USAAAO 2026, I кръг — Задача 27

USAAAO 2026 - First Round · 9 февруари 2026 г.

Problem writers

Problem writers: Srihari (Hari) Balaji, Vincent Bian, Ferdinand, Hagan Hensley, Elizabeth Lee, Joe McCarty, Lucas Pinheiro, Feodor Yevtushenko

Условие

When plotting the distribution of asteroids in the asteroid belt by their semi-major axis, we can see several regions, known as “Kirkwood gaps,” where asteroids’ orbits are unstable due to an orbital resonance with Jupiter (a=5.20a = 5.20 AU). What orbital resonance is responsible for the gap marked with the arrow?

(a) 8:5

(b) 11:6

Histogram of the number of asteroids n (x200/AU, axis 0 to 140) against semi-major axis a (AU) from 2 to 3.5; orange bars with clear gaps, one of them near a ≈ 2.82 AU marked by a small red arrow below the axis.

(c) 9:4

(d) 5:2

(e) 3:1

Отговори

Решение

Оригинал в Архива: usaaao_first_exam_2026.pdf · официални решения: usaaao_first_exam_solutions_2026.pdf