Density from Orbit

This formula lets you estimate the average density of a central body from the period of a very close circular orbit around it. It comes from setting the gravitational force equal to the centripetal force for orbital motion, then replacing the central body's mass with its density times volume. The result shows that a shorter orbital period around a given radius implies a denser object, and in the close-orbit limit the density can be inferred without knowing the body's size directly.

Use this when you know the orbital period of a satellite, moon, or test particle in a near-surface circular orbit and want an estimate of the central object's mean density. It is especially useful in astrophysics for compact objects or exoplanets when direct size measurements are difficult.

• Using a period in hours or days without converting to seconds
• Forgetting that this relation is for a close circular orbit, not a highly elliptical one
• Confusing mean density with surface density or local atmospheric density