Two heavenly bodies $S_1$ and $S_2$,not far from each other,are seen to revolve in orbits:

The centripetal force acting on a satellite orbiting around the Earth and the gravitational force of the Earth acting on the satellite are both equal to $F$. The net force on the satellite is

$A$ planet revolves around the Sun in an elliptical orbit. When it is closest to the Sun,its distance from the Sun is $1.6 \times 10^{12} \ m$ and its velocity is $60 \ m/s$. What is its velocity in $m/s$ when it is farthest from the Sun,given its distance is $8 \times 10^{12} \ m$?

$A$ double star is a system of two stars rotating about their centre of mass only under their mutual gravitational attraction. Let the stars have masses $m$ and $2m$ and their separation be $l$. Their time period of rotation about their centre of mass will be proportional to:

Two particles of equal mass $m$ move in a circle of radius $r$ under the action of their mutual gravitational attraction. The speed of each particle will be ($G=$ Universal gravitational constant).

An artificial satellite of mass $m$ revolves around the earth at a height $h$ with a speed $v$. How much power (energy per second) will it require to keep itself moving with constant speed in the orbit of radius $r$?