expression for escape velocity of an object on the surface of earth.

Escape Velocity

• Escape velocity is defined to be the minimum velocity that an object must have in order to escape the gravitational field of the earth (i.e., escape the earth without ever falling back).

• Expression for escape velocity:

Assume earth to be a perfect sphere of mass M_E and radius R_E. A body of mass ‘m’ is projected from point ‘A’ on the surface of earth. Take two points, P and Q, on the line joining O and A.

Gravitational force of attraction on the body at point P is

Small amount of work done in bringing the body from P to Q against gravitational attraction,

Total work done in taking the body against gravitational attraction from the surface of earth to a region beyond the gravitational field of earth (i.e, from x = R_E to x = ∞) is given by,

This work done is at the cost of kinetic energy given to the body at the surface of the earth.

Kinetic energy of the body

Where, is the escape velocity of the body projected

As (),

For earth, g = 9.8 ms⁻², R_E = 6.4 × 10⁶ m