Two satellites of Earth, $S_1$ and $S_2$, are moving in the same orbit. The mass of $S_1$ is four times the ma

Question

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?

Accepted Answer

1. **Orbital Speed:** The orbital speed of a satellite orbiting the Earth is given by $v = \sqrt{\frac{GM_E}{r}}$, where $M_E$ is the mass of the Earth and $r$ is the orbital radius [Eq. 7.36]. This expression is independent of the mass of the satellite ($m$). Since both satellites are in the same orbit (same $r$), they move at the same speed.
2. **Time Period:** The time period is given by $T^2 = \frac{4\pi^2 r^3}{GM_E}$ [Eq. 7.38]. This is also independent of the satellite's mass. Thus, their time periods are equal.
3. **Potential Energy:** Potential energy is $V = -\frac{GM_E m}{r}$ [Eq. 7.41]. It is directly proportional to the mass of the satellite ($m$). Since $m_1 = 4m_2$, the potential energy of $S_1$ is four times that of $S_2$.
4. **Kinetic Energy:** Kinetic energy is $K = \frac{GM_E m}{2r}$ [Eq. 7.40]. It is also directly proportional to the mass $m$. Thus, the kinetic energy of $S_1$ is four times that of $S_2$.

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