Orbital Mechanics: Gravity, Eccentricity & Kepler's Laws (2D)

The 3D original behind this page turned out to be a decorative "research station" template with fake slider dashboards and no gravity model at all, despite a title promising orbital mechanics and celestial-body interactions — so this 2D companion builds the real thing instead: a single massive body fixed at the origin and one or two orbiting bodies integrated under genuine Newtonian gravity (a sub-stepped semi-implicit scheme for numerical stability). Drag the central-mass slider to change the star's gravitational pull, or the launch-speed slider to launch a body slower than, equal to, or faster than the local circular velocity and watch the orbit shape respond — a near-circular ring, a stretched ellipse, or an unbound hyperbola that escapes entirely. Add a second body and switch on mutual gravity to see it perturb the first body's path, nudging its ellipse away from a clean Keplerian curve. A live panel derives distance, speed, eccentricity, semi-major axis, orbital period, specific energy and angular momentum straight from the body's current position and velocity — the same vis-viva and conic-section equations that describe real satellites and planets.