USAAAO 2024, I кръг — Задача 8

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

The mass density of the Milky Way galaxy determines the orbital velocity of planets, stars, and other objects orbiting around its center. Assuming a constant surface mass density $\sigma$ for the Milky Way and modeling it as a perfect circular disk, identify the dependence of the circular orbital velocity $v(r)$ of a point mass at radius $r$ from the galaxy’s center.

(a) $1/\sqrt{r}$

(b) $1/r$

(c) $\sqrt{r}$

(d) $r$

(e) $r^{3/2}$

Отговори

Решение

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