IOAA 2013, Теория, дълги задачи — Задача 1

$7^{th}$ International Olympiad on Astronomy & Astrophysics · 27 July – 5 August 2013, Volos Greece · Theoretical Exam - Long Questions · 27 юли 2013 г.

Условие

Question 1

In a homogeneous and isotropic universe, the matter (baryonic matter + dark matter) density parameter $\Omega_m=\frac{\rho_m}{\rho_c}=32\%$, where $\rho_m$ is the matter density and $\rho_c$ is the critical density of the Universe.

(1) Calculate the average matter density in our local neighbourhood.

(2) Calculate the escape velocity of a galaxy 100 Mpc away from us. Assume that the recession velocity of galaxies in Hubble's law equals the corresponding escape velocity at that distance, for the critical density of the Universe that we observe.

(3) The particular galaxy is orbiting around the centre of our cluster of galaxies on a circular orbit. What is the angular velocity of this galaxy on the sky?

(4) Will we ever discriminate two such galaxies that are initially at the same line of sight, if they are both moving on circular orbits but at different radii (answer “Yes” or “No”)?

[Assume that the Earth is located at the centre of our local cluster.]

Решение

Теми и трудност

Трудност: неоценена.

Галактики и космология · Небесна механика · Космология · Гравитационни системи

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Оригинал в Архива: LongQuestions.pdf