USAAAO 2026, I кръг — Задача 24
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
Suppose the Honeyhive galaxy and the Gold Leaf galaxy are diametrically opposite when viewed from the Earth, and the following sequence of events happens:
(a) A type Ia supernova happens in the Honeyhive galaxy.
(b) Astronomers on Earth measure the redshift of (the spectral lines) in the Honeyhive supernova to be . At the same time, another supernova happens in the Milky Way galaxy.
(c) Aliens in the Gold Leaf galaxy measure the redshifts of the the supernovae in the Honeyhive and Milky Way galaxies.
If the alien astronomers measure the redshift of the Milky Way supernova to be , what redshift would they measure for the Honeyhive supernova?
You may assume that the local velocities of the galaxies are negligible, that the universe is simple homogeneous, and isotropically expanding, and that redshift depends only on the scale factor and is the same function of distance for all observers.
(a) 0.2
(b) 0.4
(c) 1.3
(d) 1.7
(e) 2.7
Отговори
- D
Решение
Solution: Suppose some known spectral line in the Honeyhive galaxy supernova has wavelength . By the definition of redshift, this spectral line has wavelength when it reaches Earth. Similarly, any light emitted from the supernova in the Milky Way with have its wavelength multiplied by 1.8 when it reaches the Gold Leaf galaxy.
Since the light from the Honeyhive galaxy supernova passes through the Milky Way and starts heading towards the Gold Leaf galaxy at the same time as the Milky Way supernova, it will be redshifted by the same amount. Thus, any spectral line with wavelength at the time it leaves the Honeyhive galaxy will have wavelength , meaning the measured redshift for the Honeyhive galaxy will be .
Answer: D
Оригинал в Архива: usaaao_first_exam_2026.pdf · официални решения: usaaao_first_exam_solutions_2026.pdf