USAAAO 2024, I кръг — Задача 10
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
Ben Chen is an alien living on a system identical to earth, except his planet’s obliquity is . Located at latitude , he wants to observe M52. Due to the open cluster being so dim, Ben needs perfect conditions to observe M52. Due to atmospheric effects, M52 can only be observed above an altitude of . Additionally, it must be during astronomical twilight (when the Sun is more than below the horizon). Of the following dates, which is the earliest after the vernal equinox that Ben can observe the cluster? The coordinates of M52 are approximately and .
(a) April 21st
(b) June 21st
(c) August 21st
(d) October 21st
(e) December 21st
Отговори
- A
Решение
Solution:
Drawing a spherical triangle between the NCP, zenith, and M52 reveals that the hour angle at which M52 is at altitude is 6h51m. Drawing a spherical triangle between the Sun, NCP, and zenith reveals that the Sun’s hour angle at astronomical twilight is 7h39m. Since the Sun’s rises later throughout the year, relative to M52, the first case where M52 is observable is when M52 reaches right before the end of astronomical twilight. This means the Sun’s right ascension is 7h39m - 6h51m = 48m, which occurs 13 days after March 21st.
Answer: A
Оригинал в Архива: usaaao_first_exam_2024-3.pdf · официални решения: usaaao_first_exam_2024_solutions-1.pdf