An artificial satellite of mass $500 \ kg$ is orbiting the Earth. If its areal velocity is $4 \times 10^4 \ m^2s^{-1}$,find its angular momentum.

An artificial satellite is moving around the Earth in a circular orbit with a speed equal to one-fourth the escape speed of a body from the surface of the Earth. The height of the satellite above the Earth's surface is ............ ($R$ is the radius of the Earth). (in $R$)

Two satellites of equal mass are launched in circular orbits at heights $R$ and $2R$ above the surface of the Earth. The ratio of their kinetic energies is ($R =$ radius of the Earth).

$A$ satellite is in an elliptic orbit around the Earth with an aphelion of $6R$ and a perihelion of $2R$,where $R = 6400 \, km$ is the radius of the Earth. Find the eccentricity of the orbit. Find the velocity of the satellite at apogee and perigee. What should be done if this satellite has to be transferred to a circular orbit of radius $6R$? $(G = 6.67 \times 10^{-11} \, SI \text{ units and } M = 6 \times 10^{24} \, kg)$

The orbital angular momentum of a satellite revolving at a distance $r$ from the centre is $L$. If the distance is increased to $16r$,then the new angular momentum will be

$A$ geostationary satellite is taken to a new orbit such that its distance from the centre of the earth is doubled. Find the time period of this satellite in the new orbit.