def calculate_lunar_geocentric_location(self, t_struct):
"""
Calculate the geocentric right ascension and declination of the moon using
an approximation as described on page D22 of the 2008 Astronomical Almanac
All of the variables in this method use the same names as those described
in the text: lambda = Ecliptic longitude (degrees) beta = Ecliptic latitude
(degrees) pi = horizontal parallax (degrees) r = distance (Earth radii)
NOTE: The text does not give a specific time period where the approximation
is valid, but it should be valid through at least 2009.
"""
# First, calculate the number of Julian centuries from J2000.0.
t = (calculate_julian_day(t_struct) - 2451545.0) / 36525.0
# Second, calculate the approximate geocentric orbital elements.
lambda_val = (
218.32
+ 481267.881 * t
+ 6.29 * math.sin(Geometry.degrees_to_radians(135.0 + 477198.87 * t))
- 1.27 * math.sin(Geometry.degrees_to_radians(259.3 - 413335.36 * t))
+ 0.66 * math.sin(Geometry.degrees_to_radians(235.7 + 890534.22 * t))
+ 0.21 * math.sin(Geometry.degrees_to_radians(269.9 + 954397.74 * t))
- 0.19 * math.sin(Geometry.degrees_to_radians(357.5 + 35999.05 * t))
- 0.11 * math.sin(Geometry.degrees_to_radians(186.5 + 966404.03 * t))
)
beta = (
5.13 * math.sin(Geometry.degrees_to_radians(93.3 + 483202.02 * t))
+ 0.28 * math.sin(Geometry.degrees_to_radians(228.2 + 960400.89 * t))
- 0.28 * math.sin(Geometry.degrees_to_radians(318.3 + 6003.15 * t))
- 0.17 * math.sin(Geometry.degrees_to_radians(217.6 - 407332.21 * t))
)
# Third, convert to RA and Dec.
l = math.cos(Geometry.degrees_to_radians(beta)) * math.cos(Geometry.degrees_to_radians(lambda_val))
m = 0.9175 * math.cos(Geometry.degrees_to_radians(beta)) * math.sin(
Geometry.degrees_to_radians(lambda_val)
) - 0.3978 * math.sin(Geometry.degrees_to_radians(beta))
n = 0.3978 * math.cos(Geometry.degrees_to_radians(beta)) * math.sin(
Geometry.degrees_to_radians(lambda_val)
) + 0.9175 * math.sin(Geometry.degrees_to_radians(beta))
ra = Geometry.radians_to_degrees(Geometry.mod_2_pi(math.atan2(m, l)))
dec = Geometry.radians_to_degrees(math.asin(n))
return RaDec(ra, dec)
def calculate_lunar_geocentric_location(self, t_struct):
'''
Calculate the geocentric right ascension and declination of the moon using
an approximation as described on page D22 of the 2008 Astronomical Almanac
All of the variables in this method use the same names as those described
in the text: lambda = Ecliptic longitude (degrees) beta = Ecliptic latitude
(degrees) pi = horizontal parallax (degrees) r = distance (Earth radii)
NOTE: The text does not give a specific time period where the approximation
is valid, but it should be valid through at least 2009.
'''
# First, calculate the number of Julian centuries from J2000.0.
t = ((calculate_julian_day(t_struct) - 2451545.0) / 36525.0)
# Second, calculate the approximate geocentric orbital elements.
lambda_val = 218.32 + 481267.881 * t + 6.29 \
* math.sin(Geometry.degrees_to_radians(135.0 + 477198.87 * t)) - 1.27 \
* math.sin(Geometry.degrees_to_radians(259.3 - 413335.36 * t)) + 0.66 \
* math.sin(Geometry.degrees_to_radians(235.7 + 890534.22 * t)) + 0.21 \
* math.sin(Geometry.degrees_to_radians(269.9 + 954397.74 * t)) - 0.19 \
* math.sin(Geometry.degrees_to_radians(357.5 + 35999.05 * t)) - 0.11 \
* math.sin(Geometry.degrees_to_radians(186.5 + 966404.03 * t))
beta = 5.13 \
* math.sin(Geometry.degrees_to_radians(93.3 + 483202.02 * t)) + 0.28 \
* math.sin(Geometry.degrees_to_radians(228.2 + 960400.89 * t)) - 0.28 \
* math.sin(Geometry.degrees_to_radians(318.3 + 6003.15 * t)) - 0.17 \
* math.sin(Geometry.degrees_to_radians(217.6 - 407332.21 * t))
