Binding Energy
The energy required to remove a satellite from its orbit around the earth ( planet ) to infinity is called binding energy of the satellite .
Binding energy of the satellite of mass m is given by BE = + GMm / 2r
Escape Velocity
Escape velocity on earth is the minimum velocity with which a body has to be projected vertically upwards from the earth ’ s surface so that it just crosses the earth ’ s gravitational field and never returns .
Escape velocity of any object ve = √2GM / R = √2gR = √8πp GR 2 / 3
Escape velocity does not depend upon the mass or shape or size of the body as well as the direction of projection of the body .
Escape velocity at earth is 11.2 km / s .
Some Important Escape Velocities
Heavenly body Escape velocity Moon 2.3 km / s Mercury 4.28 km / s Earth 11.2 km / s Jupiter 60 km / s Sun 618 km / s Neutron star 2 x 10 5 km / s
Relation between escape velocity and orbital velocity of the satellite
ve = √2 vo
If velocity of projection U is equal the escape velocity ( v = ve ), then the satellite will escape away following a parabolic path .
If velocity of projection u of satellite is greater than the escape velocity ( v > ve ), then the satellite will escape away following a hyperbolic path .