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 direction(self, focus):
"""Return the angle (clockwise from North) to face focus when
standing in location, location. Subject to errors near focus and
its antipode."""
y = sin_degrees(focus.longitude - self.longitude)
x = ((cos_degrees(self.latitude) * tan_degrees(focus.latitude)) -
(sin_degrees(self.latitude) * cos_degrees(self.longitude - focus.longitude)))
if x == y == 0 or focus.latitude == 90:
return 0
elif focus.latitude == -90:
return 180
else:
return arctan_degrees(y, x)
def equation_of_time(cls, tee):
"""Return the equation of time (as fraction of day) for moment, tee.
Adapted from "Astronomical Algorithms" by Jean Meeus,
Willmann_Bell, Inc., 1991."""
c = cls.julian_centuries(tee)
lamb = poly(c, [mpf(280.46645), mpf(36000.76983), mpf(0.0003032)])
anomaly = poly(c, [mpf(357.52910), mpf(35999.05030), mpf(-0.0001559), mpf(-0.00000048)])
eccentricity = poly(c, [mpf(0.016708617), mpf(-0.000042037), mpf(-0.0000001236)])
varepsilon = cls.obliquity(tee)
y = pow(tan_degrees(varepsilon / 2), 2)
equation = ((1/2 / pi) *
(y * sin_degrees(2 * lamb) +
-2 * eccentricity * sin_degrees(anomaly) +
(4 * eccentricity * y * sin_degrees(anomaly) *
cos_degrees(2 * lamb)) +
-0.5 * y * y * sin_degrees(4 * lamb) +
-1.25 * eccentricity * eccentricity * sin_degrees(2 * anomaly)))
return signum(equation) * min(abs(equation), Clock.days_from_hours(mpf(12)))
def right_ascension(cls, tee, beta, lam):
"""Return right ascension at moment UT 'tee' of object at
latitude 'lam' and longitude 'beta'."""
varepsilon = cls.obliquity(tee)
return arctan_degrees((sin_degrees(lam) * cos_degrees(varepsilon)) - (tan_degrees(beta) * sin_degrees(varepsilon)), cos_degrees(lam))
