeg(8.794 / 3600) / (MoonDistance(jdate) / GCMath.AU))
h = GCEarthData.star_time(jdate) - longitude - self.rektaszension
delta_alpha = GCMath.arcTanDeg(
(-rho_cos * GCMath.sinDeg(self.parallax) * GCMath.sinDeg(h)) /
(GCMath.cosDeg(self.declination) -
rho_cos * GCMath.sinDeg(self.parallax) * GCMath.cosDeg(h)))
self.rektaszension = self.rektaszension + delta_alpha
self.declination = GCMath.arcTanDeg(
((GCMath.sinDeg(self.declination) - rho_sin *
GCMath.sinDeg(self.parallax)) * GCMath.cosDeg(delta_alpha)) /
(GCMath.cosDeg(self.declination) -
rho_cos * GCMath.sinDeg(self.parallax) * GCMath.cosDeg(h)))
def getTopocentricEquatorial(self, obs, jdate):
b_a = 0.99664719
tec = GCCoords.GCEquatorialCoords()
altitude = 0
# geocentric position of observer on the earth surface
# 10.1 - 10.3
u = GCMath.arcTanDeg(b_a * b_a * GCMath.tanDeg(obs.latitude_deg))
rho_sin = b_a * GCMath.sinDeg(
u) + altitude / 6378140.0 * GCMath.sinDeg(obs.latitude_deg)
rho_cos = GCMath.cosDeg(u) + altitude / 6378140.0 * GCMath.cosDeg(
obs.latitude_deg)
# equatorial horizontal paralax
# 39.1
parallax = GCMath.arcSinDeg(
GCMath.sinDeg(8.794 / 3600) / (self.radius / GCMath.AU))
# geocentric hour angle of the body
h = GCEarthData.star_time(
jdate) + obs.longitude_deg - self.rektaszension
# 39.2
delta_alpha = GCMath.arcTanDeg(
(-rho_cos * GCMath.sinDeg(self.parallax) * GCMath.sinDeg(h)) /
(GCMath.cosDeg(self.declination) -
rho_cos * GCMath.sinDeg(self.parallax) * GCMath.cosDeg(h)))
tec.rightAscension = self.rektaszension + delta_alpha
tec.declination = GCMath.arcTanDeg(
((GCMath.sinDeg(self.declination) - rho_sin *
GCMath.sinDeg(self.parallax)) * GCMath.cosDeg(delta_alpha)) /
(GCMath.cosDeg(self.declination) -
rho_cos * GCMath.sinDeg(self.parallax) * GCMath.cosDeg(h)))
return tec
def MoonDistance(jdate):
arg_lr = [[0, 0, 1, 0], [2, 0, -1, 0], [2, 0, 0, 0], [0, 0, 2, 0],
[0, 1, 0, 0], [0, 0, 0, 2], [2, 0, -2, 0], [2, -1, -1, 0],
[2, 0, 1, 0], [2, -1, 0, 0], [0, 1, -1, 0], [1, 0, 0, 0],
[0, 1, 1, 0], [2, 0, 0, -2], [0, 0, 1, 2], [0, 0, 1, -2],
[4, 0, -1, 0], [0, 0, 3, 0], [4, 0, -2, 0], [2, 1, -1, 0],
[2, 1, 0, 0], [1, 0, -1, 0], [1, 1, 0, 0], [2, -1, 1, 0],
[2, 0, 2, 0], [4, 0, 0, 0], [2, 0, -3, 0], [0, 1, -2, 0],
[2, 0, -1, 2], [2, -1, -2, 0], [1, 0, 1, 0], [2, -2, 0, 0],
[0, 1, 2, 0], [0, 2, 0, 0], [2, -2, -1, 0], [2, 0, 1, -2],
[2, 0, 0, 2], [4, -1, -1, 0], [0, 0, 2, 2], [3, 0, -1, 0],
[2, 1, 1, 0], [4, -1, -2, 0], [0, 2, -1, 0], [2, 2, -1, 0],
