Question

Two satellites orbit the same planet. if a satellite A has an orbit radius r and satellite B has an orbit radius 2r, find the ratio of the period of satellite B to the period of satellite A.

Answer 1

Given :

Two satellites orbit the same planet. if a satellite A has an orbit radius r and satellite B has an orbit radius 2r.

To Find :

The ratio of the period of satellite B to the period of satellite A.

Solution :

We know, square of time period (T) is directly proportional to cube root of radius (r) .

So,

`(T_B^2)/(T_A^2)=((2r)^3)/(r^3)\\\\(T_B)/(T_A)=2√(2)`

Therefore, the ratio of the period of satellite B to the period of satellite A is 2√2 .