← Theory of RelativityPart 2 — General Relativity · 13

Mercury’s Stubborn Orbit

▶ DRILL

Newton's gravity says a planet's orbit is a fixed ellipse — Mercury should retrace the same loop forever. It doesn't: the whole ellipse slowly spins around the Sun, tracing a flower-like rosette. Even after adding up the pulls of every other planet, Newton's math came up short by a stubborn 43 arcseconds per century — and Einstein's idea that the Sun curves the space around it predicted that leftover exactly. It was general relativity's first triumph. Use the Explain it for a kid / a grown-up switch to set the depth.

EXPLAIN IT FORsimple words & pictures
GRAVITY
SLOW-MOnormal
orbits: 0 · perihelion turned: 0°
☀️ Mercury's orbit slowly spins around — a rosette🔭 George watchingclosest pointSunMercury

The big idea — Mercury's orbit doesn't quite close up: the whole ellipse slowly spins around the Sun. Newton's gravity — even with every other planet added in — couldn't explain a stubborn leftover of 43 arcseconds per century. Einstein's general relativity, where the Sun curves the space around it, predicted that 43 exactly — its first triumph. (Here the wobble and the egg-shape are cranked way up so you can see them; the real turn is far too slow to notice in one orbit.)

# number43 arcseconds per century — the part of Mercury's precession Newton (plus all planets) can't explain
# formulaGR perihelion advance Δφ = 6πGM / (c²·a·(1 − e²)) per orbit
# scalethe rosette's spin and Mercury's eccentricity are hugely exaggerated; the real advance is ≈ 0.1″ per orbit
# historyLe Verrier flagged the anomaly in 1859; Einstein resolved it in 1915 — general relativity's first observational success