The two bodies with masses and attract each other with a force .

Where .

Find the escape velocity that is needed to propel a rocket of mass out of the gravitational field of a planet with mass and radius .

Potential energy:

The gravitational potential energy between two objects at some separation is defined as the work required to move them from a zero reference point to that given separation.The zero reference point from gravitation is at an infinite separation.

Since the work required to move an object from the zero reference point of potential energy to some point in space is negative, the potential energy at that point is also considered negative.

.

Here is the mass of the earth, is mass of the propel, is the radius of earth.

.

The initial kinetic energy is .

Thus the total energy is equal to potential energy plus kinetic energy.

In order to escape the gravitational field the body must have total energy greater or equal to zero.

Substitute and .

.

The escape velocity is .

The escape velocity is .