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 $\sqrt { 2 }$ .
B)2V.
C)V.
D)V/ $\sqrt { 2 }$ .
E)V/2.

Question

Quizplus · Accepted Answer

The orbital speed $ V $ of a satellite is given by $ V = \sqrt{\frac{GM}{r}} $. If the mass $ M $ of the planet is halved, the new speed $ V' $ becomes $ V' = \sqrt{\frac{G(M/2)}{r}} = \frac{V}{\sqrt{2}} $.

A Satellite Having Orbital Speed V Orbits a Planet of Mass