Foucault pendulum · Coriolis precession

Can a swinging pendulum reveal that the Earth turns — without ever looking at the sky?

▶ Run the simulationSee the measured result

Units: hours (full swing-plane rotation at the Paris Panthéon, φ = 48°50'47" N; Foucault 1851 reported ~11.3°/h ≈ 31.8 h)

How the lab tests it

Integrate the rotating-frame 2-D oscillator with energy-conserving RK4 at latitude φ; at each turning point record the swing-line azimuth, least-squares fit azimuth against time, and compare the fitted precession rate to Ω·sin φ. The 'day' is sped up so the rosette precesses in ~1 minute. ?lat=<deg> sets the latitude.

What it checks

the swing plane PRECESSES at the rate Ω·sin φ — a full turn per sidereal day at the pole, none at the equator — so the slow rotation of the swing line is the ground (the Earth) turning beneath the pendulum, exactly as Foucault demonstrated in 1851. The measured rate matches Ω·sin φ to 0.00% at 90°, 45°, 30° and 0°.

Foucault pendulum precession, period & latitude calculator

How fast a pendulum's swing plane turns where you are standing, and how long it takes to come all the way round. Foucault's claim in 1851 was not that the plane turns — it was that it turns at the sine of the latitude, which is a strange rate: a full turn per day at the pole, nothing at all on the equator, and backwards in the southern hemisphere. Nothing about the Earth's rotation is typed into this page. The sidereal day is ASSEMBLED, from the fact that a planet turns once more per year against the stars than against the sun — T_sid = year/(N_solar + 1) — so 86400 s and 365.256363004 days give 23.934472128 h and Ω = 7.292115083e-5 rad/s, and the Panthéon's famous 31.79-hour rosette comes back out as 31.7876983 h with the answer never having gone in. Run backwards, the same law makes the pendulum a surveying instrument: Foucault's own reported 11.3°/hour inverts to latitude 48.701°, about 16 km from where he was standing, which is roughly how good a pendulum is. The page also prices the systematic that ruins real ones — Airy's finite-amplitude ellipse precession, which turns the plane with the planet held perfectly still — and fits a one-parameter family through this lab's own six-latitude scan that has Foucault's law at one end and his contemporaries' "the plane just follows the Earth" at the other. The scan kills the rival by 7089 of its own error bars. Three things this page will not do: re-run the simulation, model air drag or the launch asymmetry a real pendulum fights, or claim the sine law is confirmed to within the fit's statistical bar — it is not, and the residual is a systematic with a name and a closed form.