It is the specific velocity required for a setallite to remain, continuously moving around the earth, in a particular orbit. It is denoted by v0 . For the satellite to orbit around the earth, in a circular path of radius r, the centripetal force required is \(\frac{mv^2_0}{r}\) . This must be provided by the gravitational force exerted by earth on the satellite.
If h is the height of the satellite from the surface of the earth, then
r = R + h
Note that orbital velocity (v0) does not depend on the mass of the satellite.
Also, longer the radius of the orbit smaller will be the value of orbital velocity. If the satellite is very near to the earth surface, h << R, then
This shows that if the orbital velocity, of a satellite nearer to earth’s surface, is increased to √2 v0 , it will escape in to outer space.
Note that this means we are increasing the velocity of the satellite by 41.4% of its orbital velocity tomake it escape from the gravitational field of earth.
