The formula for gravitational potential energy is:

GPE = − GMm / r

They get this formula by integrating the formula for the force of gravity.

The value of GM for the Earth is 399 trillion meters cubed per seconds squared. The mean radius of the Earth is 6,371,000 meters. The gravitational potential energy of a one kilogram body on the surface of the Earth is:

GPE = − 399 trillion m ³ ∕ s ² × 1 kg ÷ 6,371,000 m = − 62,627,531 J

The gravitational potential energy of a one kilogram body at a height of one meter is:

GPE = − 399 trillion m ³ ∕ s ² × 1 kg ÷ 6,371,001 m = − 62,627,521 J

If a one kilogram body falls one meter near the surface f the Earth, the change in gravitational potential energy is:

ΔGPE = − 62,627,531 J − − 62,627,521 J = − 10 J

If a body is raised to a height, the gravity bonds between the body and the Earth get weaker. Weaker bonds mean more energy. The energy that goes up when a body is raised to a height is gravitational potential energy.

The formula for rest weight is:

RW = GMm / r

The rest weight of a one kilogram body on the surface of the Earth is:

RW = = 399 trillion m ³ ∕ s ² × 1 kg ÷ 6,371,000 m = 62,627,531 J

The rest weight of a one kilogram body at a height of one meter is:

RW = = 399 trillion m ³ ∕ s ² × 1 kg ÷ 6,371,001 m = 62,627,521 J

If a one kilogram body falls one meter near the surface f the Earth, the change in rest weight is:

ΔRW = 62,627,531 J − 62,627,521 J = 10 J

Gravitational potential energy go down the same amount as rest weigh goes up. The gravitational potential energy of the body goes down ten joules.