Kepler's Laws 2D: Elliptical Orbits & Equal-Area Sweep

This 2D orbital-mechanics lab solves the real two-body Kepler problem for four independent planets, each with its own adjustable semi-major axis and eccentricity. Every position on screen comes from Newton-Raphson solving Kepler's equation for the eccentric anomaly, not a scripted loop — so the shapes and speeds you see are the genuine physics. Reshape an orbit's eccentricity to watch it stretch from a circle into a narrow ellipse while its period stays fixed, then study the selected planet's equal-time sweep wedges: because orbital angular momentum is conserved, every wedge carries the same area even though the planet visibly speeds up near perihelion and crawls near aphelion — Kepler's Second Law made visible. The live table on the left checks Kepler's Third Law across all four planets at once, confirming that T squared divided by a cubed lands on the same constant, 4π² ≈ 39.48, regardless of how eccentric each orbit is.