A satellite `S_(1)` of mass m is revolving at a distance of R from centre of earth and the other satellite `S_(2)` of mass 4m is revolving at a distance of 4R from the centre of earth. The time periods of revolution of two satellites are in the raito 1 : n. Find the value of n.

Answer

8

Explanation

`V_(1)` and `V_(2)` are orbital velocities of satellites `S_(1)` and `S_(2)` and M is mass of earth.
`V_(1) = sqrt((GM)/(R )), V_(2) = sqrt((GM)/(4R))`
`(V_(1))/(V_(2)) = sqrt((GM.4R)/(R.G(M))) = 2`
`(T_(1))/(T_(2)) = (2pi r_(1) V_(2))/(V_(1) 2pi r_(2)) = (r_(1))/(r_(2)) (V_(2))/(V_(1))`
`= (1)/(4).(1)/(2) = (1)/(8)`
`T_(1) : T_(2) = 1:8`