def longitude_true_ascending_node(epoch):
"""This method computes the longitude of the true ascending node of the
Moon in degrees, for a given instant, measured from the mean equinox of
the date.
:param epoch: Instant to compute the Moon's true ascending node, as an
py:class:`Epoch` object
:type epoch: :py:class:`Epoch`
:returns: The longitude of the true ascending node.
:rtype: py:class:`Angle`
:raises: TypeError if input value is of wrong type.
>>> epoch = Epoch(1913, 5, 27.0)
>>> Omega = Moon.longitude_true_ascending_node(epoch)
>>> print(round(Omega, 4))
0.8763
"""
# First check that input values are of correct types
if not (isinstance(epoch, Epoch)):
raise TypeError("Invalid input type")
# Let's start computing the longitude of the MEAN ascending node
Omega = Moon.longitude_mean_ascending_node(epoch)
# Get the time from J2000.0 in Julian centuries
t = (epoch - JDE2000) / 36525.0
# Mean elongation of the Moon
D = 297.8501921 + (445267.1114034
+ (-0.0018819
+ (1.0/545868.0 - t/113065000.0) * t) * t) * t
# Sun's mean anomaly
M = 357.5291092 + (35999.0502909 + (-0.0001536 + t/24490000.0) * t) * t
# Moon's mean anomaly
Mprime = 134.9633964 + (477198.8675055
+ (0.0087414
+ (1.0/69699.9
+ t/14712000.0) * t) * t) * t
# Moon's argument of latitude
F = 93.2720950 + (483202.0175233
+ (-0.0036539
+ (-1.0/3526000.0 + t/863310000.0) * t) * t) * t
# Reduce the angles to a [0 360] range
D = Angle(Angle.reduce_deg(D)).to_positive()
Dr = D.rad()
M = Angle(Angle.reduce_deg(M)).to_positive()
Mr = M.rad()
Mprime = Angle(Angle.reduce_deg(Mprime)).to_positive()
Mprimer = Mprime.rad()
F = Angle(Angle.reduce_deg(F)).to_positive()
Fr = F.rad()
# Compute the periodic terms
corr = (-1.4979 * sin(2.0 * (Dr - Fr)) - 0.15 * sin(Mr)
- 0.1226 * sin(2.0 * Dr) + 0.1176 * sin(2.0 * Fr)
- 0.0801 * sin(2.0 * (Mprimer - Fr)))
Omega += Angle(corr)
return Omega
def test_angle_reduce_deg():
"""Tests reduce_deg() static method of Angle class"""
d = Angle.reduce_deg(745.67)
assert abs(d - 25.67) < TOL, \
"ERROR: In 1st reduce_deg() test, degrees value doesn't match"
d = Angle.reduce_deg(-360.86)
assert abs(d - (-0.86)) < TOL, \
"ERROR: In 2nd reduce_deg() test, degrees value doesn't match"
def geocentric_ecliptical_pos(epoch):
"""This method computes the geocentric ecliptical position (longitude,
latitude) of the Moon for a given instant, referred to the mean equinox
of the date, as well as the Moon-Earth distance in kilometers and the
equatorial horizontal parallax.
:param epoch: Instant to compute the Moon's position, as an
py:class:`Epoch` object
:type epoch: :py:class:`Epoch`
:returns: Tuple containing:
* Geocentric longitude of the center of the Moon, as an
py:class:`Epoch` object.
* Geocentric latitude of the center of the Moon, as an
py:class:`Epoch` object.
* Distance in kilometers between the centers of Earth and Moon, in
kilometers (float)
* Equatorial horizontal parallax of the Moon, as an
py:class:`Epoch` object.
:rtype: tuple
:raises: TypeError if input value is of wrong type.
