# What is the formula for gravitational potential energy?

### Peter Jones

Experienced and passionate tutor, and recent PhD recipient

Gravitational potential energy is a tricky concept. The GPE of an object of mass m at a distance r from another object of mass M is: U = - GmM/r where G is Newton's gravitational constant. This gives you the absolute value of GPE, which you study in A-level physics. Often we are interested in the *change* in GPE when moving an object through a height h. This is what you study at GCSE for example, and in AS. If the object with mass m moves from a distance r to a distance (r+h) away from the mass M then we can use the above formula to find the change in GPE: Change in GPE = - GmM/(r+h) + GmM/r If you are close to the surface of the earth then you can take r=R (radius of earth) and h is much much smaller than R. In this case, some A-level maths can convince you that the above formula reduces approximately to: Change in GPE = mgh where g= GM/R ~ 9.81, and this is the formula we all know and love.

### Usman Mohammed

Maths and Physics just got a whole lot easier...

GPE = mass x gravitational field strength x height Mass of the object is usually measured in kg. Gravitational field strength is a measure of “how strong gravity is”. On Earth it is 10 (N/kg) and on the moon it is about 2(N/kg). Height is the distance we move the object. We usually measure this in metres.