[2, 1, -2, 0], [2, -1, 0, -2], [4, 0, 1, 0], [0, 0, 4, 0],
[4, -1, 0, 0], [1, 0, -2, 0], [2, 1, 0, -2], [0, 0, 2, -2],
[1, 1, 1, 0], [3, 0, -2, 0], [4, 0, -3, 0], [2, -1, 2, 0],
[0, 2, 1, 0], [1, 1, -1, 0], [2, 0, 3, 0], [2, 0, -1, -2]]
sigma_r = [
-20905355, -3699111, -2955968, -569925, 48888, -3149, 246158, -152138,
-170733, -204586, -129620, 108743, 104755, 10321, 0, 79661, -34782,
-23210, -21636, 24208, 30824, -8379, -16675, -12831, -10445, -11650,
14403, -7003, 0, 10056, 6322, -9884, 5751, 0, -4950, 4130, 0, -3958, 0,
3258, 2616, -1897, -2117, 2354, 0, 0, -1423, -1117, -1571, -1739, 0,
-4421, 0, 0, 0, 0, 1165, 0, 0, 8752
]
t = (jdate - 2451545.0) / 36525.0
# (* mean elongation of the moon
d = 297.8502042 + (445267.1115168 +
(-0.0016300 +
(1.0 / 545868 - 1.0 / 113065000 * t) * t) * t) * t
# (* mean anomaly of the sun
m = 357.5291092 + (35999.0502909 +
(-0.0001536 + 1.0 / 24490000 * t) * t) * t
# (* mean anomaly of the moon
ms = 134.9634114 + (477198.8676313 +
(0.0089970 +
(1.0 / 69699 - 1.0 / 1471200 * t) * t) * t) * t
# (* argument of the longitude of the moon
f = 93.2720993 + (483202.0175273 +
(-0.0034029 +
(-1.0 / 3526000 + 1.0 / 863310000 * t) * t) * t) * t
# (* correction term due to excentricity of the earth orbit
e = 1.0 + (-0.002516 - 0.0000074 * t) * t
# (* mean longitude of the moon
ls = 218.3164591 + (481267.88134236 +
(-0.0013268 +
(1.0 / 538841 - 1.0 / 65194000 * t) * t) * t) * t
sr = 0
for i in range(60):
temp = sigma_r[i] * GCMath.cosDeg(arg_lr[i][0] * d + arg_lr[i][1] * m +
arg_lr[i][2] * ms + arg_lr[i][3] * f)
if math.fabs(arg_lr[i][1]) == 1: temp = temp * e
if math.fabs(arg_lr[i][1]) == 2: temp = temp * e * e
sr = sr + temp
return 385000.56 + sr / 1000
def CalculateEcliptical(self, jdate):
arg_lr = [[0, 0, 1, 0], [2, 0, -1, 0], [2, 0, 0, 0], [0, 0, 2, 0],
[0, 1, 0, 0], [0, 0, 0, 2], [2, 0, -2, 0], [2, -1, -1, 0],
[2, 0, 1, 0], [2, -1, 0, 0], [0, 1, -1, 0], [1, 0, 0, 0],
[0, 1, 1, 0], [2, 0, 0, -2], [0, 0, 1, 2], [0, 0, 1, -2],
[4, 0, -1, 0], [0, 0, 3, 0], [4, 0, -2, 0], [2, 1, -1, 0],
[2, 1, 0, 0], [1, 0, -1, 0], [1, 1, 0, 0], [2, -1, 1, 0],
[2, 0, 2, 0], [4, 0, 0, 0], [2, 0, -3, 0], [0, 1, -2, 0],
[2, 0, -1, 2], [2, -1, -2, 0], [1, 0, 1, 0], [2, -2, 0, 0],
[0, 1, 2, 0], [0, 2, 0, 0], [2, -2, -1, 0], [2, 0, 1, -2],
[2, 0, 0, 2], [4, -1, -1, 0], [0, 0, 2, 2], [3, 0, -1, 0],
[2, 1, 1, 0], [4, -1, -2, 0], [0, 2, -1, 0], [2, 2, -1, 0],
