def lunar_latitude(cls, tee):
"""Return the latitude of moon (in degrees) at moment, tee.
Adapted from "Astronomical Algorithms" by Jean Meeus,
Willmann_Bell, Inc., 1998."""
c = cls.julian_centuries(tee)
cap_L_prime = cls.mean_lunar_longitude(c)
cap_D = cls.lunar_elongation(c)
cap_M = Solar.solar_anomaly(c)
cap_M_prime = cls.lunar_anomaly(c)
cap_F = cls.moon_node(c)
cap_E = poly(c, [1, mpf(-0.002516), mpf(-0.0000074)])
args_lunar_elongation = \
[0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 4, 0, 0, 0,
1, 0, 0, 0, 1, 0, 4, 4, 0, 4, 2, 2, 2, 2, 0, 2, 2, 2, 2, 4, 2, 2,
0, 2, 1, 1, 0, 2, 1, 2, 0, 4, 4, 1, 4, 1, 4, 2]
args_solar_anomaly = \
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, -1, -1, -1, 1, 0, 1,
0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1,
0, -1, -2, 0, 1, 1, 1, 1, 1, 0, -1, 1, 0, -1, 0, 0, 0, -1, -2]
args_lunar_anomaly = \
[0, 1, 1, 0, -1, -1, 0, 2, 1, 2, 0, -2, 1, 0, -1, 0, -1, -1, -1,
0, 0, -1, 0, 1, 1, 0, 0, 3, 0, -1, 1, -2, 0, 2, 1, -2, 3, 2, -3,
-1, 0, 0, 1, 0, 1, 1, 0, 0, -2, -1, 1, -2, 2, -2, -1, 1, 1, -2,
0, 0]
args_moon_node = \
[1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1,
-1, 1, 3, 1, 1, 1, -1, -1, -1, 1, -1, 1, -3, 1, -3, -1, -1, 1,
-1, 1, -1, 1, 1, 1, 1, -1, 3, -1, -1, 1, -1, -1, 1, -1, 1, -1,
-1, -1, -1, -1, -1, 1]
sine_coefficients = \
[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]
beta = ((1.0/1000000.0) *
sigma([sine_coefficients,
args_lunar_elongation,
args_solar_anomaly,
args_lunar_anomaly,
args_moon_node],
lambda v, w, x, y, z: (v *
pow(cap_E, abs(x)) *
sin_degrees((w * cap_D) +
(x * cap_M) +
(y * cap_M_prime) +
(z * cap_F)))))
venus = ((175/1000000) *
(sin_degrees(mpf(119.75) + c * mpf(131.849) + cap_F) +
sin_degrees(mpf(119.75) + c * mpf(131.849) - cap_F)))
flat_earth = ((-2235/1000000) * sin_degrees(cap_L_prime) +
(127/1000000) * sin_degrees(cap_L_prime - cap_M_prime) +
(-115/1000000) * sin_degrees(cap_L_prime + cap_M_prime))
extra = ((382/1000000) *
sin_degrees(mpf(313.45) + c * mpf(481266.484)))
return beta + venus + flat_earth + extra
def lunar_longitude(cls, tee):
"""Return longitude of moon (in degrees) at moment tee.
Adapted from "Astronomical Algorithms" by Jean Meeus,
Willmann_Bell, Inc., 2nd ed., 1998."""
