Two satellites of Earth, $S_1$ and $S_2$, are moving in the exact same circular orbit. The mass of $

Question

Two satellites of Earth, $S_1$ and $S_2$, are moving in the exact same circular orbit. The mass of $S_1$ is three times the mass of $S_2$. Which one of the following statements is true?

Professor PC Thomas Classes · Answer

(a) : For satellites in the same orbit, the orbital radius $r$ is identical. Orbital speed $v = \sqrt{\frac{GM}{r}}$ and time period $T = 2\pi \sqrt{\frac{r^3}{GM}}$ depend only on the mass of the central body ($M$) and orbital radius ($r$), making them independent of the satellite's mass. Thus, their speeds and time periods are equal. However, Kinetic Energy $K = \frac{GMm}{2r}$ is directly proportional to the mass $m$ of the satellite. Since $m_{S1} = 3m_{S2}$, it follows that $K_{S1} = 3 K_{S2}$.