[2, 1, -2, 0], [2, -1, 0, -2], [4, 0, 1, 0], [0, 0, 4, 0],
[4, -1, 0, 0], [1, 0, -2, 0], [2, 1, 0, -2], [0, 0, 2, -2],
[1, 1, 1, 0], [3, 0, -2, 0], [4, 0, -3, 0], [2, -1, 2, 0],
[0, 2, 1, 0], [1, 1, -1, 0], [2, 0, 3, 0], [2, 0, -1, -2]]
arg_b = [[0, 0, 0, 1], [0, 0, 1, 1], [0, 0, 1, -1], [2, 0, 0, -1],
[2, 0, -1, 1], [2, 0, -1, -1], [2, 0, 0, 1], [0, 0, 2, 1],
[2, 0, 1, -1], [0, 0, 2, -1], [2, -1, 0, -1], [2, 0, -2, -1],
[2, 0, 1, 1], [2, 1, 0, -1], [2, -1, -1, 1], [2, -1, 0, 1],
[2, -1, -1, -1], [0, 1, -1, -1], [4, 0, -1, -1], [0, 1, 0, 1],
[0, 0, 0, 3], [0, 1, -1, 1], [1, 0, 0, 1], [0, 1, 1, 1],
[0, 1, 1, -1], [0, 1, 0, -1], [1, 0, 0, -1], [0, 0, 3, 1],
[4, 0, 0, -1], [4, 0, -1, 1], [0, 0, 1, -3], [4, 0, -2, 1],
[2, 0, 0, -3], [2, 0, 2, -1], [2, -1, 1, -1], [2, 0, -2, 1],
[0, 0, 3, -1], [2, 0, 2, 1], [2, 0, -3, -1], [2, 1, -1, 1],
[2, 1, 0, 1], [4, 0, 0, 1], [2, -1, 1, 1], [2, -2, 0, -1],
[0, 0, 1, 3], [2, 1, 1, -1], [1, 1, 0, -1], [1, 1, 0, 1],
[0, 1, -2, -1], [2, 1, -1, -1], [1, 0, 1, 1], [2, -1, -2, -1],
[0, 1, 2, 1], [4, 0, -2, -1], [4, -1, -1, -1], [1, 0, 1, -1],
[4, 0, 1, -1], [1, 0, -1, -1], [4, -1, 0, -1], [2, -2, 0, 1]]
sigma_r = [
-20905355, -3699111, -2955968, -569925, 48888, -3149, 246158,
-152138, -170733, -204586, -129620, 108743, 104755, 10321, 0,
79661, -34782, -23210, -21636, 24208, 30824, -8379, -16675, -12831,
-10445, -11650, 14403, -7003, 0, 10056, 6322, -9884, 5751, 0,
-4950, 4130, 0, -3958, 0, 3258, 2616, -1897, -2117, 2354, 0, 0,
-1423, -1117, -1571, -1739, 0, -4421, 0, 0, 0, 0, 1165, 0, 0, 8752
]
sigma_l = [
6288774, 1274027, 658314, 213618, -185116, -114332, 58793, 57066,
53322, 45758, -40923, -34720, -30383, 15327, -12528, 10980, 10675,
10034, 8548, -7888, -6766, -5163, 4987, 4036, 3994, 3861, 3665,
-2689, -2602, 2390, -2348, 2236, -2120, -2069, 2048, -1773, -1595,
1215, -1110, -892, -810, 759, -713, -700, 691, 596, 549, 537, 520,
-487, -399, -381, 351, -340, 330, 327, -323, 299, 294, 0
]
sigma_b = [
5128122, 280602, 277693, 173237, 55413, 46271, 32573, 17198, 9266,
8822, 8216, 4324, 4200, -3359, 2463, 2211, 2065, -1870, 1828,
-1794, -1749, -1565, -1491, -1475, -1410, -1344, -1335, 1107, 1021,
833, 777, 671, 607, 596, 491, -451, 439, 422, 421, -366, -351, 331,
315, 302, -283, -229, 223, 223, -220, -220, -185, 181, -177, 176,
166, -164, 132, -119, 115, 107
]
t = (jdate - 2451545.0) / 36525.0
# (* mean elongation of the moon
d = 297.8502042 + (445267.1115168 +
