The Mathematics of the Autumnal Equinox

The September equinox occurs around 22–23 September, but the 5th is a good time to discuss the mathematics of seasons. The equinox is when the Sun’s declination is 0°, crossing the celestial equator. Day and night are nearly equal (not exactly due to atmospheric refraction and the definition of sunrise/sunset). The date varies due to leap years and Earth’s elliptical orbit. The equation of time (analemma) shows how solar noon differs from mean noon. The equinox is a root of the equation of time. Spherical trigonometry gives the sunrise azimuth = 90° at the equator.