Perihelion Precession — General Relativity vs Newton

Relativistic Correction

GR correction strength 6.0×

Orbit eccentricity 0.55

Central mass (M) 1.00

Simulation speed 1.0×

Live Readouts

Orbital radius r

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Orbits completed

Last precession Δφ

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Avg precession/orbit

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How it works

Newtonian gravity alone gives a closed, non-rotating ellipse — the perihelion (closest point) always lands in the same spot. General relativity adds a small extra pull that falls off as 1/r⁴, which breaks that closure: the ellipse itself slowly rotates, tracing a rosette. This is exactly the mechanism behind Mercury's famous 43″-per-century anomalous perihelion shift, the first real experimental confirmation of GR (1915).

Newtonian:      a = -GM/r² r̂
GR correction:  a = -GM/r² r̂ · [1 + k·L²/(c²r²)]
Per-orbit shift (real Mercury): Δφ = 6πGM / (c²·a(1-e²))

The simulator integrates the full radial equation of motion with a symplectic (leapfrog) scheme so energy and angular momentum stay conserved over thousands of steps. The correction term is scaled by GM·L²/c² — since the real effect is a fraction of an arcsecond per orbit, the GR correction strength slider exaggerates the coefficient so the rosette is visible within a handful of orbits; at 0 the orbit is exactly a fixed Newtonian ellipse.

GR correction strength — multiplies the 1/r⁴ relativistic term; 0 disables it entirely.
Eccentricity — how elongated the starting ellipse is (0 = circle).
Central mass — scales GM, which sets orbital speed and period.
Precession is detected live: each time the orbit passes through perihelion (closest approach), the simulator records the angle and reports how far it has rotated since the previous pass.

Orbiting body Central mass Perihelion markers

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