Saturday, December 01, 2007

Our Whirling World

By Joel Marks

Published in Mercury, vol. 36, no. 4, Fall 2007, pp. 28-31

Everybody knows that the earth rotates 360 degrees each day, which is why the sun comes back to the same place in the sky after 24 hours. Indeed, that is what makes a day a day. And everybody knows that the earth does this 365&1/4 times each year, which is why the sun returns to the same place in the zodiac after 365&1/4 days. Indeed, that is what makes a year a year (although we round them out to three of 365 days followed by a leap year).

Yes, everybody knows these things, but “everybody” is wrong.

No, I am not suggesting that we return to the days of a stationary earth at the center of a cosmos that revolves around us. The point is rather that the earth turns more than most people think it does.

To understand what is going on, it helps, first, to realize that we live in a whirling universe: Everything turns! Every star, every planet, every rock in space is spinning; moons revolve around planets, planets revolve around suns, suns revolve around galaxies. It’s a dizzying fact of existence.

So our little Earth not only rotates on its axis, but also orbits Old Sol, which in turn drags us in tow around the center of the Milky Way Galaxy. The latter motion normally escapes our notice because it is so slow by human standards; it takes 250 million years for the solar system to go around the galaxy once! Furthermore, what we see in the nighttime sky are the stars in our local neighborhood, so even if we were all traveling around the galactic center at breakneck speed (which, actually, we are), the naked eye would just register the relative stability of the nearby, so-called “fixed” stars.

The temporal measure of our orbit around the sun is of course well-known to us, for it constitutes the year. It is instructive to recall, however, just how counterintuitive today’s commonplace seemed at first. Copernicus (1473-1543) famously proposed that the earth revolves around the sun and not vice versa. Thus, the earth lost its place at the center of the scheme of things. But what really rattled people was a further implication, namely, that the earth moves. Commonsense rebelled at the idea that the very prototype of immobility, the ground beneath one's feet, was in fact twirling on an axis and hurtling through space. The metaphor we use to describe this revelation indicates its emotional impact: revolutionary (that is, moving in an orbit).

Thus we seem to have a neat division between the day determined by our axial rotation and the year set by our orbital revolution. But this is where the mistake lies, for these two motions are not entirely distinct. One familiar way that their interaction intrudes upon our lives is during presidential election years, otherwise known as leap years. Why do we add a day to the calendar every four years? Because the earth does not return to the same point in its orbit around the sun after exactly 365 days, but requires an additional quarter-day to complete the 360-degree circuit. Hence, adding one day every four years brings us back in synch. Of course it is only a coincidence that this correction coincides with our presidential elections, but maybe the United States should switch the date of the elections to February 29 just to press home the point!

We now come to the moral of our little tale, for there is another interaction between diurnal rotation and annual revolution, which goes largely unrecognized. Although analogous to the leap year, it is completely distinct from it. There is, again, a misalignment between two measures that has to be made up by adding something; in this case, though, what needs to be set right is the number of degrees in the daily rotation rather than the number of days in the year.

Let us consider the question: What is a day? Its normal meaning is the solar day. This is the time it takes a point on the earth's surface to return to the same place relative to the sun. For example, if we begin when the sun is due south when viewed from Boston, then exactly one day will have elapsed by the time the sun returns to that position in the sky. This is what we count as a 24-hour day. (We can ignore for the purposes of the present discussion that this is strictly speaking the mean solar day, since the eccentricity of the earth’s orbit yields solar days of slightly differing lengths during the course of a year.)

But there is also a duration known as the sidereal day. This is the time it takes a point on the earth's surface to rotate 360 degrees relative to the more distant, “fixed” stars. If you think about the physical situation, you will realize that the sidereal day must be shorter than the solar day. This is because, while the earth is rotating at a constant speed, it is also moving in its orbit around the sun, and in the same direction as the rotation (counterclockwise as seen from the north). Hence, for Boston to come all the way back around to the same place relative to the sun, it must travel more than 360 degrees.

How much more? Well, the number of days in a year, approximately 365, is almost the same as the number of degrees in a full rotation, 360. This is surely not a coincidence but a Babylonian intention. So the earth actually rotates an extra degree each day, that is, around 361 degrees daily.

Furthermore, if you carry that through the whole year, you arrive at an even more surprising conclusion, to wit: the earth rotates 366 times in a 365-day year! This turns out to be a general rule of geometry: Any planet makes one extra rotation than there are days in its year. A limiting case, which can also help you to picture why this is so, would be a planet that has no day; it would rotate one time each year. This is because the planet would always present the same face to its sun; therefore the sun would always remain in the same place in the sky, so there would be no return to the same place to constitute a day.

(The situation is similar to the moon’s motion relative to the earth. Since the moon rotates once per revolution around the earth, the earth, on the moon’s earth-facing side, simply stays put in the lunar sky all the time.)

If all that makes your head spin, it should!

Sidebars and Illustrations

What Is a Day?

The normal meaning of a day is technically the solar day. This is the time it takes a point on the earth's surface to return to the same place relative to the sun.

ILLUSTRATION

But there is also the sidereal day. This is the time it takes a point on the earth's surface to rotate 360 degrees relative to more distant stars. Because the earth is simultaneously orbiting the sun, the sidereal day is shorter than the solar day.

ILLUSTRATION

One More Rotation

A planet that always has the same face towards its sun will rotate once per year, and hence have one sidereal day per year, but no solar day at all.

ILLUSTRATION (from north of solar system)
ILLUSTRATION (of sun’s unchanging position in sky from a given location) “It’s always noon.”

A New Twist

To add to the dizzying but fascinating complexity of the spinning, orbiting Earth, consider also the recent discovery that the earth's core rotates independently from the earth's surface or mantle, since a molten layer separates them. Researchers at Columbia University and the University of Illinois have determined that the inner core rotates faster, completing an additional full rotation in roughly a millennium. So which represents the rotation of the earth?

ILLUSTRATION


Byline

Joel Marks is professor of philosophy at the University of New Haven in West Haven, Connecticut, and an amateur astronomer. He enjoys indulging in what he has dubbed "philosophical astronomy," which means arriving at new astronomical insights by reasoning about already known phenomena.

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