Rate
- Earth rate × sin(latitude)
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Foucault pendulum
The plane of the swing turns at the Earth’s rate times the sine of the latitude. At either pole that is one turn per sidereal day. At the equator the plane does not turn.
Looking down on the pendulum. The dashed line is north–south on the floor. The solid line is the swing. The motion is sped up: at the pole the line turns once in about twelve seconds. The cards give the real period. Northern latitudes turn clockwise. Southern latitudes turn anticlockwise.
- Swing
- North–south on the floor
- Sense of the turn
One turn
- Period of the plane
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Sense
- Seen from above
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What this page shows
A Foucault pendulum is a long pendulum, free to swing in any direction. Once it is going, the plane of the swing stays fixed in inertial space, and the Earth turns underneath it. What you see, standing on the floor, is the plane turning.
The rate of that turn is the Earth’s rate times the sine of the latitude. The Earth rate used here is one turn per mean sidereal day. At 90° N or 90° S the sine is 1, so the plane turns once per sidereal day. At latitude 0° the sine is 0, so none of that turning happens. At 59° the sine is about 0.857, and one turn takes longer than a sidereal day by that factor.
North of the equator the plane turns clockwise as you look down on it. South of the equator it turns anticlockwise. Stockholm and Singapore are clockwise. Sydney is anticlockwise. Singapore is close to the equator, so the turn is slow.
Assumptions
- The pendulum is long enough, and started carefully enough, that the swing holds a plane. This page does not model the ellipse that a real swing grows, the air, or the suspension.
- The Earth rate is one turn per mean sidereal day. The day used here is 86,164.0905 s of mean solar time, which is 23 h 56 min 4.0905 s. It comes from dividing 86,400 s by 1.002737909350795.
- The rate is that Earth rate times sin φ, with φ the latitude and north positive. The period of one turn is the sidereal day divided by the absolute value of that sine.
- The drawing is sped up, in proportion to the sine. At the pole the line goes round once in about twelve seconds of watching. At the equator it holds still. The cards, not the drawing, are the period.
- The sidereal day is the turn relative to the equinox. The turn relative to the stars is a few milliseconds longer. The figures here do not show that difference.
Sources
- Foucault, L. (1851). Démonstration physique du mouvement de rotation de la Terre au moyen du pendule. Comptes rendus hebdomadaires des séances de l’Académie des sciences, 32, 135–138.
- Aoki, S., Guinot, B., Kaplan, G. H., Kinoshita, H., McCarthy, D. D., and Seidelmann, P. K. (1982). The new definition of Universal Time. Astronomy and Astrophysics, 105, 359–361. The ratio of the mean solar day to the mean sidereal day is 1.002737909350795.
- IERS Earth Orientation Centre. Useful constants. The conventional mean sidereal day is that ratio applied to 86,400 s. hpiers.obspm.fr/eop-pc/models/constants.html