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 sine_table(cls, entry):
"""Return the value for entry in the Hindu sine table.
Entry, entry, is an angle given as a multiplier of 225'."""
exact = 3438 * sin_degrees(entry * angle(0, 225, 0))
error = 0.215 * signum(exact) * signum(abs(exact) - 1716)
return iround(exact + error) / 3438
