Escape Velocity: The minimum velocity with which a body should be projected from the surface of the earth so that it escapes from the earth's gravitational field, is called the escape velocity (Ve) of the body.
Find the variation of escape velocity
Escape velocity is a function of radius and gravitational field of the planet. Its value varies from planet to planet as radius and gravity changes.
Example: The ratio of the radius of a planet A to that of planet B is r. The ratio of accelerations due to gravity for the two planets is x. Find the ratio of the escape velocities from the two planets?
Solution: Escape Velocity is given by Ve=2gR Given RBRA=r and gBgA=x Taking ratio of the escape velocities of the 2 planets, VBVA=rx
Expression for Escape velocity
Consider a satellite of mass m, stationary on the surface of earth, then binding of the satellite on the surface of earth is given by B.E.=RGMm R - radius of earth To escape from the surface of earth, the Kinetic energy of satellite equivalent to binding energy. K.E. = B.E. 21mve2=RGMm ve=R2GM..........(1) We know that g=R2GM hence, ve=2gR..........(2)