Geodesics and perihelion precession simulation
In Newton’s gravity a single planet’s orbit is a perfect ellipse that closes on itself forever. General relativity adds a small extra term, and orbits no longer close: the point of closest approach creeps forward each lap. That is what explained Mercury.
Interactive, free and runs in your browser. Part of the General Relativity simulations.
What you will see
Bodies follow true Schwarzschild orbits around a black hole on a lit funnel of curved space, tracing rosettes as their closest point advances. A dashed Newtonian ellipse stays fixed beside them for comparison. Light rays pass by and bend towards the mass, more strongly the closer they pass.
Try this
- Watch one lap of the inner orbit and see where its closest point ends up.
- Increase the mass and watch the rosettes tighten as the precession grows.
- Compare the light ray that passes close with the one that passes far.
Common misconception
Precession is not caused by the other planets alone. They contribute most of Mercury’s precession, but 43 arcseconds per century was left unexplained until general relativity accounted for it exactly.
Exam-style question
For Mercury, the relativistic advance per orbit is Δφ = 6πGM/(c²a(1 − e²)) ≈ 5.0 × 10⁻⁷ rad. Mercury completes about 415 orbits per century. What is the advance per century in arcseconds?
415 × 5.0 × 10⁻⁷ rad ≈ 2.1 × 10⁻⁴ rad. Converting: 2.1 × 10⁻⁴ × 206 265 ≈ 43 arcseconds per century, the famous result.
Key equations
d²u/dφ² = M/L² − u + 3Mu²Δφ = 6πGM / c²a(1 − e²)δ ≈ 4GM / c²b
Curriculum
Enrichment beyond A-level, IB Physics A.5.