🪐 Solar System 2D — Real N-Body Gravity

It is a real N-body integration. Every step, the gravitational force between every pair of bodies (Sun-planet and planet-planet) is computed from Newton's law and used to update velocities and positions with a leapfrog integrator. Nothing about a planet's speed or path is scripted; both emerge from the physics, which is why the app can measure each planet's period directly from its motion and compare it to the textbook value.

Each planet starts at its real perihelion distance with the exact perihelion velocity for its real eccentricity, then gravity does the rest. Kepler's third law, T squared proportional to a cubed, is never hard-coded; it is a consequence of integrating F=Gm1m2/r2 over time, which is confirmed by the live "simulated period" readout converging to the real value.

Distance is measured in astronomical units (AU, Earth's average Sun distance), time in years, and mass in solar masses, chosen so that G times the Sun's mass equals exactly 4*pi^2 — a standard convention in celestial mechanics that keeps the numbers manageable while remaining physically exact.

Mercury completes an orbit in about a quarter of a year, so at high time-scale a single large step per frame would be too coarse and the symplectic leapfrog integrator would drift or become unstable. The simulation automatically splits each frame's requested time jump into many smaller sub-steps (capped for performance) so even Mercury's orbit stays accurate and energy-conserving.

The 3D version places each planet on a circular path with a hand-tuned angular speed for visual effect. This 2D version instead simulates real gravity between real masses on real elliptical orbits, so the motion — including each orbit's eccentricity and every planet's measured period — is a genuine physical result rather than an animation.