def visible_crescent(self, date):
"""Return S. K. Shaukat's criterion for likely
visibility of crescent moon on eve of date 'date',
at location 'location'."""
tee = self.universal_from_standard(self.dusk(date - 1, mpf(4.5)))
phase = Lunar.lunar_phase(tee)
altitude = self.lunar_altitude(tee)
arc_of_light = arccos_degrees(cos_degrees(Lunar.lunar_latitude(tee)) * cos_degrees(phase))
return ((Lunar.NEW < phase < Lunar.FIRST_QUARTER) and
(mpf(10.6) <= arc_of_light <= 90) and
(altitude > mpf(4.1)))
def lunar_altitude(self, tee):
"""Return the geocentric altitude of moon at moment, tee,
at location, location, as a small positive/negative angle in degrees,
ignoring parallax and refraction. Adapted from 'Astronomical
Algorithms' by Jean Meeus, Willmann_Bell, Inc., 1998."""
lamb = Lunar.lunar_longitude(tee)
beta = Lunar.lunar_latitude(tee)
alpha = Astro.right_ascension(tee, beta, lamb)
delta = Astro.declination(tee, beta, lamb)
theta0 = Astro.sidereal_from_moment(tee)
cap_H = mod(theta0 + self.longitude - alpha, 360)
altitude = arcsin_degrees(
(sin_degrees(self.latitude) * sin_degrees(delta)) +
(cos_degrees(self.latitude) * cos_degrees(delta) * cos_degrees(cap_H)))
return mod(altitude + 180, 360) - 180
def phasis_on_or_before(self, date):
"""Return the closest fixed date on or before date 'date', when crescent
moon first became visible at location 'location'."""
mean = date - ifloor(Lunar.lunar_phase(date + 1) / 360.0 * Lunar.MEAN_SYNODIC_MONTH)
tau = ((mean - 30)
if (((date - mean) <= 3) and (not self.visible_crescent(date)))
else (mean - 2))
return next_int(tau, lambda d: self.visible_crescent(d))
def lunar_parallax(self, tee):
"""Return the parallax of moon at moment, tee, at location, location.
Adapted from "Astronomical Algorithms" by Jean Meeus,
Willmann_Bell, Inc., 1998."""
geo = self.lunar_altitude(tee)
Delta = Lunar.lunar_distance(tee)
alt = 6378140 / Delta
arg = alt * cos_degrees(geo)
return arcsin_degrees(arg)
def moonrise(self, date):
"""Return the standard time of moonrise on fixed, date,
and location, location."""
t = self.universal_from_standard(date)
waning = (Lunar.lunar_phase(t) > 180)
alt = self.observed_lunar_altitude(t)
offset = alt / 360
if waning and (offset > 0):
approx = t + 1 - offset
elif waning:
approx = t - offset
else:
approx = t + (1 / 2) + offset
rise = binary_search(approx - Clock.days_from_hours(3),
approx + Clock.days_from_hours(3),
lambda u, l: ((u - l) < Clock.days_from_hours(1/60)),
lambda x: self.observed_lunar_altitude(x) > 0)
if rise < (t + 1):
return self.standard_from_universal(rise)
raise ValueError()
def sidereal_lunar_longitude(tee):
"""Return sidereal lunar longitude at moment, tee."""
return mod(Lunar.lunar_longitude(tee) - Astro.precession(tee) + SIDEREAL_START, 360)
def new_moon_on_or_after(cls, fixed_date):
"""Return fixed date (Beijing) of first new moon on or after
fixed date, 'fixed_date'."""
tee = Lunar.new_moon_at_or_after(cls.midnight(fixed_date))
return ifloor(cls.chinese_location(tee).standard_from_universal(tee))
def new_moon_before(cls, fixed_date):
"""Return fixed date (Beijing) of first new moon before fixed date, 'fixed_date'."""
tee = Lunar.new_moon_before(cls.midnight(fixed_date))
return ifloor(cls.location(tee).standard_from_universal(tee))
def phasis_on_or_after(cls, fixed_date, location):
"""Return closest fixed date on or after date, date, on the eve
of which crescent moon first became visible at location, location."""
mean = fixed_date - ifloor(Lunar.lunar_phase(fixed_date + 1) / mpf(360) * Lunar.MEAN_SYNODIC_MONTH)
tau = fixed_date if fixed_date - mean <= 3 and not location.visible_crescent(fixed_date - 1) else mean + 29
return next_int(tau, lambda d: location.visible_crescent(d))