c = cls.julian_centuries(tee)
cap_L_prime = cls.mean_lunar_longitude(c)
cap_D = cls.lunar_elongation(c)
cap_M = Solar.solar_anomaly(c)
cap_M_prime = cls.lunar_anomaly(c)
cap_F = cls.moon_node(c)
# see eq. 47.6 in Meeus
cap_E = poly(c, [1, mpf(-0.002516), mpf(-0.0000074)])
args_lunar_elongation = \
[0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 1, 0, 2, 0, 0, 4, 0, 4, 2, 2, 1,
1, 2, 2, 4, 2, 0, 2, 2, 1, 2, 0, 0, 2, 2, 2, 4, 0, 3, 2, 4, 0, 2,
2, 2, 4, 0, 4, 1, 2, 0, 1, 3, 4, 2, 0, 1, 2]
args_solar_anomaly = \
[0, 0, 0, 0, 1, 0, 0, -1, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1,
0, 1, -1, 0, 0, 0, 1, 0, -1, 0, -2, 1, 2, -2, 0, 0, -1, 0, 0, 1,
-1, 2, 2, 1, -1, 0, 0, -1, 0, 1, 0, 1, 0, 0, -1, 2, 1, 0]
args_lunar_anomaly = \
[1, -1, 0, 2, 0, 0, -2, -1, 1, 0, -1, 0, 1, 0, 1, 1, -1, 3, -2,
-1, 0, -1, 0, 1, 2, 0, -3, -2, -1, -2, 1, 0, 2, 0, -1, 1, 0,
-1, 2, -1, 1, -2, -1, -1, -2, 0, 1, 4, 0, -2, 0, 2, 1, -2, -3,
2, 1, -1, 3]
args_moon_node = \
[0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 2, 0, 0, 0, 0,
0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0]
sine_coefficients = \
[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]
correction = ((1.0/1000000.0) *
sigma([sine_coefficients, args_lunar_elongation,
args_solar_anomaly, args_lunar_anomaly,
args_moon_node],
lambda v, w, x, y, z:
v * pow(cap_E, abs(x)) *
sin_degrees((w * cap_D) +
(x * cap_M) +
(y * cap_M_prime) +
(z * cap_F))))
A1 = mpf(119.75) + (c * mpf(131.849))
venus = ((3958/1000000) * sin_degrees(A1))
A2 = mpf(53.09) + c * mpf(479264.29)
jupiter = ((318/1000000) * sin_degrees(A2))
flat_earth = ((1962/1000000) * sin_degrees(cap_L_prime - cap_F))
return mod(cap_L_prime + correction + venus +
jupiter + flat_earth + cls.nutation(tee), 360)
def lunar_distance(cls, tee):
"""Return the distance to moon (in meters) at moment, tee.
Adapted from "Astronomical Algorithms" by Jean Meeus,
Willmann_Bell, Inc., 2nd ed."""
c = cls.julian_centuries(tee)
cap_D = cls.lunar_elongation(c)
cap_M = cls.solar_anomaly(c)
cap_M_prime = cls.lunar_anomaly(c)
cap_F = cls.moon_node(c)
cap_E = poly(c, [1, mpf(-0.002516), mpf(-0.0000074)])
args_lunar_elongation = \
[0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 1, 0, 2, 0, 0, 4, 0, 4, 2, 2, 1,
1, 2, 2, 4, 2, 0, 2, 2, 1, 2, 0, 0, 2, 2, 2, 4, 0, 3, 2, 4, 0, 2,
2, 2, 4, 0, 4, 1, 2, 0, 1, 3, 4, 2, 0, 1, 2, 2,]
args_solar_anomaly = \
[0, 0, 0, 0, 1, 0, 0, -1, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1,
0, 1, -1, 0, 0, 0, 1, 0, -1, 0, -2, 1, 2, -2, 0, 0, -1, 0, 0, 1,
-1, 2, 2, 1, -1, 0, 0, -1, 0, 1, 0, 1, 0, 0, -1, 2, 1, 0, 0]
args_lunar_anomaly = \
[1, -1, 0, 2, 0, 0, -2, -1, 1, 0, -1, 0, 1, 0, 1, 1, -1, 3, -2,
-1, 0, -1, 0, 1, 2, 0, -3, -2, -1, -2, 1, 0, 2, 0, -1, 1, 0,
-1, 2, -1, 1, -2, -1, -1, -2, 0, 1, 4, 0, -2, 0, 2, 1, -2, -3,
2, 1, -1, 3, -1]
args_moon_node = \
[0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 2, 0, 0, 0, 0,
0, 0, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, -2]
cosine_coefficients = \
[-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]
correction = sigma ([cosine_coefficients,
args_lunar_elongation,
args_solar_anomaly,
args_lunar_anomaly,
args_moon_node],
lambda v, w, x, y, z: (v *
pow(cap_E, abs(x)) *
cos_degrees((w * cap_D) +
(x * cap_M) +
(y * cap_M_prime) +
(z * cap_F))))
return 385000560 + correction
def solar_longitude(cls, tee):
"""Return the longitude of sun at moment 'tee'.
