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

$A$ body is moving in a low circular orbit about a planet of mass $M$ and radius $R$. The radius of the orbit can be taken to be $R$ itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is

An earth satellite of mass $m$ revolves in a circular orbit at a height $h$ from the surface of the earth. $R$ is the radius of the earth and $g$ is acceleration due to gravity at the surface of the earth. The velocity of the satellite in the orbit is given by

$A$ test particle is moving in a circular orbit in the gravitational field produced by a mass density $\rho(r) = \frac{K}{r^2}$. Identify the correct relation between the radius $R$ of the particle's orbit and its period $T$.

$A$ satellite can be in a geostationary orbit around a planet at a distance $r$ from the centre of the planet. If the angular velocity of the planet about its axis doubles,a satellite can now be in a geostationary orbit around the planet if its distance from the centre of the planet is

$A$ spaceship approaches the moon (mass $= M$,radius $= R$) along a parabolic path which is almost tangential to its surface. At the moment of maximum approach,the brake rocket is fired to convert the spaceship into a satellite of the moon. Find the change in speed.