## Physics Question #9094

Nicola, a 27 year old n/a from Smiljan asks on August 31, 2014,

How would a Foucault Pendulum behave on the Moon?

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### Donald J. Barry answered on September 8, 2014

[Editor: The Foucault pendulum was invented by the French physicist Léon Foucault in 1851. It is a simple device conceived as an experiment to demonstrate the rotation of the Earth. The moon does rotate, but much slower than the Earth. Instead of twirling around once a day, it takes a few days less than a month for the moon to make one rotation around it's axis. A Foucault pendulum should work even better on the moon since there is no atmosphere so no friction to slow the pendulum. As long as the swinging of the pendulum is started perfectly with no extraneous forces introduced it should behave normally, though your measurements will take longer and you may need greater precision since the change will be slower and more subtle.]

A pendulum located on the moon's pole of rotation would precess such that it would rotate through a complete circle in 27.3 days, the period at which the Moon rotates with respect to the frame of the Universe, or its "sidereal" rotation period (sidereal refers to the fixed stars). The synodic month, the average from one particular phase to its repeat, is 29.5 days, slightly different. The difference is that the Earth has proceeded farther around the Sun over the course of a month, and the Moon must move one full rotation -- and then a little more to catch up to the same angle with respect to the moving Sun.

A pendulum elsewhere on the Moon would precess more slowly -- the rate varies as the sin of the latitude. At the equator (sin latitude = 0)  a pendulum does not precess. The same is observed for Foucault pendulums on the Earth.

The spin of the Earth itself actually makes space-time in the nearby Universe whirl slightly, which would make pendulums alter their plane slightly even relative to the fixed stars. Einstein's theory of General Relativity made this unusual prediction. The effect is incredibly minute around something so "light" as the Earth: around some of the monsters in the cosmic beastiary like neutron stars and black holes, the effect is much more pronounced. The spacecraft Gravity Probe B was launched specifically to measure this tiny effect, which is so small that its claimed detection has invited some controversy. Even in close orbit around the Earth, the "whirl" induced by the Earth's rotation would spin a pendulum only once in 30 million years. At the Moon's distance, the effect is much, much smaller.

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