The motion of planets in the solar system is governed by which of the following conservation laws?

$A$ satellite of mass $m$ is revolving close to the surface of a planet of density $d$ with time period $T$. The value of the universal gravitational constant $G$ in terms of $d$ and $T$ is given by:

$A$ body moves in a circular orbit of radius $R$ under the action of a central force. The potential due to the central force is given by $V(r) = kr$ ($k$ is a positive constant). The period of revolution of the body is proportional to:

Two satellites $A$ and $B$ rotate around a planet in orbits having radii $4R$ and $R$ respectively. If the speed of satellite $A$ is $3V$,then the speed of satellite $B$ is: (in $V$)

$A$ 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:

Suppose an astronaut throws a spoon out of a spacecraft. Will the spoon fall to the Earth?