Mercury Perihelion Precession
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
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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