$A$ skylab of mass $m \ kg$ is first launched from the surface of the earth into a circular orbit of radius $2R$ (from the centre of the earth) and then it is shifted from this circular orbit to another circular orbit of radius $3R$. The minimum energy required to shift the lab from the first orbit to the second orbit is:

For a satellite,if the time of revolution is $T$,then its $K.E.$ is proportional to

$A$ satellite of mass $m$,initially at rest on the Earth,is launched into a circular orbit at a height equal to the radius of the Earth. The minimum energy required is

The additional kinetic energy to be provided to a satellite of mass $m$ revolving around a planet of mass $M$ to transfer it from a circular orbit of radius $R_1$ to another of radius $R_2$ $(R_2 > R_1)$ 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.

$A$ satellite of mass $m$ is in a circular orbit of radius $3 R_E$ about the Earth (mass of Earth $M_E$,radius of Earth $R_E$). How much additional energy is required to transfer the satellite to an orbit of radius $9 R_E$?