Perihelion Precession — General Relativity vs Newton

Newton's law of gravitation predicts a perfectly closed elliptical orbit for a two-body system — the point of closest approach, the perihelion, never moves. Einstein's general relativity adds a small correction to that inverse-square force, and the correction is enough to make the ellipse itself slowly rotate around the central mass, orbit after orbit, tracing out a rosette pattern instead of retracing the same curve. This is precisely the mechanism behind the anomalous 43 arcseconds per century that Mercury's orbit shifts beyond what Newtonian mechanics (including the pull of the other planets) can explain — a discrepancy known since 1859 and resolved only when Einstein published general relativity in 1915. This simulator integrates the real two-body equation of motion, Newtonian plus a 1/r⁴ relativistic correction term, with a symplectic leapfrog integrator so momentum and energy stay physically conserved, and exaggerates the correction strength (tunable down to zero) so the precession is visible within a handful of orbits instead of requiring centuries of real time.