Adapted from 'Planetary Programs and Tables from -4000 to +2800'
by Pierre Bretagnon and Jean_Louis Simon, Willmann_Bell, Inc., 1986.
See also pag 166 of 'Astronomical Algorithms' by Jean Meeus, 2nd Ed 1998,
with corrections Jun 2005."""
c = cls.julian_centuries(tee)
coefficients = [403406, 195207, 119433, 112392, 3891, 2819, 1721,
660, 350, 334, 314, 268, 242, 234, 158, 132, 129, 114,
99, 93, 86, 78,72, 68, 64, 46, 38, 37, 32, 29, 28, 27, 27,
25, 24, 21, 21, 20, 18, 17, 14, 13, 13, 13, 12, 10, 10, 10,
10]
multipliers = [mpf(0.9287892), mpf(35999.1376958), mpf(35999.4089666),
mpf(35998.7287385), mpf(71998.20261), mpf(71998.4403),
mpf(36000.35726), mpf(71997.4812), mpf(32964.4678),
mpf(-19.4410), mpf(445267.1117), mpf(45036.8840), mpf(3.1008),
mpf(22518.4434), mpf(-19.9739), mpf(65928.9345),
mpf(9038.0293), mpf(3034.7684), mpf(33718.148), mpf(3034.448),
mpf(-2280.773), mpf(29929.992), mpf(31556.493), mpf(149.588),
mpf(9037.750), mpf(107997.405), mpf(-4444.176), mpf(151.771),
mpf(67555.316), mpf(31556.080), mpf(-4561.540),
mpf(107996.706), mpf(1221.655), mpf(62894.167),
mpf(31437.369), mpf(14578.298), mpf(-31931.757),
mpf(34777.243), mpf(1221.999), mpf(62894.511),
mpf(-4442.039), mpf(107997.909), mpf(119.066), mpf(16859.071),
mpf(-4.578), mpf(26895.292), mpf(-39.127), mpf(12297.536),
mpf(90073.778)]
addends = [mpf(270.54861), mpf(340.19128), mpf(63.91854), mpf(331.26220),
mpf(317.843), mpf(86.631), mpf(240.052), mpf(310.26), mpf(247.23),
mpf(260.87), mpf(297.82), mpf(343.14), mpf(166.79), mpf(81.53),
mpf(3.50), mpf(132.75), mpf(182.95), mpf(162.03), mpf(29.8),
mpf(266.4), mpf(249.2), mpf(157.6), mpf(257.8),mpf(185.1),
mpf(69.9), mpf(8.0), mpf(197.1), mpf(250.4), mpf(65.3),
mpf(162.7), mpf(341.5), mpf(291.6), mpf(98.5), mpf(146.7),
mpf(110.0), mpf(5.2), mpf(342.6), mpf(230.9), mpf(256.1),
mpf(45.3), mpf(242.9), mpf(115.2), mpf(151.8), mpf(285.3),
mpf(53.3), mpf(126.6), mpf(205.7), mpf(85.9), mpf(146.1)]
lam = (mpf(282.7771834) +
mpf(36000.76953744) * c +
mpf(0.000005729577951308232) *
sigma([coefficients, addends, multipliers],
lambda x, y, z: x * sin_degrees(y + (z * c))))
return mod(lam + cls.aberration(tee) + cls.nutation(tee), 360)
def nth_new_moon(cls, n):
"""Return the moment of n-th new moon after (or before) the new moon
of January 11, 1. Adapted from "Astronomical Algorithms"
by Jean Meeus, Willmann_Bell, Inc., 2nd ed., 1998."""
