The angular momentum of a planet of mass $M$ moving around the sun in an elliptical orbit is $\overrightarrow{ L }$. The magnitude of the areal velocity of the planet is:

A planet takes $200$ days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution

The planet Mars has two moons, if one of them has a period $7\, hours,\, 30\, minutes$ and an orbital radius of $9.0 \times 10^{3}\, {km} .$ Find the mass of Mars.

$\left\{\operatorname{Given} \frac{4 \pi^{2}}{G}=6 \times 10^{11} {N}^{-1} {m}^{-2} {kg}^{2}\right\}$

A geostationary satellite is orbiting the earth at a height $5R$ above the surface of the earth , $R$ being the radius of the earth. The time period of another satellite in hours at a height of $2R$ from the surface of the earth is

The time period of a satellite of earth is $5\, hours$. If the separation between the centre of earth and the satellite is increased to $4\, times$ the previous value, the new time period will become ……. $h$