A satellite of mass $m$ moves in a circular orbit of radius $r$ around the earth. Calculate the total energy required to place the satellite in the orbit from the earth's surface. Assuming initially it to be at rest.

A satellite is lifted from earth to a height $h.$ Let the work done by the external agent be $W_1.$ Then it is projected with a speed $v$ so as to move in a circular orbit doing an extra work $W_2.$ Compare these works done.

A spaceship is launched into a circular orbit close to the earth's surface. What additional velocity has now to be imparted to the spaceship in the orbit to overcome the gravitational pull?

[ Radius of the earth $=6,400 \mathrm{km},g=9.8 \mathrm{m}{ \mathrm{s}}^{-2}$]

An artificial satellite is moving in a circular orbit around the Earth with a speed equal to half the magnitude of escape velocity from the Earth.
(a) Determine the height of the satellite above the Earth's surface.
(b) If the satellite is stopped suddenly in its orbit and allowed to fall freely on the Earth, find the speed with which it hits and surface of Earth.

Given $M=$Mass of Earth & $R=$Radius of earth.