Relative Angular Momentum

In celestial mechanics, the relative angular momentum of an orbiting body relative to a central body is the moment of 's relative linear momentum:

where:

• is the orbital position vector of the orbiting body relative to the central body,
• is the orbital velocity vector of the orbiting body relative to the central body,
• is mass of the orbiting body.

For a body in an unperturbed orbit about a central body, the orbital plane is stationary, and the relative angular momentum is perpendicular to the orbital plane.
For perturbed orbits where the orbital plane is in motion, the relative angular momentum vector is perpendicular to the (osculating) orbital plane at only two points in the orbit.