Two satellites $A$ and $B$,having a ratio of masses $3 : 1$,are in circular orbits of radius $r$ and $4r$ respectively. Calculate the ratio of the total mechanical energy of $A$ and $B$.

What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ into a circular orbit at an altitude of $2R$?

$A$ satellite of mass $m$ is orbiting the Earth (of radius $R$) at a height equal to the radius of the Earth. The total energy of the satellite in terms of $g$ (acceleration due to gravity on Earth's surface) is

Write an equation of total energy of a satellite. Why is the total energy of a satellite negative?

An artificial satellite moving in a circular orbit at a distance $h$ from the centre of the Earth has a total energy $E_0$. Then,its potential energy is

$A$ satellite orbits the Earth at a height of $400 \; km$ above the surface. How much energy must be expended to rocket the satellite out of the Earth's gravitational influence? (Mass of the satellite $= 200 \; kg$; mass of the Earth $= 6.0 \times 10^{24} \; kg$; radius of the Earth $= 6.4 \times 10^{6} \; m$; $G = 6.67 \times 10^{-11} \; N m^{2} kg^{-2}$)