An artificial satellite of mass $m$ revolves around the earth at a height $h$ with a speed $v$. How much power (energy per second) will it require to keep itself moving with constant speed in the orbit of radius $r$?

$A$ satellite $S$ is moving in an elliptical orbit around the Earth. The mass of the satellite is very small compared to the mass of the Earth.

The largest and the shortest distance of the earth from the sun are ${r_1}$ and ${r_2}$ respectively. What is its distance from the sun when it is at a position perpendicular to the major axis of the orbit drawn from the sun?

$A$ 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

If $r$ represents the radius of the orbit of a satellite of mass $m$ moving around a planet of mass $M$,the velocity of the satellite is given by

The orbital speed of a satellite revolving around a planet in a circular orbit is $v_0$. If its speed is increased by $10 \%$,then ..........