(-0.0016300 +
(1.0 / 545868 - 1.0 / 113065000 * t) * t) * t) * t
# (* mean anomaly of the sun
m = 357.5291092 + (35999.0502909 +
(-0.0001536 + 1.0 / 24490000 * t) * t) * t
# (* mean anomaly of the moon
ms = 134.9634114 + (477198.8676313 +
(0.0089970 +
(1.0 / 69699 - 1.0 / 1471200 * t) * t) * t) * t
# (* argument of the longitude of the moon
f = 93.2720993 + (483202.0175273 +
(-0.0034029 +
(-1.0 / 3526000 + 1.0 / 863310000 * t) * t) * t) * t
# (* correction term due to excentricity of the earth orbit
e = 1.0 + (-0.002516 - 0.0000074 * t) * t
# (* mean longitude of the moon
ls = 218.3164591 + (481267.88134236 +
(-0.0013268 +
(1.0 / 538841 - 1.0 / 65194000 * t) * t) * t) * t
# (* arguments of correction terms
a1 = 119.75 + 131.849 * t
a2 = 53.09 + 479264.290 * t
a3 = 313.45 + 481266.484 * t
sr = 0
for i in range(60):
temp = sigma_r[i] * GCMath.cosDeg(arg_lr[i][0] * d + arg_lr[i][1] *
m + arg_lr[i][2] * ms +
arg_lr[i][3] * f)
if math.fabs(arg_lr[i][1]) == 1: temp = temp * e
if math.fabs(arg_lr[i][1]) == 2: temp = temp * e * e
sr = sr + temp
sl = 0
for i in range(60):
temp = sigma_l[i] * GCMath.sinDeg(arg_lr[i][0] * d + arg_lr[i][1] *
m + arg_lr[i][2] * ms +
arg_lr[i][3] * f)
if math.fabs(arg_lr[i][1]) == 1: temp = temp * e
if math.fabs(arg_lr[i][1]) == 2: temp = temp * e * e
sl = sl + temp
# (* correction terms
sl =sl +3958*GCMath.sinDeg(a1) \
+1962*GCMath.sinDeg(ls-f) \
+318*GCMath.sinDeg(a2)
sb = 0
for i in range(60):
temp = sigma_b[i] * GCMath.sinDeg(arg_b[i][0] * d + arg_b[i][1] *
m + arg_b[i][2] * ms +
arg_b[i][3] * f)
if math.fabs(arg_b[i][1]) == 1: temp = temp * e
if math.fabs(arg_b[i][1]) == 2: temp = temp * e * e
sb = sb + temp
# (* correction terms
sb = sb - 2235 * GCMath.sinDeg(ls) + 382 * GCMath.sinDeg(
a3) + 175 * GCMath.sinDeg(a1 - f) + 175 * GCMath.sinDeg(
a1 + f) + 127 * GCMath.sinDeg(ls - ms) - 115 * GCMath.sinDeg(
ls + ms)
coords = GCCoords.GCEclipticalCoords()
coords.longitude = ls + sl / 1000000
coords.latitude = sb / 1000000
coords.distance = 385000.56 + sr / 1000
return coords
def calc_epsilon_phi(date):
arg_mul = [[0, 0, 0, 0, 1], [-2, 0, 0, 2, 2], [0, 0, 0, 2, 2],
[0, 0, 0, 0, 2], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0],
[-2, 1, 0, 2, 2], [0, 0, 0, 2, 1], [0, 0, 1, 2, 2],
[-2, -1, 0, 2, 2], [-2, 0, 1, 0, 0], [-2, 0, 0, 2, 1],
[0, 0, -1, 2, 2], [2, 0, 0, 0, 0], [0, 0, 1, 0, 1],
[2, 0, -1, 2, 2], [0, 0, -1, 0, 1], [0, 0, 1, 2, 1],
