IOAA 2015, Теория, кратки задачи, български — Задача 7

1

We have the total energy of the escaping galaxy:

$E_T = E_K + E_P = \frac{mV^2}{2} - \frac{GMm}{R}$

[15]

2

Where $V$ is velocity of galaxy and $R$ radius of galaxy cluster

Galaxy will escape from galaxy cluster if the total energy, $E_T = 0$

[10]

3

$E_T = 0 \rightarrow \frac{mV^2}{2} - \frac{GMm}{R} = 0$

$V^2 = \frac{2GM}{R}$

[15]

4

Escape velocity

[20]

5

Density of cluster

[15]

6

V=700 km/s

R=10 Mpc

$G=6.6378\times10^{-11}\mathrm{Nm^2kg}$

$\rho=9.20121\times10^{-27}\mathrm{kg/m^3}$

[25]