USAAAO 2024, I кръг — Задача 14
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 surface of the Sun exhibits differential rotation, with different rotational periods at different latitudes. We can measure this rotation speed using Doppler spectroscopy or by tracking the motion of sunspots.
If the rotation speed of the Sun’s surface at the equator is 2021 m/s, and at South is 809 m/s, how long would it take for a sunspot at the equator to do a full extra lap around the Sun compared to a sunspot at South?
(a) 6.2 days
(b) 25.0 days
(c) 31.2 days
(d) 41.7 days
(e) 126 days
Отговори
- E
Решение
Solution:
A point at latitude on the surface of a body of radius is located a distance away from the axis of rotation. Thus, the total distance a point on the surface needs to travel for one full rotation is . We can use this to find the orbital period as a function of the rotational velocity:
Plugging in the given values as well as the Sun’s radius for , we get days at the equator, and days at latitude.
The time it takes for one sunspot to do a full extra lap around the Sun relative to another is conceptually identical to the synodic period between two planets, and can be calculated by the same formula:
days
Answer: E
Оригинал в Архива: usaaao_first_exam_2024-3.pdf · официални решения: usaaao_first_exam_2024_solutions-1.pdf