Kepler's Laws
Interactive simulation — adjust parameters and watch the visualization update in real time.
How it works
Kepler I: bound orbits are ellipses with the central mass at one focus. Kepler II: the radius vector sweeps equal areas in equal times — here, colored wedges use equal Δt and should have nearly equal area (numerical spread shown). Kepler III: for this two-body model, T² ∝ a³ with constant GM; adjust a and GM and watch T²/a³ track the inverse of GM scaling.
Key equations
M = E − e sin E ···→ planet (a(cos E − e), b sin E)
T = 2π √(a³ / GM), n = 2π / T
dA/dt = L / (2m) = const.