Two satellites of masses $m$ and $4m$ are revolving in the same orbit around the Earth. Which one of the following statements is correct?

If $r$ denotes the distance between the sun and the earth,then the angular momentum of the earth around the sun is proportional to

The rotation period of an earth satellite close to the surface of the earth is $83$ minutes. The time period of another earth satellite in an orbit at a distance of three earth radii from its surface will be .......... $\min$

Two satellites $S_{1}$ and $S_{2}$ are revolving around a planet in the opposite sense in coplanar circular concentric orbits. At time $t=0$,the satellites are farthest apart. The periods of revolution of $S_{1}$ and $S_{2}$ are $3 \,h$ and $24 \,h$,respectively. The radius of the orbit of $S_{1}$ is $3 \times 10^{4} \,km$. Then,the orbital speed of $S_{2}$ as observed from

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 is revolving around the sun in an elliptical orbit. Its closest distance from the sun is $r_{min}$,and the farthest distance from the sun is $r_{max}$. If the orbital angular velocity of the planet when it is nearest to the sun is $\omega$,then the orbital angular velocity at the point when it is at the farthest distance from the sun is: