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

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

Quizplus · Accepted Answer

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

A Satellite Having Orbital Speed V Orbits a Planet