Q. Two satellites of earth, $S_{1}\ and\ S_{2},$ are moving in the same orbit. The mass of $S_{1}$ is four times the mass of $S_{2}.$ Which one of the following statements is true?
A) The time period of $S_{1}$ is four times that of $S_{2}$
B) The potential energies of earth and satellite in the two cases are equal
C) $S_{1}$ and $S_{2}$ are moving with the same speed
D) The kinetic energies of the two satellites are equal
Explanation
(c) When two satellite of earth are moving in same orbit, then time period of both are equal. From Kepler’s third law
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ T^{2} \propto r^{3}$
Time period is independent of mass, hence their time periods will be equal.
The potential energy and kinetic energy are mass dependent, hence the PE and KE of satellites are not equal.
But, if they are orbiting in a same orbit, then they have equal orbital speed.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.