$A$ satellite of mass $m$ is revolving around the Earth of mass $M$ in an orbit of radius $r$ with constant angular velocity $\omega$. The angular momentum of the satellite is ($G$ = gravitational constant).

The planet Mars has two moons. If one of them has a period of $7\, \text{hours}, 30\, \text{minutes}$ and an orbital radius of $9.0 \times 10^{3}\, \text{km}$, find the mass of Mars. $\left\{\text{Given}: \frac{4 \pi^{2}}{G} = 6 \times 10^{11}\, \text{N}^{-1} \text{m}^{-2} \text{kg}^{2}\right\}$

$A$ planet revolves around the sun in an elliptical orbit. When it is closest to the sun,its distance from the sun is $d_1$ and its velocity is $v_1$. When it is farthest from the sun,its distance from the sun is $d_2$ and its velocity is $v_2$. Find the value of $v_2$.

The time period of a satellite,revolving above earth's surface at a height equal to $R$ will be (Given $g = \pi^2 \ m/s^2$,$R =$ radius of earth).

$A$ planet of mass $m$ moves in an elliptical orbit around an unknown star of mass $M$ such that its maximum and minimum distances from the star are equal to $r_1$ and $r_2$ respectively. The angular momentum of the planet relative to the centre of the star is

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