def apparent_longitude(t=None):
"""Returns the apparent longitude of the Sun."""
T = util.julian_centuries(t)
omega = 259.18 - 1934.142 * T
true_long = true_longitude(t)
result = true_long - 0.00569 - 0.00479 * math.sin(np.radians(omega))
return result
def mean_anomaly(t=None):
"""Returns the mean anomaly (the angle through which the Sun has moved
assuming a circular orbit) as a function of time."""
T = util.julian_centuries(t)
result = 358.475830 + 35999.049750 * T - 0.0001500 * T ** 2 - 0.00000330 * T ** 3
result = result % 360.0
return result
def equation_of_center(t=None):
"""Returns the Sun's equation of center (in degrees)"""
T = util.julian_centuries(t)
mna = mean_anomaly(t)
result = ((1.9194600 - 0.0047890 * T - 0.0000140 * T
** 2) * np.sin(np.radians(mna) + (0.0200940 - 0.0001000 * T) *
np.sin(np.radians(2 * mna)) + 0.0002930 * np.sin(np.radians(3 * mna))))
return result
def solar_north(t=None):
"""Returns the position of the Solar north pole in degrees."""
T = util.julian_centuries(t)
ob1 = true_obliquity_of_ecliptic(t)
# in degrees
i = 7.25
k = 74.3646 + 1.395833 * T
lamda = true_longitude(t) - 0.00569
omega = apparent_longitude(t)
lamda2 = lamda - 0.00479 * math.sin(np.radians(omega))
diff = np.radians(lamda - k)
x = np.degrees(math.atan(-math.cos(np.radians(lamda2) * math.tan(np.radians(ob1)))))
y = np.degrees(math.atan(-math.cos(diff) * math.tan(np.radians(i))))
result = x + y
return result
def heliographic_solar_center(t=None):
"""Returns the position of the solar center in heliographic coordinates."""
jd = util.julian_day(t)
T = util.julian_centuries(t)
# Heliographic coordinates in degrees
theta = (jd - 2398220) * 360 / 25.38
i = 7.25
k = 74.3646 + 1.395833 * T
lamda = true_longitude(t) - 0.00569
omega = apparent_longitude(t)
lamda2 = lamda - 0.00479 * math.sin(np.radians(omega))
diff = np.radians(lamda - k)
# Latitude at center of disk (deg):
he_lat = np.degrees(math.asin(math.sin(diff) * math.sin(np.radians(i))))
# Longitude at center of disk (deg):
y = -math.sin(diff) * math.cos(np.radians(i))
x = -math.cos(diff)
rpol = cmath.polar(complex(x, y))
he_lon = np.degrees(rpol[1]) - theta
he_lon = he_lon % 360
if he_lon < 0:
he_lon = he_lon + 360.0
return [he_lon, he_lat]
def mean_ecliptic_longitude(t=None):
"""Returns the mean ecliptic longitude."""
T = util.julian_centuries(t)
result = 279.696680 + 36000.76892 * T + 0.0003025 * T ** 2
result = result % 360.0
return result
def eccentricity_SunEarth_orbit(t=None):
"""Returns the eccentricity of the Sun Earth Orbit."""
T = util.julian_centuries(t)
result = 0.016751040 - 0.00004180 * T - 0.0000001260 * T ** 2
return result
def true_obliquity_of_ecliptic(t=None):
T = util.julian_centuries(t)
result = 23.452294 - 0.0130125 * T - 0.00000164 * T ** 2 + 0.000000503 * T ** 3
return result
def geometric_mean_longitude(t=None):
"""Returns the geometric mean longitude (in degrees)"""
T = util.julian_centuries(t)
result = 279.696680 + 36000.76892 * T + 0.0003025 * T ** 2
result = result % 360.0
return result
