The radius of a planet is $R$. $A$ satellite revolves around it in a circle of radius $r$ with angular velocity $\omega_0$. The acceleration due to gravity on the planet's surface is

$A$ body $A$ of mass $m$ is moving in a circular orbit of radius $R$ about a planet. Another body $B$ of mass $\frac{m}{2}$ collides with $A$ with a velocity which is half $\left(\frac{\overrightarrow{v}}{2}\right)$ the instantaneous velocity $\overrightarrow{v}$ of $A$. The collision is completely inelastic. Then,the combined body

An artificial satellite is placed into a circular orbit around the Earth at such a height that it always remains above a definite place on the surface of the Earth. Its height from the surface of the Earth is ........... $km$.

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).

The orbital angular momentum of a satellite is $L$,when it is revolving in a circular orbit at height $h$ from the earth's surface. If the distance of the satellite from the earth's centre is increased by eight times its initial value,then the new angular momentum will be $............\,L$.

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