$A$ particle of mass $m$ moves in a horizontal circle of radius $r$ under the influence of a centripetal force given by $F = -k/r^2$,where $k$ is a constant. Calculate the total energy of the particle.

$A$ satellite is revolving around a planet of mass $M$ in an elliptical orbit of semi-major axis $a$. What is the speed of the satellite when it is at a distance $a/2$ from the planet?

The total energy of a satellite in a circular orbit at a distance $(R+h)$ from the centre of the Earth varies as [ $R$ is the radius of the Earth and $h$ is the height of the orbit from Earth's surface].

The radius of the orbit of an Earth satellite is $R$. Its kinetic energy is proportional to:

If the time period of revolution of a satellite is $T$,then its kinetic energy is proportional to

$A$ satellite orbits the Earth at a height of $400 \; km$ above the surface. How much energy must be expended to rocket the satellite out of the Earth's gravitational influence? (Mass of the satellite $= 200 \; kg$; mass of the Earth $= 6.0 \times 10^{24} \; kg$; radius of the Earth $= 6.4 \times 10^{6} \; m$; $G = 6.67 \times 10^{-11} \; N m^{2} kg^{-2}$)