def new_year(cls, gregorian_year):
"""Return fixed date of Observational (classical)
Nisan 1 occurring in Gregorian year, 'gregorian_year'."""
jan1 = GregorianDate.new_year(gregorian_year)
equinox = Solar.solar_longitude_after(Astro.SPRING, jan1)
sset = JAFFA.universal_from_standard(JAFFA.sunset(ifloor(equinox)))
return cls.phasis_on_or_after(ifloor(equinox) - (14 if (equinox < sset) else 13), JAFFA)
def minor_solar_term_on_or_after(cls, fixed_date):
"""Return moment (in Beijing) of the first Chinese minor solar
term (jieqi) on or after fixed date, 'fixed_date'. The minor terms
begin when the sun's longitude is an odd multiple of 15 degrees."""
s = Solar.solar_longitude(cls.midnight(fixed_date))
l = mod(30 * iceiling((s - 15) / 30) + 15, 360)
return cls.solar_longitude_on_or_after(l, fixed_date)
def major_solar_term_on_or_after(cls, fixed_date):
"""Return moment (in Beijing) of the first Chinese major
solar term (zhongqi) on or after fixed date, 'fixed_date'. The
major terms begin when the sun's longitude is a
multiple of 30 degrees."""
s = Solar.solar_longitude(cls.midnight(fixed_date))
l = mod(30 * iceiling(s / 30), 360)
return cls.solar_longitude_on_or_after(l, fixed_date)
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 sine_offset(self, local_time, alpha):
"""Return sine of angle between position of sun at
local time tee and when its depression is alpha at location, location.
Out of range when it does not occur."""
phi = self.latitude
tee_prime = self.universal_from_local(local_time)
delta = Astro.declination(tee_prime, mpf(0), Solar.solar_longitude(tee_prime))
return ((tan_degrees(phi) * tan_degrees(delta)) +
(sin_degrees(alpha) / (cos_degrees(delta) *
cos_degrees(phi))))
def lunar_phase(cls, tee):
"""Return the lunar phase, as an angle in degrees, at moment tee.
An angle of 0 means a new moon, 90 degrees means the
first quarter, 180 means a full moon, and 270 degrees
means the last quarter."""
phi = mod(cls.lunar_longitude(tee) - Solar.solar_longitude(tee), 360)
t0 = cls.nth_new_moon(0)
n = iround((tee - t0) / cls.MEAN_SYNODIC_MONTH)
phi_prime = (360 *
mod((tee - cls.nth_new_moon(n)) / cls.MEAN_SYNODIC_MONTH, 1))
if abs(phi - phi_prime) > 180:
return phi_prime
else:
return phi
def new_year_on_or_before(cls, fixed_date):
"""Return fixed date of Future Bahai New Year on or
before fixed date, 'fixed_date'."""
approx = Solar.estimate_prior_solar_longitude(Astro.SPRING, cls.sunset_in_haifa(fixed_date))
return next_int(ifloor(approx) - 1, lambda day: Solar.solar_longitude(cls.sunset_in_haifa(day)) <= Astro.SPRING + 2)
def sidereal_solar_longitude(tee):
"""Return sidereal solar longitude at moment, tee."""
return mod(Solar.solar_longitude(tee) - Astro.precession(tee) + SIDEREAL_START, 360)
def ayanamsha(tee):
"""Return the difference between tropical and sidereal solar longitude."""
return Solar.solar_longitude(tee) - sidereal_solar_longitude(tee)
def new_year_on_or_before(cls, date):
"""Return the fixed date of Astronomical Persian New Year on or
before fixed date, date."""
approx = Solar.estimate_prior_solar_longitude(Astro.SPRING, cls.midday_in_tehran(date))
return next_int(ifloor(approx) - 1, lambda day: (Solar.solar_longitude(cls.midday_in_tehran(day)) <= (Astro.SPRING + 2)))
def current_minor_solar_term(cls, fixed_date):
"""Return last Chinese minor solar term (jieqi) before date, 'fixed_date'."""
s = Solar.solar_longitude(cls.location(fixed_date).universal_from_standard(fixed_date))
return amod(3 + quotient(s - 15, 30), 12)
def major_solar_term(cls, fixed_date):
"""Return last Chinese major solar term (zhongqi) before
fixed date, 'fixed_date'."""
s = Solar.solar_longitude(cls.location(fixed_date).universal_from_standard(fixed_date))
return amod(2 + quotient(int(s), 30), 12)
def solar_longitude_on_or_after(cls, lam, fixed_date):
"""Return moment (Beijing time) of the first date on or after
fixed date, 'fixed_date', (Beijing time) when the solar longitude
will be 'lam' degrees."""
tee = Solar.solar_longitude_after(lam, cls.location(fixed_date).universal_from_standard(fixed_date))
return cls.location(tee).standard_from_universal(tee)
def winter_solstice_on_or_before(cls, fixed_date):
"""Return fixed date, in the Chinese zone, of winter solstice
on or before fixed date, 'fixed_date'."""
approx = Solar.estimate_prior_solar_longitude(Astro.WINTER, cls.midnight(fixed_date + 1))
return next_int(ifloor(approx) - 1, lambda day: Astro.WINTER < Solar.solar_longitude(cls.midnight(1 + day)))
def new_year_on_or_before(cls, date):
"""Return fixed date of French Revolutionary New Year on or
before fixed date, date."""
approx = Solar.estimate_prior_solar_longitude(Astro.AUTUMN, cls.midnight_in_paris(date))
return next_int(ifloor(approx) - 1, lambda day: Astro.AUTUMN <= Solar.solar_longitude(cls.midnight_in_paris(day)))