# Third, convert to RA and Dec.
l = math.cos(Geometry.degrees_to_radians(beta)) \
* math.cos(Geometry.degrees_to_radians(lambda_val))
m = 0.9175 * math.cos(Geometry.degrees_to_radians(beta)) \
* math.sin(Geometry.degrees_to_radians(lambda_val)) - 0.3978 \
* math.sin(Geometry.degrees_to_radians(beta))
n = 0.3978 * math.cos(Geometry.degrees_to_radians(beta)) \
* math.sin(Geometry.degrees_to_radians(lambda_val)) + 0.9175 \
* math.sin(Geometry.degrees_to_radians(beta))
ra = Geometry.radians_to_degrees(Geometry.mod_2_pi(math.atan2(m, l)))
dec = Geometry.radians_to_degrees(math.asin(n))
return RaDec(ra, dec)
def get_orbital_elements(self, t_struct):
# Centuries since J2000
jc = julian_centuries(t_struct)
if self.id == planet_enum.MERCURY:
a = 0.38709927 + 0.00000037 * jc
e = 0.20563593 + 0.00001906 * jc
i = Geometry.degrees_to_radians(7.00497902 - 0.00594749 * jc)
l = Geometry.mod_2_pi(Geometry.degrees_to_radians(252.25032350 + 149472.67411175 * jc))
w = Geometry.degrees_to_radians(77.45779628 + 0.16047689 * jc)
o = Geometry.degrees_to_radians(48.33076593 - 0.12534081 * jc)
return OrbitalElements(a, e, i, o, w, l)
elif self.id == planet_enum.VENUS:
a = 0.72333566 + 0.00000390 * jc
e = 0.00677672 - 0.00004107 * jc
i = Geometry.degrees_to_radians(3.39467605 - 0.00078890 * jc)
l = Geometry.mod_2_pi(Geometry.degrees_to_radians(181.97909950 + 58517.81538729 * jc))
w = Geometry.degrees_to_radians(131.60246718 + 0.00268329 * jc)
o = Geometry.degrees_to_radians(76.67984255 - 0.27769418 * jc)
return OrbitalElements(a, e, i, o, w, l)
elif self.id == planet_enum.SUN:
# Note that this is the orbital data for Earth.
a = 1.00000261 + 0.00000562 * jc
e = 0.01671123 - 0.00004392 * jc
i = Geometry.degrees_to_radians(-0.00001531 - 0.01294668 * jc)
l = Geometry.mod_2_pi(Geometry.degrees_to_radians(100.46457166 + 35999.37244981 * jc))
w = Geometry.degrees_to_radians(102.93768193 + 0.32327364 * jc)
o = 0.0
return OrbitalElements(a, e, i, o, w, l)
elif self.id == planet_enum.MARS:
a = 1.52371034 + 0.00001847 * jc
e = 0.09339410 + 0.00007882 * jc
i = Geometry.degrees_to_radians(1.84969142 - 0.00813131 * jc)
l = Geometry.mod_2_pi(Geometry.degrees_to_radians(-4.55343205 + 19140.30268499 * jc))
w = Geometry.degrees_to_radians(-23.94362959 + 0.44441088 * jc)
o = Geometry.degrees_to_radians(49.55953891 - 0.29257343 * jc)
return OrbitalElements(a, e, i, o, w, l)
elif self.id == planet_enum.JUPITER:
a = 5.20288700 - 0.00011607 * jc
e = 0.04838624 - 0.00013253 * jc
i = Geometry.degrees_to_radians(1.30439695 - 0.00183714 * jc)
l = Geometry.mod_2_pi(Geometry.degrees_to_radians(34.39644051 + 3034.74612775 * jc))
w = Geometry.degrees_to_radians(14.72847983 + 0.21252668 * jc)
o = Geometry.degrees_to_radians(100.47390909 + 0.20469106 * jc)
