The Laws of Orbital Mechanics
From Kepler's ellipses to the chaos of three bodies — each law reveals one piece of how things move through space.
- Kepler's First Law Planets orbit in ellipses with the Sun at one focus.
- Kepler's Second Law A line from planet to Sun sweeps equal areas in equal times.
- Kepler's Third Law Orbital period scales with orbit size.
- Newton's Gravitation Every mass attracts every other mass.
- Brachistochrone The fastest path under gravity is a cycloid.
- Escape Velocity The speed needed to leave a body forever.
- Hohmann Transfer The minimum-Δv transfer between two circular orbits.
- Gravity Assists Use a moving planet to trade energy and redirect a trajectory.
- Lagrange Points Stable and unstable balance points in rotating systems.
- Three-Body Problem Three gravitating bodies create sensitive, chaotic futures.