The time period of revolution of a satellite orbiting very close to a planet of radius $R$ is $T$. What is the period of revolution around another planet,whose radius is $3R$ but having the same density?

Choose the correct statement from the following: Weightlessness of an astronaut moving in a satellite is a situation of

$A$ man inside an artificial satellite feels weightlessness because the force of attraction due to the Earth is

Two satellites are launched at a distance $R$ from a planet of negligible radius. Both satellites are launched in the tangential direction. The first satellite launches correctly at a speed $v_0$ and enters a circular orbit. The second satellite,however,is launched at a speed $\frac{1}{2}v_0$. What is the minimum distance between the second satellite and the planet over the course of its orbit?

Imagine a light planet revolving around a very massive star in a circular orbit of radius $R$ with a period of revolution $T$. If the gravitational force of attraction between the planet and the star is proportional to $R^{-5/2}$,then ${T^2}$ is proportional to:

The centripetal force acting on a satellite orbiting around the Earth and the gravitational force of the Earth acting on the satellite are both equal to $F$. The net force on the satellite is