return OrbitalElements(a, e, i, o, w, l)
elif self.id == planet_enum.SATURN:
a = 9.53667594 - 0.00125060 * jc
e = 0.05386179 - 0.00050991 * jc
i = Geometry.degrees_to_radians(2.48599187 + 0.00193609 * jc)
l = Geometry.mod_2_pi(Geometry.degrees_to_radians(49.95424423 + 1222.49362201 * jc))
w = Geometry.degrees_to_radians(92.59887831 - 0.41897216 * jc)
o = Geometry.degrees_to_radians(113.66242448 - 0.28867794 * jc)
return OrbitalElements(a, e, i, o, w, l)
elif self.id == planet_enum.URANUS:
a = 19.18916464 - 0.00196176 * jc
e = 0.04725744 - 0.00004397 * jc
i = Geometry.degrees_to_radians(0.77263783 - 0.00242939 * jc)
l = Geometry.mod_2_pi(Geometry.degrees_to_radians(313.23810451 + 428.48202785 * jc))
w = Geometry.degrees_to_radians(170.95427630 + 0.40805281 * jc)
o = Geometry.degrees_to_radians(74.01692503 + 0.04240589 * jc)
return OrbitalElements(a, e, i, o, w, l)
elif self.id == planet_enum.NEPTUNE:
a = 30.06992276 + 0.00026291 * jc
e = 0.00859048 + 0.00005105 * jc
i = Geometry.degrees_to_radians(1.77004347 + 0.00035372 * jc)
l = Geometry.mod_2_pi(Geometry.degrees_to_radians(-55.12002969 + 218.45945325 * jc))
w = Geometry.degrees_to_radians(44.96476227 - 0.32241464 * jc)
o = Geometry.degrees_to_radians(131.78422574 - 0.00508664 * jc)
return OrbitalElements(a, e, i, o, w, l)
elif self.id == planet_enum.PLUTO:
a = 39.48211675 - 0.00031596 * jc
e = 0.24882730 + 0.00005170 * jc
i = Geometry.degrees_to_radians(17.14001206 + 0.00004818 * jc)
l = Geometry.mod_2_pi(Geometry.degrees_to_radians(238.92903833 + 145.20780515 * jc))
w = Geometry.degrees_to_radians(224.06891629 - 0.04062942 * jc)
o = Geometry.degrees_to_radians(110.30393684 - 0.01183482 * jc)
return OrbitalElements(a, e, i, o, w, l)
else:
raise RuntimeError("Unknown Planet:" + str(self.id))
def get_orbital_elements(self, t_struct):
# Centuries since J2000
jc = julian_centuries(t_struct)
if self.id == planet_enum.MERCURY:
a = 0.38709927 + 0.00000037 * jc
e = 0.20563593 + 0.00001906 * jc
i = Geometry.degrees_to_radians(7.00497902 - 0.00594749 * jc)
l = Geometry.mod_2_pi(Geometry.degrees_to_radians(252.25032350 + 149472.67411175 * jc))
w = Geometry.degrees_to_radians(77.45779628 + 0.16047689 * jc)
o = Geometry.degrees_to_radians(48.33076593 - 0.12534081 * jc)
return OrbitalElements(a, e, i, o, w, l)
elif self.id == planet_enum.VENUS:
a = 0.72333566 + 0.00000390 * jc
e = 0.00677672 - 0.00004107 * jc
i = Geometry.degrees_to_radians(3.39467605 - 0.00078890 * jc)
l = Geometry.mod_2_pi(Geometry.degrees_to_radians(181.97909950 + 58517.81538729 * jc))
w = Geometry.degrees_to_radians(131.60246718 + 0.00268329 * jc)
o = Geometry.degrees_to_radians(76.67984255 - 0.27769418 * jc)
return OrbitalElements(a, e, i, o, w, l)
elif self.id == planet_enum.SUN:
# Note that this is the orbital data for Earth.
a = 1.00000261 + 0.00000562 * jc
e = 0.01671123 - 0.00004392 * jc
i = Geometry.degrees_to_radians(-0.00001531 - 0.01294668 * jc)
l = Geometry.mod_2_pi(Geometry.degrees_to_radians(100.46457166 + 35999.37244981 * jc))
w = Geometry.degrees_to_radians(102.93768193 + 0.32327364 * jc)
o = 0.0
return OrbitalElements(a, e, i, o, w, l)
elif self.id == planet_enum.MARS:
a = 1.52371034 + 0.00001847 * jc
e = 0.09339410 + 0.00007882 * jc
i = Geometry.degrees_to_radians(1.84969142 - 0.00813131 * jc)
l = Geometry.mod_2_pi(Geometry.degrees_to_radians(-4.55343205 + 19140.30268499 * jc))
w = Geometry.degrees_to_radians(-23.94362959 + 0.44441088 * jc)
o = Geometry.degrees_to_radians(49.55953891 - 0.29257343 * jc)
return OrbitalElements(a, e, i, o, w, l)
elif self.id == planet_enum.JUPITER:
a = 5.20288700 - 0.00011607 * jc
e = 0.04838624 - 0.00013253 * jc
i = Geometry.degrees_to_radians(1.30439695 - 0.00183714 * jc)
l = Geometry.mod_2_pi(Geometry.degrees_to_radians(34.39644051 + 3034.74612775 * jc))
w = Geometry.degrees_to_radians(14.72847983 + 0.21252668 * jc)
o = Geometry.degrees_to_radians(100.47390909 + 0.20469106 * jc)
return OrbitalElements(a, e, i, o, w, l)
elif self.id == planet_enum.SATURN:
a = 9.53667594 - 0.00125060 * jc
e = 0.05386179 - 0.00050991 * jc
i = Geometry.degrees_to_radians(2.48599187 + 0.00193609 * jc)
l = Geometry.mod_2_pi(Geometry.degrees_to_radians(49.95424423 + 1222.49362201 * jc))
w = Geometry.degrees_to_radians(92.59887831 - 0.41897216 * jc)
o = Geometry.degrees_to_radians(113.66242448 - 0.28867794 * jc)
return OrbitalElements(a, e, i, o, w, l)
elif self.id == planet_enum.URANUS:
a = 19.18916464 - 0.00196176 * jc
e = 0.04725744 - 0.00004397 * jc
i = Geometry.degrees_to_radians(0.77263783 - 0.00242939 * jc)
l = Geometry.mod_2_pi(Geometry.degrees_to_radians(313.23810451 + 428.48202785 * jc))
w = Geometry.degrees_to_radians(170.95427630 + 0.40805281 * jc)
o = Geometry.degrees_to_radians(74.01692503 + 0.04240589 * jc)
return OrbitalElements(a, e, i, o, w, l)
elif self.id == planet_enum.NEPTUNE:
a = 30.06992276 + 0.00026291 * jc
e = 0.00859048 + 0.00005105 * jc
i = Geometry.degrees_to_radians(1.77004347 + 0.00035372 * jc)
l = Geometry.mod_2_pi(Geometry.degrees_to_radians(-55.12002969 + 218.45945325 * jc))
w = Geometry.degrees_to_radians(44.96476227 - 0.32241464 * jc)
o = Geometry.degrees_to_radians(131.78422574 - 0.00508664 * jc)
return OrbitalElements(a, e, i, o, w, l)
elif self.id == planet_enum.PLUTO:
a = 39.48211675 - 0.00031596 * jc
e = 0.24882730 + 0.00005170 * jc
i = Geometry.degrees_to_radians(17.14001206 + 0.00004818 * jc)
l = Geometry.mod_2_pi(Geometry.degrees_to_radians(238.92903833 + 145.20780515 * jc))
w = Geometry.degrees_to_radians(224.06891629 - 0.04062942 * jc)
o = Geometry.degrees_to_radians(110.30393684 - 0.01183482 * jc)
return OrbitalElements(a, e, i, o, w, l)
else:
raise RuntimeError("Unknown Planet:" + str(self.id))
