Gravity and Orbits

Model planetary motion and orbital mechanics

Gravity provides the centripetal force needed for orbital motion. For circular orbits, v = √(GM/r) — the orbital speed depends only on the central mass and radius. Kepler's Third Law states T² ∝ r³ for all planets around the same star. Elliptical orbits arise when the initial velocity differs from the circular orbit speed. Escape velocity is √2 times the circular orbit speed.