$A$ satellite of mass $m$ is placed at a distance $r$ from the centre of the Earth (mass $M$). The mechanical energy of the satellite is

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

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 $B$.

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.

$A$ satellite of mass $m$ rotates around the Earth in a circular orbit of radius $R$. If the angular momentum of the satellite is $J$, then its kinetic energy $(K)$ and the total energy $(E)$ of the satellite are:

$A$ satellite moves around the earth in a circular orbit of radius $r$ with speed $v$. If the mass of the satellite is $M$,its total energy is