In a satellite,if the time of revolution is $T$,then the potential energy $(PE)$ is proportional to ..........

An astronaut takes a ball of mass $m$ from Earth to space. He throws the ball into a circular orbit about Earth at an altitude of $318.5 \ km$. From Earth's surface to the orbit,the change in total mechanical energy of the ball is $x \frac{GM_e m}{21 R_e}$. The value of $x$ is (take $R_e = 6370 \ km$).

What is the ratio of the kinetic energies of two satellites at heights $R$ and $3R$ from the surface of the Earth? ($R$ = radius of the Earth)

Binding energy of a revolving satellite at height $h$ is $3.5 \times 10^8 \ J$. 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 $= 6.4 \times 10^{6} \; m$; $G = 6.67 \times 10^{-11} \; N m^{2} kg^{-2}$)

$A$ satellite is revolving around the Earth with orbital speed $v_0$. If it stops suddenly,the speed with which it will strike the surface of the Earth would be: ($v_e =$ escape velocity of a particle on the Earth's surface)