Why the Moon Is the Hardest Object to Track

The Sun required just 3 sine terms for 0.01-degree accuracy. The Moon needs 60. Why such a dramatic difference? Three factors conspire to make lunar motion extraordinarily complex. First, proximity: the Moon orbits at 356,000 to 407,000 km — close enough that parallax (the shift in apparent position due to the observer's location on Earth's surface) reaches nearly 1 degree. Second, speed: the Moon covers ~13.2 degrees per day, completing a full orbit in 27.3 days. A small percentage error in position means a large error in time. Third and most importantly, the Sun's gravity: the Sun pulls on the Moon with a force comparable to Earth's, creating massive perturbations that simply don't exist for the Sun's apparent motion.

Five fundamental arguments drive all Moon position calculations. L' (Moon's mean longitude) ≈ 218.32° + 481267.88° x T — note the rate is 13.2x faster than the Sun's 36000.77°. D (mean elongation) = 297.85° + 445267.11° x T measures the angular separation between the Moon and Sun. M (Sun's mean anomaly) = 357.53° + 35999.05° x T — the same M used in the solar algorithm. M' (Moon's mean anomaly) = 134.96° + 477198.87° x T tracks position in the Moon's elliptical orbit. F (argument of latitude) = 93.27° + 483202.02° x T measures the Moon's distance from its orbital ascending node.