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.