How do Kepler's laws apply to moons and artificial satellites?

Johannes Kepler’s laws of planetary motion are not limited to planets; they apply broadly to the motions of both natural and artificial satellites, as well as to stellar systems and extrasolar planets.1

Application to Moons and Satellites

• Orbital Geometry: Like planets orbiting the Sun, moons and artificial satellites follow elliptical paths around their primary bodies. For instance, the Moon and Earth orbit a common center of mass called the barycenter, which follows an elliptical path around the Sun in accordance with Kepler’s laws.12
• Variable Velocity: In line with Kepler’s second law, a satellite travels faster when it is closer to its primary body (perigee) and slower when it is farther away (apogee). This principle is observable in the Moon’s motion, where changes in speed contribute to libration, allowing observers on Earth to see slightly more than half of the lunar surface over time.23
• Generalization: Kepler’s laws apply to any bodies subject to inverse-square-law forces, such as gravity. While these laws provide a foundational framework, they do not account for complex gravitational perturbations caused by other bodies or non-gravitational factors, which are significant in multi-body systems.1