$A$ satellite of mass $m$ is in a circular orbit of radius $2R_E$ around the Earth. The energy required to transfer it to a circular orbit of radius $4R_E$ is (where $M_E$ and $R_E$ are the mass and radius of the Earth,respectively).

If the time period of revolution of a satellite is $T$,then its kinetic energy is proportional to

An artificial satellite moves in a circular orbit around the earth. The total energy of the satellite is given by $E$. The potential energy of the satellite 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.

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:

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