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 $R_e = 6370 \ km$).

$A$ satellite has kinetic energy $K$,potential energy $V$,and total energy $E$. Which of the following statements is true?

If a satellite of mass $400 \, kg$ revolves around the earth in an orbit with speed $200 \, m/s$,then its potential energy is .......... $MJ$.

$A$ planet is moving in an elliptical orbit around the sun. If $T, V, E$,and $L$ stand respectively for its kinetic energy,gravitational potential energy,total energy,and magnitude of angular momentum about the centre of force,which of the following is correct?

$A$ 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 $= 6.4 \times 10^{6} \; m$; $G = 6.67 \times 10^{-11} \; N m^{2} kg^{-2}$)

When a satellite going round the Earth in a circular orbit of radius $r$ and speed $v$ loses some of its energy,then $r$ and $v$ change as: