def ephemeris_physical_observations(epoch):
"""This method uses Carrington's formulas to compute the following
quantities:
- P : position angle of the northern extremity of the axis of rotation
- B0 : heliographic latitude of the center of the solar disk
- L0 : heliographic longitude of the center of the solar disk
:param epoch: Epoch to compute the parameters
:type epoch: :py:class:`Epoch`
:returns: Parameters P, B0 and L0, in a tuple
:rtype: tuple
:raises: TypeError if input value is of wrong type.
>>> epoch = Epoch(1992, 10, 13)
>>> p, b0, l0 = Sun.ephemeris_physical_observations(epoch)
>>> print(round(p, 2))
26.27
>>> print(round(b0, 2))
5.99
>>> print(round(l0, 2))
238.63
"""
# First check that input values are of correct types
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input type")
# Compute the auxiliary parameters
epoch += 0.00068
theta = (epoch() - 2398220.0) * 360.0 / 25.38
theta = Angle(theta)
i = Angle(7.25)
k = 73.6667 + 1.3958333 * (epoch() - 2396758.0) / 36525.0
k = Angle(k)
lon, lat, r = Sun.apparent_geocentric_position(epoch, nutation=False)
eps = true_obliquity(epoch)
dpsi = nutation_longitude(epoch)
lonp = lon + dpsi
x = atan(-cos(lonp.rad()) * tan(eps.rad()))
x = Angle(x, radians=True)
delta = lon - k
y = atan(-cos(delta.rad()) * tan(i.rad()))
y = Angle(y, radians=True)
p = x + y
b0 = asin(sin(delta.rad()) * sin(i.rad()))
b0 = Angle(b0, radians=True)
eta = atan(tan(delta.rad()) * cos(i.rad()))
eta = Angle(eta, radians=True)
l0 = eta - theta
return p, b0, l0.to_positive()
def test_coordinates_nutation_longitude():
"""Tests the nutation_longitude() method of Coordinates module"""
dpsi = nutation_longitude(1987, 4, 10)
a = dpsi.dms_tuple()
assert abs(a[0] - 0.0) < TOL, \
"ERROR: 1st nutation_longitude() test, 'degrees' value doesn't match"
assert abs(a[1] - 0.0) < TOL, \
"ERROR: 2nd nutation_longitude() test, 'minutes' value doesn't match"
assert abs(round(a[2], 3) - 3.788) < TOL, \
"ERROR: 3rd nutation_longitude() test, 'seconds value doesn't match"
assert abs(a[3] - (-1.0)) < TOL, \
"ERROR: 4th nutation_longitude() test, 'sign' value doesn't match"
def equation_of_time(epoch):
"""This method computes the equation of time for a given epoch,
understood as the difference between apparent and mean time, or the
difference between the hour angle of the true Sun and the mean Sun.
:param epoch: Epoch to compute the equation of time, as an Epoch object
:type epoch: :py:class:`Epoch`
:returns: Difference between apparent and mean time, as a tuple, in
minutes (int) and seconds (float) of time
:rtype: tuple
:raises: TypeError if input values are of wrong type.
>>> epoch = Epoch(1992, 10, 13.0)
>>> m, s = Sun.equation_of_time(epoch)
>>> print(m)
13
>>> print(round(s, 1))
42.6
"""
# First check that input values are of correct types
if not isinstance(epoch, Epoch):
raise TypeError("Invalid input type")
# Compute time in Julian millenia from J2000.0
t = (epoch - JDE2000) / 365250
l0 = (280.4664567 + t * (360007.6982779 + t *
(0.03032028 + t *
(1.0 / 49931.0 + t *
(-1.0 / 15300.0 - t * 1.0 / 2000000.0)))))
l0 = Angle(l0)
l0 = l0.to_positive()
# Compute the apparent position of the Sun
lon, lat, r = Sun.apparent_geocentric_position(epoch)
# Now, get the true obliquity
epsilon = true_obliquity(epoch)
# Transform from eclliptical to equatorial coordinates
alpha, dec = ecliptical2equatorial(lon, lat, epsilon)
alpha = alpha.to_positive()
# Now we need the nutation in longitude
deltapsi = nutation_longitude(epoch)
e = l0() - 0.0057183 - alpha + deltapsi * cos(epsilon.rad())
e *= 4.0
# Extract seconds
s = (abs(e()) % 1) * 60.0
m = int(e())
return m, s
def apparent_ecliptical_pos(epoch):
"""This method computes the apparent 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:
* Apparent geocentric longitude of the center of the Moon, as an
py:class:`Epoch` object.
* Apparent 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.apparent_ecliptical_pos(epoch)
>>> print(round(Lambda, 5))
133.16726
>>> 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")
# Now, let's call the method geocentric_ecliptical_pos()
Lambda, Beta, Delta, ppi = Moon.geocentric_ecliptical_pos(epoch)
# Compute the nutation in longitude (deltaPsi)
deltaPsi = nutation_longitude(epoch)
# Correct the longitude to obtain the apparent longitude
aLambda = Lambda + deltaPsi
return aLambda, Beta, Delta, ppi