Match the following columns.

$A$. Potential energy of satellite	$I$. Positive
$B$. Total energy of satellite	$II$. Negative
$C$. Kinetic energy of satellite	$III$. Zero
$D$. Gravitational potential energy of satellite at infinity	$IV$. Infinity

$A$ 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

$A$ satellite orbits the Earth at a height of $400 \; km$ above the surface. How much energy must be expended to rocket the satellite out of the Earth's gravitational influence? (Mass of the satellite $= 200 \; kg$; mass of the Earth $= 6.0 \times 10^{24} \; kg$; radius of the Earth $= 6.4 \times 10^{6} \; m$; $G = 6.67 \times 10^{-11} \; N m^{2} kg^{-2}$)

$A$ 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 $9 R_E$?

$A$ 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.

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