Two satellites of earth `S_(1)` and `S_(2)` are moving in the same orbit. The mass of `S_(1)` is four times the mass of `S_(2)`. Which one of the following statements is true?

Options

A. The potential energies of earth and satellite in the two cases are equal
B. `S_(1)` and `S_(2)` are moving with the same period
C. The kinetic energy of two satellites are equal
D. The time period of `S_(1)` is four times that `S_(2)`.

Answer

B

Explanation

Both period orbital speed of satellite `v_(0)=sqrt((GM_(E))/r)` and time period of revolution of satellite, `T=[(4pi^(2)r^(3))/(GM_(E))]^(1//2)` are independent of mass of satellite. Therefore orbital speed and time period of revolution of both the satellites are same. Hence, option (b) is correct.
The kinetic energy of satellite, `K=(GM_(E)m)/(2r)` and potential energy of a satellite, `U=-(GM_(E)m)/r`
Both depends on mass of satellite, very with mass of satellite.