# As the Earth Turns

There's stargazing and stargazing. One way is with telescopes and sky charts. I'm pretty good at that. Another is the way I'm really good at is lying on my back on a summer's night and just gazing. It only takes a few minutes of this to realize that the dome of the night sky is rotating, counterclockwise. A long camera exposure shows circular star trails which confirm that the axis of rotation is aimed -- roughly -- towards Polaris, the North Star.

Relative to the stars, and thus to an invisible grid created by the rest of the universe, Earth rotates once every 23 hours 56 minutes. (Relative to the sun, the rotation takes 24 hours, of course -- the four-minute daily difference adds up to a day over the year, to compensate for the one extra rotation we get "for free" as we orbit the sun.)

Imagine a pendulum swinging over the North Pole -- in winter, when it's continuously dark, so you can see the night sky. The stars slowly rotate counterclockwise around Polaris, taking nearly 24 hours to make a full rotation. From the stars' point of view, it's Earth that's spinning -- and there are a lot more of them than there are of us!. Since the pendulum is suspended from a point on Earth's axis everything's symmetrical, so it's not getting any information about which way to swing from the Earth. Instead, its motion is guided by the invisible gravitational "grid" which permeates space, defined by the universe as a whole and represented to us by the visible stars. It's from that "grid" that the pendulum takes its orders: its swing-plane follows the stars, taking 23 hours 56 minutes to complete a full rotation.

Now let's move that pendulum down to the equator. Earth's spin is now asymmetric, forcing the it to swing in tune with Earth. Instead of the pendulum's swing-plane following the stars, it would stay swinging -- from our ground-based frame of reference -- in the same plane from which it started. Its period is infinite.

Let's move the pendulum a little closer to home -- specifically, to the California Academy of Sciences in Golden Gate Park. There, a so-called Foucault pendulum allows us to visualize Earth spinning in space from the stars point of view. (Léon Foucault installed his original pendulum in the church of Sainte-Geneviève in Paris in 1850, using a 62 lb. cannon ball suspended from 200 feet of piano wire.) At the latitude of San Francisco, the period of the swing plane must be somewhere between 23 hours 56 minutes (at the pole) and infinity (at the equator).

Like so much in nature, the variation is sinusoidal. Divide the pole-period by the sine of the latitude, and you get, for San Francisco, a period of about 39 hours for one full rotation, or about 9 degrees per hour. Which you can observe for yourself, next time you're in the Bay Area and you've got an hour to spare.

Barry Evans swings to the rhythms of Old Town Eureka, where he lives.

ILLUSTRATION: A pendulum swinging over the North Pole is affected symmetrically by Earth's rotation so has no preferred frame of reference relative to our planet. It responds instead to the distant stars and its swing-plane rotates with them. (Adapted from my book Everyday Wonders)

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#### Barry Evans

Bio:
Barry Evans lives in Old Town Eureka with his girlfriend (and wife) Louisa Rogers, several kayaks and bikes, and a stuffed gorilla named “Nameless.” A recovering civil engineer, he is the author of two McGraw-Hill popular science books and has taught science and history. His Field Notes anthologies are available... more

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