A satellite in a circular orbit of radius R around planet X has an orbital period T.If Planet X had one-fourth as much mass,the orbital period of this satellite in an orbit of the same radius would be
A) 4T.
B) 2T.
C) T
D) T/2.
E) T/4.

Question

A satellite in a circular orbit of radius R around planet X has an orbital period T.If Planet X had one-fourth as much mass,the orbital period of this satellite in an orbit of the same radius would be
A) 4T. 
B) 2T. 
C) T 
D) T/2. 
E) T/4.

Quizplus · Accepted Answer

The orbital period of a satellite in a circular orbit depends only on the mass of the central body and the orbital radius of the satellite. It is given by:

T = 2π√(R³/GM)

Where R is the radius of the orbit, G is the gravitational constant, and M is the mass of the central body.

If the mass of the central body is reduced by a factor of 4, the orbital period would become:

T' = 2π√(R³/G(M/4))
   = 2π√(R³/GM/2)
   = 2π/√2 √(R³/GM)
   = √2T

Therefore, the orbital period of the satellite would be 2 times its original period (i.e., 2T).

A Satellite in a Circular Orbit of Radius R Around