USAAAO 2026, I кръг — Задача 15

USAAAO 2026 - First Round · 9 февруари 2026 г.

Problem writers

Problem writers: Srihari (Hari) Balaji, Vincent Bian, Ferdinand, Hagan Hensley, Elizabeth Lee, Joe McCarty, Lucas Pinheiro, Feodor Yevtushenko

Условие

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 $7.3\times10^{22}$ kg. Hint: $(1+x)^{\beta} \approx 1 + \beta x$ for $|x| \ll 1$.

(a) 230 $\mu$s

(b) 350 $\mu$s

(c) 380 $\mu$s

(d) 690 $\mu$s

(e) 230 ms

Отговори

Решение

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Оригинал в Архива: usaaao_first_exam_2026.pdf · официални решения: usaaao_first_exam_solutions_2026.pdf