The motion of planets in the solar system is an example of the conservation of

$A$ planet is revolving around the sun in an elliptical orbit. Its closest distance from the sun is $r_{min}$,and the farthest distance from the sun is $r_{max}$. If the orbital angular velocity of the planet when it is nearest to the sun is $\omega$,then the orbital angular velocity at the point when it is at the farthest distance from the sun is:

$A$ satellite revolves around the earth in an elliptical orbit. Its speed

$Assertion$ : An astronaut experiences weightlessness in a space satellite.
$Reason$ : When a body falls freely,it does not experience gravity.

The period of moon's rotation around the earth is nearly $29$ days. If moon's mass were $2$ fold, its present value and all other things remained unchanged, the period of moon's rotation would be nearly ......... $days$.

Does the orbital velocity of a planet depend on its mass?