HPC Tier Module
Mercury Perihelion Precession (GR)
Reproduce Mercury's 42.98 arcsec/century GR precession from the Schwarzschild geodesic, in your browser.
See it run - a worked example, 100% in this browser tab
The problem
Reproducing the classic general-relativity test - Mercury's anomalous perihelion advance - normally lives in a notebook with no in-browser, verifiable path.
The local-first solution
This plugin integrates the Schwarzschild geodesic orbit equation with RK4 in the browser, measures the per-orbit perihelion shift, and reproduces Einstein's published 42.98 arcsec/century as an earned residual against the literature value.
What it does
RK4 integration of u'' + u = GM/L^2 + 3GM u^2/c^2 over many orbits
Newton-refined perihelion detection where u'(phi) crosses zero
Measured per-orbit advance scaled to arcsec/century via Mercury's 415.2 orbits/century
Comparison to the closed-form 6 pi GM / c^2 a(1-e^2) and the published 42.98 arcsec/century
3D rosette visualization with a labeled, exaggeration-free measurement path
Honest scope
This is the weak-field, test-particle Schwarzschild result for a single planet around a static point mass - NOT full numerical relativity, NOT an N-body ephemeris, and it excludes the planetary perturbations that dominate Mercury's total observed precession. The 42.98 arcsec/century is specifically the GR residual; the 3D rosette may exaggerate the GR term for visibility, labeled, while the reported number uses true constants.
Authorities cited
- A. Einstein (1915). Erklarung der Perihelbewegung des Merkur aus der allgemeinen Relativitatstheorie. Sitzungsber. Preuss. Akad. Wiss., 831-839 (perihelion of Mercury: 43 arcsec/century).
- C. W. Misner, K. S. Thorne, J. A. Wheeler (1973). Gravitation. W. H. Freeman, Sec. 25.3 - Delta_phi = 6 pi G M / (c^2 a (1-e^2)).
- Observed GR residual: 42.98 +/- 0.04 arcsec/century (after planetary perturbations removed).
Measure the GR precession
Run the integration in the browser and save the result to Sandbox, attach it to a Worklog case, or route it into a Gate client portal. Nothing is uploaded to anyone's cloud.