Why not just add a small planet to Newton's model?

Perturbations from other planets already explain most of Mercury's precession (~532″/century in older analyses). The leftover ~43″/century is what GR explains; turning GR off in the simulator mimics "Newton + known planets" at a cartoon level.

Does the formula include all GR effects?

The displayed Δω is the leading weak-field result for a test particle. Higher multipoles of the Sun, frame dragging from solar rotation, and solar oblateness give smaller corrections relevant to precision ephemerides.

Mercury Perihelion Precession

GR Δω per orbit vs Newton; ~43″/century readout; amplified animation.

About this model

In pure Newtonian gravity with an ideal inverse-square central force, bound orbits are closed ellipses with a fixed perihelion direction. General relativity predicts an additional slow rotation of that axis: for nearly Keplerian motion the lowest-order Schwarzschild contribution gives Δω ≈ 6πGM/(c²a(1−e²)) radians per orbit. Mercury's excess perihelion advance, about 43 arcseconds per century after subtracting planetary perturbations, was an early triumph of GR. The simulator separates a large animation gain so the pink perihelion arm visibly creeps, while numeric readouts quote the physical small-angle formula with Mercury-like semi-major axis and adjustable eccentricity.

Who it's for: Intermediate mechanics students who have seen Kepler's laws; bridges to gravitational lensing and black-hole pages conceptually.

Key terms

Perihelion precession
General relativity
Schwarzschild metric
Mercury
Inverse-square law
Orbital eccentricity
Arcseconds per century

How it works

Newtonian inverse-square orbits are closed ellipses with a fixed perihelion direction. General relativity adds a small non-Newtonian correction that makes the axis precess: to leading order Δω ≈ 6πGM/(c²a(1−e²)) radians per orbit for a nearly Keplerian path. For Mercury, this is only about 43 arcseconds per century after subtracting planetary perturbations—famous early test of GR. The canvas greatly amplifies the rotation of the perihelion line so you can see the effect; numeric readouts use the physical formula. Set GR strength to 0 for a frozen perihelion arm.

Key equations

Δω_orbit ≈ 6πGM⊙/(c²a(1−e²)) rad · ~43″/century Mercury (net GR)

Frequently asked questions

Why not just add a small planet to Newton's model?: Perturbations from other planets already explain most of Mercury's precession (~532″/century in older analyses). The leftover ~43″/century is what GR explains; turning GR off in the simulator mimics "Newton + known planets" at a cartoon level.
Does the formula include all GR effects?: The displayed Δω is the leading weak-field result for a test particle. Higher multipoles of the Sun, frame dragging from solar rotation, and solar oblateness give smaller corrections relevant to precision ephemerides.

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Mercury Perihelion Precession

About this model

How it works

Key equations

Frequently asked questions

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Mercury Perihelion Precession

About this model

How it works

Key equations

Frequently asked questions