Example: Consider the Earth-Moon system. We can equate the gravitational force and the centrifugal force, and determine scaling relations between fundamental parameters.

We define the angular velocity, or angular frequency, as follows.

[NMSU, N. Vogt]

We next consider the energy of the system.

With no external forces, the center of mass (COM) has no net forces acting upon it. Both bodies orbit around this point. Is the Earth-Moon system in equilibrium?

[NMSU, N. Vogt]

We can match the gravitational and centrifugal forces as follows.

For the case where m₁ >> m₂, r₁ << r₂, leading us towards a well-known result.