Question

A few years ago, an X-ray telescope detected a source called Cygnus X-3, whose intensity changed with a period of 4.8 hours. This type of astronomical object emitting periodic signals could be a binary X-ray source, which is a star that is in orbit around a much more massive black hole. The period of the X-ray signal is then the period of the star’s orbit. If the distance between the centers of the star and the black hole is one-fiftieth of the distance between the centers of the Earth and our Sun, then determine how many times more massive the black hole is than our Sun. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Answer 1

Answer:

Explanation:

The star is revolving the black hole like earth revolves around the sun .so time period of rotation  T is given by the following relation

T² = $\frac{4\pi^2\times R^3}{GM }$ , R is distance between black hole and star , M is mass of black hole

Given T = 4.8 hours

4.8² =  $\frac{4\pi^2\times R^3}{GM }$

Using the same equation for earth sun system

24² =  $\frac{4\pi^2\times (50R)^3}{GM_s }$  , Ms is mass of the sun and 50R is distance between the sun and the earth .

Dividing the equation

$(\frac{4.8}{24})^2$ = $\frac{M_s}{M}\times\frac{1^3}{50^3}$

$\frac{M}{M_s}$ = 2x 10⁻⁴