Gravitational Potential

The definition of the gravitational potential field is

The potential is defined as the work done in bringing a body of unit mass from infinity to a point. Since work is done by gravity on the body the work done is negative.

In mathematical terms,

The zero for gravitational potential is taken at infinity because it is a convenient reference point for any object in the universe. Remember that for the zero of gravitational potential energy, we choose the Earth as a convenient reference point. There is no inconsistancy with this as only differences in potential are significant.

Gravitational potential is always negative indicating that the field does work in moving an object closer. The figure below shows the gravitational potential for the Earth and moon. The potential fields add together algebraically. We can see that to send a rocket to the moon we need only provide the force for the rocket to escape the Earths gravitational potential field and enter the moon’s gravitational potential field. After this the rocket will accelerate towards the moon by the pull of the moon’s potential.

The gravitational potentential of the Earth, Moon and their sum. The force on an object at a given potential is given by the slope of the potential at that point.