Escape speed on the earth is defined as the minimum speed with which a body should be projected vertically upwards from the surface of the earth so that it just escapes out from gravitational field of the earth and never return on its own.
Let a body of mass m lying at distance x from the centre of the earth. Let M be the mass and R be the radius of the earth.
According to Newton’s law of gravitation, the gravitational force F of attraction between the body and the earth is given by
If dw be the work done to displace the body through a small distance dx, then
Thus the escape speed of a body depends upon the mass and radius of the planet from which the body is projected.