[-2, 0, 2, 0, 0], [0, 0, -2, 2, 1], [2, 0, 0, 2, 2],
[0, 0, 2, 2, 2], [0, 0, 2, 0, 0], [-2, 0, 1, 2, 2],
[0, 0, 0, 2, 0], [-2, 0, 0, 2, 0], [0, 0, -1, 2, 1],
[0, 2, 0, 0, 0], [2, 0, -1, 0, 1], [-2, 2, 0, 2, 2],
[0, 1, 0, 0, 1]]
arg_phi = [[-171996, -1742], [-13187, -16], [-2274, -2], [2062, 2],
[1426, -34], [712, 1], [-517, 12], [-386, -4], [-301, 0],
[217, -5], [-158, 0], [129, 1], [123, 0], [63, 0], [63, 1],
[-59, 0], [-58, -1], [-51, 0], [48, 0], [46, 0], [-38, 0],
[-31, 0], [29, 0], [29, 0], [26, 0], [-22, 0], [21, 0],
[17, -1], [16, 0], [-16, 1], [-15, 0]]
arg_eps = [[92025, 89], [5736, -31], [977, -5], [-895, 5], [54, -1],
[-7, 0], [224, -6], [200, 0], [129, -1], [-95, 3], [0, 0],
[-70, 0], [-53, 0], [0, 0], [-33, 0], [26, 0], [32, 0], [27, 0],
[0, 0], [-24, 0], [16, 0], [13, 0], [0, 0], [-12, 0], [0, 0],
[0, 0], [-10, 0], [0, 0], [-8, 0], [7, 0], [9, 0]]
t = (date - 2451545.0) / 36525
delta_phi = 0.0
# longitude of rising knot
omega = GCMath.putIn360(125.04452 +
(-1934.136261 +
(0.0020708 + 1.0 / 450000 * t) * t) * t)
if True:
l = 280.4665 + 36000.7698 * t
ls = 218.3165 + 481267.8813 * t
delta_epsilon = 9.20 * GCMath.cosDeg(omega) + 0.57 * GCMath.cosDeg(
2 * l) + 0.10 * GCMath.cosDeg(2 * ls) - 0.09 * GCMath.cosDeg(
2 * omega)
delta_phi = (-17.20 * GCMath.sinDeg(omega) -
1.32 * GCMath.sinDeg(2 * l) - 0.23 * GCMath.sinDeg(2 * ls)
+ 0.21 * GCMath.sinDeg(2 * omega)) / 3600
else:
# mean elongation of moon to sun
d = GCMath.putIn360(297.85036 + (445267.111480 +
(-0.0019142 + t / 189474) * t) * t)
# mean anomaly of the sun
m = GCMath.putIn360(357.52772 + (35999.050340 +
(-0.0001603 - t / 300000) * t) * t)
# mean anomaly of the moon
ms = GCMath.putIn360(134.96298 + (477198.867398 +
(0.0086972 + t / 56250) * t) * t)
# argument of the latitude of the moon
f = GCMath.putIn360(93.27191 + (483202.017538 +
(-0.0036825 + t / 327270) * t) * t)
delta_phi = 0
delta_epsilon = 0
for i in range(31):
s = arg_mul[i][0] * d + arg_mul[i][1] * m + arg_mul[i][
2] * ms + arg_mul[i][3] * f + arg_mul[i][4] * omega
delta_phi = delta_phi + (
arg_phi[i][0] + arg_phi[i][1] * t * 0.1) * GCMath.sinDeg(s)
delta_epsilon = delta_epsilon + (
arg_eps[i][0] + arg_eps[i][1] * t * 0.1) * GCMath.cosDeg(s)
delta_phi = delta_phi * 0.0001 / 3600
delta_epsilon = delta_epsilon * 0.0001 / 3600
# angle of ecliptic
epsilon_0 = 84381.448 + (-46.8150 + (-0.00059 + 0.001813 * t) * t) * t
epsilon = (epsilon_0 + delta_epsilon) / 3600
return delta_phi, epsilon