USAAAO 2024, I кръг — Задача 20

USAAAO 2024 - First Round · 10 февруари 2024 г.

Problem writers

Wesley Andrade, Abhay Bestrapalli, Austin Chen, Justin Chen, Ved Gund, Hagan Hensley, Sandesh Kalantre, Evan Kim, David Lee, Joe McCarty, Arjun Patel, Sahil Pontula, Tara Rezaei, Raul Teixeira, Leo Yao, David Zhang

Условие

Imagine a very long cylindrical planet that has a satellite orbiting around it. Considering that the average density of the planet is $\rho$ and the radius is $R$, find the expression that relates the period $P$ of the satellite with its distance $d$ to the center of the planet.

(a) $\frac{2d}{R}\sqrt{\frac{2\pi}{G\rho}}$

(b) $\frac{d}{R}\sqrt{\frac{2\pi}{G\rho}}$

(c) $\frac{d}{2R}\sqrt{\frac{4\pi}{G\rho}}$

(d) $\frac{d}{R}\sqrt{\frac{4\pi}{G\rho}}$

(e) $\frac{d}{R}\sqrt{\frac{\pi}{G\rho}}$

Отговори

Решение

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Оригинал в Архива: usaaao_first_exam_2024-3.pdf · официални решения: usaaao_first_exam_2024_solutions-1.pdf