Define escape velocity. Derive an expression for escape velocity. Find the value of escape velocity.

Escape velocity is minimum velocity with which a body must be thrown upward so that it may just escape.
Expression for escape velocity:
Let a body of mass m be escaped from gravitational field of the earth. During the course of motion, let at any instant body be at a distance r from the centre of the earth.

The gravitational force between body and the earth is,
                               
and work done to raise the body by distance dr is,
                             
   Total work done W in raising the body from the surface of the earth to infinity is,
                             
                                 

If we throw the body upward with a velocity v_e, then work done to raise the body from surface of the earth to infinity is done by kinetic energy,
                                 
or                                
or                                 
Substituting the values, g = 9.81m/sec and R = 6.4 x 10⁶m, we have,