Two satellites of masses $m_1$ and $m_2$ $(m_1 > m_2)$ are revolving around the Earth in circular orbits of radii $r_1$ and $r_2$ $(r_1 > r_2)$ respectively. Which of the following statements is true regarding their speeds $v_1$ and $v_2$?

$A$ satellite is revolving very close to a planet of density $\rho$. The period of revolution of the satellite is

$A$ geostationary satellite above the equator is orbiting around the earth at a fixed distance $r_1$ from the center of the earth. $A$ second satellite is orbiting in the equatorial plane in the opposite direction to the earth's rotation,at a distance $r_2$ from the center of the earth,such that $r_1 = 1.21 r_2$. The time period of the second satellite as measured from the geostationary satellite is $\frac{24}{p}$ hours. The value of $p$ is $....$

The period of moon's rotation around the earth is nearly $29$ days. If moon's mass were $2$ fold, its present value and all other things remained unchanged, the period of moon's rotation would be nearly ......... $days$.

The period of a satellite in a circular orbit around a planet is independent of

Which of the following is the evidence to show that there must be a force acting on the earth and directed towards the sun?