n0 = 24724
k = n - n0
c = k / mpf(1236.85)
approx = (cls.J2000 +
poly(c, [mpf(5.09766),
cls.MEAN_SYNODIC_MONTH * mpf(1236.85),
mpf(0.0001437),
mpf(-0.000000150),
mpf(0.00000000073)]))
cap_E = poly(c, [1, mpf(-0.002516), mpf(-0.0000074)])
solar_anomaly = poly(c, [mpf(2.5534), (mpf(1236.85) * mpf(29.10535669)), mpf(-0.0000014), mpf(-0.00000011)])
lunar_anomaly = poly(c, [mpf(201.5643), (mpf(385.81693528) * mpf(1236.85)), mpf(0.0107582), mpf(0.00001238), mpf(-0.000000058)])
moon_argument = poly(c, [mpf(160.7108), (mpf(390.67050284) * mpf(1236.85)), mpf(-0.0016118), mpf(-0.00000227), mpf(0.000000011)])
cap_omega = poly(c, [mpf(124.7746), (mpf(-1.56375588) * mpf(1236.85)), mpf(0.0020672), mpf(0.00000215)])
E_factor = [0, 1, 0, 0, 1, 1, 2, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0]
solar_coeff = [0, 1, 0, 0, -1, 1, 2, 0, 0, 1, 0, 1, 1, -1, 2,
0, 3, 1, 0, 1, -1, -1, 1, 0]
lunar_coeff = [1, 0, 2, 0, 1, 1, 0, 1, 1, 2, 3, 0, 0, 2, 1, 2,
0, 1, 2, 1, 1, 1, 3, 4]
moon_coeff = [0, 0, 0, 2, 0, 0, 0, -2, 2, 0, 0, 2, -2, 0, 0,
-2, 0, -2, 2, 2, 2, -2, 0, 0]
sine_coeff = [mpf(-0.40720), mpf(0.17241), mpf(0.01608),
mpf(0.01039), mpf(0.00739), mpf(-0.00514),
mpf(0.00208), mpf(-0.00111), mpf(-0.00057),
mpf(0.00056), mpf(-0.00042), mpf(0.00042),
mpf(0.00038), mpf(-0.00024), mpf(-0.00007),
mpf(0.00004), mpf(0.00004), mpf(0.00003),
mpf(0.00003), mpf(-0.00003), mpf(0.00003),
mpf(-0.00002), mpf(-0.00002), mpf(0.00002)]
correction = ((mpf(-0.00017) * sin_degrees(cap_omega)) +
sigma([sine_coeff, E_factor, solar_coeff,
lunar_coeff, moon_coeff],
lambda v, w, x, y, z: (v *
pow(cap_E, w) *
sin_degrees((x * solar_anomaly) +
(y * lunar_anomaly) +
(z * moon_argument)))))
add_const = [mpf(251.88), mpf(251.83), mpf(349.42), mpf(84.66),
mpf(141.74), mpf(207.14), mpf(154.84), mpf(34.52),
mpf(207.19), mpf(291.34), mpf(161.72), mpf(239.56),
mpf(331.55)]
add_coeff = [mpf(0.016321), mpf(26.651886), mpf(36.412478),
mpf(18.206239), mpf(53.303771), mpf(2.453732),
mpf(7.306860), mpf(27.261239), mpf(0.121824),
mpf(1.844379), mpf(24.198154), mpf(25.513099),
mpf(3.592518)]
add_factor = [mpf(0.000165), mpf(0.000164), mpf(0.000126),
mpf(0.000110), mpf(0.000062), mpf(0.000060),
mpf(0.000056), mpf(0.000047), mpf(0.000042),
mpf(0.000040), mpf(0.000037), mpf(0.000035),
mpf(0.000023)]
extra = (mpf(0.000325) * sin_degrees(poly(c, [mpf(299.77), mpf(132.8475848), mpf(-0.009173)])))
additional = sigma([add_const, add_coeff, add_factor],
lambda i, j, l: l * sin_degrees(i + j * k))
return cls.universal_from_dynamical(approx + correction + extra + additional)