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?

Express the constant $k$ of $T^{2}=k(R_{E}+h)^{3}$ in days and kilometres. Given $k = 10^{-13} \; s^{2} \; m^{-3}$. The moon is at a distance of $3.84 \times 10^{5} \; km$ from the earth. Obtain its time period of revolution in days.

The motion of planets in the solar system is governed by which of the following conservation laws?

$A$ particle moves in a circular orbit of radius $r$ under a central attractive force $F = -\frac{k}{r}$,where $k$ is a constant. The periodic time of this motion is proportional to:

The percentage increase in the energy for an artificial satellite to shift it from an orbit of radius $r$ to an orbit of radius $\frac{3r}{2}$ is

An earth satellite of mass $m$ revolves in a circular orbit at a height $h$ from the surface of the earth. $R$ is the radius of the earth and $g$ is acceleration due to gravity at the surface of the earth. The velocity of the satellite in the orbit is given by