A satellite of mass m is revolving close to surface of planet of density d with time period T - Physics - Gravitation

Question

A satellite of mass m is revolving close to surface of planet of
density d with time period T the value of gravitational constant on
planet is given by

Vara · Accepted Answer

Expression for orbital velocity:

v=GMr=G43πr3Dr=G43πr2D

Expression for time period:

T=2πrv   =2πrG43πr2D  =4π2r2G43πr2D =3πGDT2=3πGDG=3πT2D

A satellite of mass m is revolving close to surface of planet of density d with time period T. the value of gravitational constant on planet is given by