The radius of a planet is R_1 and a satellite revolve round of in a circle of radius R_2. The time period of revolution is T. The acceleration due to the gravitation of the planet at its surface.

The radius of a planet is R_1 and a satellite revolve round of in a ci

1.	The radius of a planet is R_1 and a satellite revolve round of in a circle of radius R_2. The time period of revolution is T. The acceleration due to the gravitation of the planet at its surface.
Answer» Solution :ORBITAL VELOCITY of the satellite `V_0=SQRT(g^1R_2)` Where `g^1=g(R_1/R_2)^2` angular velocity `omega=V_0/R_2=sqrt(g^1/R_2)=sqrt((g(R_1)^2)/R_2^3)` But TIME period of revolution `T=(2pi)/omega=2pisqrt(R_2^3/(gR_1^2))` (or)`T^2=4pi^2 R_2^3/(gR_1^2)` (or) `g=(4pi^2)/T^2 R_2^3/R_1^2`