Earth revolves around the sun in a circular orbit of radius $R$. The angular momentum of the revolving earth is directly proportional to

Two stars of masses $M$ and $2M$ are at a distance $d$ apart and are revolving around their common center of mass. The angular velocity of the system of the two stars is ($G$ is the universal gravitational constant).

$A$ 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 $8 \times 10^{12} \ m$?

$A$ satellite revolves in the geostationary orbit but in a direction east to west. The time interval between its successive passing above a point on the equator is ........ $hrs$.

Two satellites $S_{1}$ and $S_{2}$ are revolving in circular orbits around a planet with radii $R_{1} = 3200 \, km$ and $R_{2} = 800 \, km$ respectively. The ratio of the speed of satellite $S_{1}$ to the speed of satellite $S_{2}$ in their respective orbits is $\frac{1}{x}$,where $x =$

$A$ planet is revolving around the sun in a circular orbit with a radius $r$. The time period is $T$. If the force between the planet and the star is proportional to $r^{-3/2}$,then the square of the time period is proportional to