A satellite having orbital speed V orbits a planet of mass M.If the planet had half as much mass,the orbital speed of the satellite at the same distance from the center would be
A)V .
B)2V.
C)V.
D)V/ .
E)V/2.

Question

A satellite having orbital speed V orbits a planet of mass M.If the planet had half as much mass,the orbital speed of the satellite at the same distance from the center would be
A)V . 
B)2V. 
C)V. 
D)V/ . 
E)V/2.

Quizplus · Accepted Answer

According to Kepler's Third Law, the square of the orbital period (T) of a satellite is directly proportional to the cube of the semi-major axis (a) of its orbit. This means that T^2/a^3 is a constant. Therefore, if we keep the distance from the center of the planet the same, the orbital period of the satellite will remain unchanged. 
Now, the orbital speed of a satellite is given by V=sqrt(GM/r), where G is the gravitational constant, M is the mass of the planet, and r is the distance from the center of the planet. If we halve the mass of the planet, the new orbital speed (V') will be given by V'=sqrt((G(M/2))/r)=sqrt((GM)/2r)=V/sqrt(2). Therefore, the answer is D) V/sqrt(2).

A Satellite Having Orbital Speed V Orbits a Planet of Mass