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 $R_e = 6370 \ km$).

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 around the earth has a total (kinetic + potential) energy $E_0$. Its potential energy is

Given below are two statements:
Statement $I:$ If $E$ be the total energy of a satellite moving around the earth,then its potential energy will be $\frac{E}{2}$.
Statement $II:$ The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy $E$.
In the light of the above statements,choose the most appropriate answer from the options given below.

Two satellites $A$ and $B$,with a mass ratio of $3:1$,are in circular orbits of radii $r$ and $4r$ respectively. The ratio of the total mechanical energy of $A$ to $B$ is:

The ratio of energy required to raise a satellite to a height $h$ above the earth's surface to that required to put it into the orbit at the same height is ($R=$ radius of earth).