$A$ satellite is revolving around a planet of mass $M$ in an elliptical orbit of semi-major axis $a$. What is the speed of the satellite when it is at a distance $a/2$ from the planet?

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 $2R$ is

In order to shift a body of mass $m$ from a circular orbit of radius $3R$ to a higher radius $5R$ around the earth,the work done is

$A$ star like the sun has several bodies moving around it at different distances. Consider that all of them are moving in circular orbits. Let $r$ be the distance of the body from the centre of the star and let its linear velocity be $v$,angular velocity $\omega$,kinetic energy $K$,gravitational potential energy $U$,total energy $E$ and angular momentum $l$. As the radius $r$ of the orbit increases,determine which of the above quantities increase and which ones decrease.

Obtain an expression for the total energy of a satellite revolving around the Earth.

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