USAAAO — 2026 First Round

Lunar laser ranging experiments show that, due to tidal effects, the semi-major axis of the Moon’s orbit increases by around 38 mm per year. Assuming that the recession rate is constant, by approximately how much does this recession increase the Moon’s sidereal orbital period each year? The mass of the Moon is 7.3 × 10²² kg. Hint: (1 + x)^β ≈ 1 + βx for |x| ≪ 1.