>>> epoch = Epoch(1992, 4, 12.0)
>>> Lambda, Beta, Delta, ppi = Moon.geocentric_ecliptical_pos(epoch)
>>> print(round(Lambda, 6))
133.162655
>>> print(round(Beta, 6))
-3.229126
>>> print(round(Delta, 1))
368409.7
>>> print(round(ppi, 5))
0.99199
"""
# First check that input values are of correct types
if not (isinstance(epoch, Epoch)):
raise TypeError("Invalid input type")
# Get the time from J2000.0 in Julian centuries
t = (epoch - JDE2000) / 36525.0
# Compute Moon's mean longitude, referred to mean equinox of date
Lprime = 218.3164477 + (481267.88123421
+ (-0.0015786
+ (1.0/538841.0
- t/65194000.0) * t) * t) * t
# Mean elongation of the Moon
D = 297.8501921 + (445267.1114034
+ (-0.0018819
+ (1.0/545868.0 - t/113065000.0) * t) * t) * t
# Sun's mean anomaly
M = 357.5291092 + (35999.0502909 + (-0.0001536 + t/24490000.0) * t) * t
# Moon's mean anomaly
Mprime = 134.9633964 + (477198.8675055
+ (0.0087414
+ (1.0/69699.9
+ t/14712000.0) * t) * t) * t
# Moon's argument of latitude
F = 93.2720950 + (483202.0175233
+ (-0.0036539
+ (-1.0/3526000.0 + t/863310000.0) * t) * t) * t
# Let's compute some additional arguments
A1 = 119.75 + 131.849 * t
A2 = 53.09 + 479264.290 * t
A3 = 313.45 + 481266.484 * t
# Eccentricity of Earth's orbit around the Sun
E = 1.0 + (-0.002516 - 0.0000074 * t) * t
E2 = E * E
# Reduce the angles to a [0 360] range
Lprime = Angle(Angle.reduce_deg(Lprime)).to_positive()
Lprimer = Lprime.rad()
D = Angle(Angle.reduce_deg(D)).to_positive()
Dr = D.rad()
M = Angle(Angle.reduce_deg(M)).to_positive()
Mr = M.rad()
Mprime = Angle(Angle.reduce_deg(Mprime)).to_positive()
Mprimer = Mprime.rad()
F = Angle(Angle.reduce_deg(F)).to_positive()
Fr = F.rad()
A1 = Angle(Angle.reduce_deg(A1)).to_positive()
A1r = A1.rad()
A2 = Angle(Angle.reduce_deg(A2)).to_positive()
A2r = A2.rad()
A3 = Angle(Angle.reduce_deg(A3)).to_positive()
A3r = A3.rad()
# Let's store this results in a list, in preparation for using tables
arguments = [Dr, Mr, Mprimer, Fr]
# Now we use the tables of periodic terms. First for sigmal and sigmar
sigmal = 0.0
sigmar = 0.0
for i, value in enumerate(PERIODIC_TERMS_LR_TABLE):
argument = 0.0
for j in range(4):
if PERIODIC_TERMS_LR_TABLE[i][j]: # Avoid multiply by zero
argument += PERIODIC_TERMS_LR_TABLE[i][j] * arguments[j]
coeffl = value[4]
coeffr = value[5]
if abs(value[1]) == 1:
coeffl = coeffl * E
coeffr = coeffr * E
elif abs(value[1]) == 2:
coeffl = coeffl * E2
coeffr = coeffr * E2
sigmal += coeffl * sin(argument)
sigmar += coeffr * cos(argument)
# Add the additive terms to sigmal
sigmal += (3958.0 * sin(A1r) + 1962.0 * sin(Lprimer - Fr)
+ 318.0 * sin(A2r))
# Now use the tabla for sigmab
sigmab = 0.0
for i, value in enumerate(PERIODIC_TERMS_B_TABLE):
argument = 0.0
for j in range(4):
if PERIODIC_TERMS_B_TABLE[i][j]: # Avoid multiply by zero
argument += PERIODIC_TERMS_B_TABLE[i][j] * arguments[j]
coeffb = value[4]
if abs(value[1]) == 1:
coeffb = coeffb * E
elif abs(value[1]) == 2:
coeffb = coeffb * E2
sigmab += coeffb * sin(argument)
# Add the additive terms to sigmab
sigmab += (-2235.0 * sin(Lprimer) + 382.0 * sin(A3r)
+ 175.0 * sin(A1r - Fr) + 175.0 * sin(A1r + Fr)
+ 127.0 * sin(Lprimer - Mprimer)
- 115.0 * sin(Lprimer + Mprimer))
Lambda = Lprime + (sigmal / 1000000.0)
Beta = Angle(sigmab / 1000000.0)
Delta = 385000.56 + (sigmar / 1000.0)
ppii = asin(6378.14 / Delta)
ppi = Angle(ppii, radians=True)
return Lambda, Beta, Delta, ppi
