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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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 = , R is distance between black hole and star , M is mass of black hole

Given T = 4.8 hours

4.8² =  

Using the same equation for earth sun system

24² =    , Ms is mass of the sun and 50R is distance between the sun and the earth .

Dividing the equation

=

= 2x 10⁻⁴

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.