THE ORBITAL PRECESSION — a dart

THE ORBITAL PRECESSION the ellipse that slowly turns

A perfect 1/r² orbit closes into a fixed ellipse. Real orbits precess — the ellipse itself slowly rotates. Mercury’s perihelion advances 43 arcseconds per century that Newton could not explain; general relativity supplies exactly that, 6πGM / c²a(1−e²) per orbit. It was Einstein’s first triumph — a known anomaly, predicted to the arcsecond.

THE TECHNIQUE Δφ = 6πGM / c²a(1−e²) per orbit

The demo evaluates the denominator factor (1−e²) and confirms the GR precession is positive: live demo

HISTORY & CREDIT Einstein · 1915 (Mercury)

“All of Mercury’s precession is relativistic.” — most (~90%) is Newtonian from other planets; GR supplies the leftover 43″/century. cited

the drift · the perihelion advances a little each orbit.
the leftover · Newton + planets left 43″/century unexplained; GR gives 6πGM/c²a(1−e²).
1915 · Albert Einstein matched it to the arcsecond — general relativity’s first test.

An anomaly that became a proof. physics

RECOMMEND FOR I-13 the factor, on the compiler

On i-13, (1−e²) > 0 and the GR precession is positive (Mercury advances):

$ i13 run gw_precession.i13 # 6*pi*mu / (c^2 a (1-e^2)) RUN OK · 28 step(s) one_minus_e2 = 0.7975 positive = 1 mercury_precesses = 1

Recommend as a NULL — a theorem (B39). The GR precession per orbit is an exact function of the orbit; a pinned prediction, not a same-function difference. NULL — the ellipse that slowly turns.