The formula for force is:

F = ma

The formula for the force of gravity is:

Fg = GMm ⁄ r ²

The force of gravity between the Earth and a body on its surface is the weight of the body.

The formula for kinetic energy is:

KE = ½ mv ²

The formula for gravitational potential energy is:

GPE = –GMm ⁄ r

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

Mechanical energy is equal to kinetic energy plus gravitational potential energy. The formula for mechanical energy is:

ME = ½ mv ² − GMm ⁄ r