USAAAO 2024, I кръг — Задача 30
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
VOIDED Austin is now observing LARES, but in this problem he is allowed to observe LARES at any declination. Assume that LARES is a uniform spherical ball, and for the purposes of this problem, assume that LARES is a perfect blackbody; i.e. THA-18N has an albedo of 0. What is the brightest apparent magnitude Austin can observe LARES? You can use the fact that the Sun’s apparent magnitude is .
(a) 6.78
(b) 7.77
(c) 8.76
(d) 9.75
(e) 10.74
Отговори
B
The question is printed as VOIDED; the official solutions still give answer B.
Решение
Solution:
The shortest distance Austin can be from LARES is simply its orbiting distance (when LARES is directly overhead Austin):
Let the radius of LARES be . Power LARES receives from the Sun:
Flux LARES emits to Boston:
Magnitude-Flux relation with the Sun:
Answer: B
Оригинал в Архива: usaaao_first_exam_2024-3.pdf · официални решения: usaaao_first_exam_2024_solutions-1.pdf