Why Moonrise Is Harder Than Sunrise

For sunrise, we used an elegant hour-angle formula that assumes the Sun's position is essentially fixed during the rise event. The Sun moves only ~1° per day, so its declination and right ascension barely change in the ~6 hours between noon and sunrise. The Moon shatters this assumption. Moving ~13.2° per day means the Moon shifts ~0.5° in a single hour – comparable to the refraction and parallax corrections we're trying to apply. An analytical formula that computes moonrise from a "snapshot" position would be off by 10-30 minutes.

Three factors conspire to make moonrise especially difficult: (1) Rapid motion: the Moon completes a full orbit in 27.3 days versus the Sun's 365.25 – 13.4 times faster. (2) Large parallax: the Moon is close enough to Earth that the observer's surface position shifts the apparent Moon position by up to ~1° – 400 times larger than the Sun's 0.0025° parallax. (3) Variable semi-diameter: the Moon's elliptical orbit causes its apparent size to vary from 14.7' (apogee) to 16.7' (perigee), which also affects the rise threshold.