Mercury's ellipse does not close. Its long axis creeps forward by an extra 43 arcseconds a century — a residual Newton's inverse-square law could not spend. Einstein spent it in one line of curved spacetime: the first triumph of general relativity. Rendered, not quoted — the engine computes the advance live from the metric.
A geodesic in the Schwarzschild metric is a Kepler ellipse plus a slow rotation of its apse. Per orbit the perihelion advances by
The Newtonian ellipse closes exactly (Bertrand's theorem: only inverse-square and Hooke forces give closed orbits). The apsidal angle for a force F∝rⁿ is π/√(3+n); for n=−2 it is exactly π, so precession is zero. The 1/c² term is the whole story — it vanishes as c→∞.
| a (semi-major) | — |
| e (eccentricity) | — |
| apsidal angle (n=−2) | — |
Mercury's turning orbit — Einstein 1915. Δφ=6πGM/(a(1−e²)c²) closes Le Verrier's 43-arcsec gap. The orbit is a geodesic of curved spacetime — the path the-geodesic bends. Closer in and more eccentric orbits precess faster; the binary pulsar PSR B1913+16 turns 4.2° per year by the same law.
Re-computes Δφ for Mercury on every render and compares to the measured 43″/century. Confirms green; flips red the instant the metric is tampered.
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Mercury's known orbit and the exact constants of gravity and light:
| G | 6.67430×10⁻¹¹ |
| c | 2.99792458×10⁸ |
| M☉ | 1.98892×10³⁰ |
| a | 5.79091×10¹⁰ m |
| e | 0.205630 |
| period | 87.969 d |
The rosette: a Kepler ellipse whose apse rotates by Δφ each lap (advance exaggerated for the eye; the number below is the true Mercury value).
| Δφ per orbit | — |
| orbits / century | — |
| advance / century | — |
The proven residual — general relativity, no free parameters:
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Le Verrier's unexplained 43″/century, delivered by 6πGM/(a(1−e²)c²).
The Newtonian ellipse precesses on its own. → No. Pure inverse-square gives a closed orbit (Bertrand); apsidal angle = π exactly, precession = 0.
The total observed shift (~5600″/cy) is the GR effect. → Most is coordinate (equinox) precession + planetary tugs; the GR piece is only the 43″ residual.
Drop a constant and it's "close enough." → Drop the 6 and you get ~7″ — see window 6. The coefficient is not decorative.
The disclosed planted void: replace 6πGM with πGM (one-sixth). Mercury's advance falls to ~7″/century and misses the measured 43. The WITNESS in window 7 catches it live.
selfcheck() re-plants this void headless every boot, asserts the value now differs, then restores — failing loud if the witness ever misses it.