Turn, turn, turn: in addition to its daily spin and its annual trip around the Sun, the Earth wobbles—affecting the seasons, the "north star," and human history

Donald Goldsmith

Winter brings the year's longest nights--extra hours of darkness in which to watch the stars wheel their ways around our basic point of reference in the sky: a star named Polaris. Known today as the North Star (for its unique status as the star most closely aligned with the projection of the Earth's north pole on the sky), Polaris seems to stay steady no matter how long the dark night. The explorers who first sailed between continents clung to it for orientation in their travels. And yet, as surely as the nights will again grow shorter and the seasons will change, Polaris will lose its role as our north star. A slow cycle of the heavens will eventually bring Polaris back to its familiar role--but not for another 26,000 years, and not before other stars have taken their turn as celestial beacons for the stargazers of the distant future.

Centuries of effort by the world's finest thinkers have led to a basic understanding of why the winter nights are cold and dark. Today most schoolchildren know that the Earth rotates on its axis once each day and revolves around the Sun once every year--discoveries that long ago shook the very core of human understanding and led to the abandonment of the idea that the Earth lay at the center of the cosmos. Those two rhythms rule our lives: the Earth's daily spin produces sunrise, sunset, and the alternation of night and day. Our planet's annual trip around the Sun takes us through the cycle of seasons, winter to spring to summer to fall.

And just how, exactly, does spring emerge from winter every year? Not, as many believe, because the Earth's elliptical path takes us closer to the Sun. Changes in the distance between Earth and Sun have only a modest effect on the seasonal cycle. Instead, seasonal variations arise because the Earth's axis of rotation, the imaginary line through the north and south poles, does not stand upright with respect to the plane of the Earth's orbit around the Sun. The rotation axis tilts by about 23.5 degrees from perpendicular. It also maintains a constant orientation in space--in other words, with respect to the stars--throughout the course of a year. So our annual motion alternately exposes each hemisphere, northern, then southern, then northern again, to more direct sunlight.

That direct sunlight, as the Sun rises higher and stays longer in the sky, causes summer in the hemisphere that tilts toward the Sun and winter in the hemisphere that tilts away. (The higher Sun and the longer days make roughly the same contribution to the seasonal differences, though of course the two effects are closely intertwined.) On two days of the year, the spring and fall equinoxes (which fall on or close to March 21 and September 22 each year), the Earth's rotation axis tilts neither toward nor away from the Sun. On those two days, day and night have equal lengths all over the world. In fact, if our planet's rotation axis were perpendicular to the plane of its orbit, rather than tilted, day and night would be equal throughout the year, and there would be no seasons to celebrate.

Lurking within the faithful cycles of day and night, winter and summer, is a third cyclical motion, which arises from the Earth's daily rotation and interacts with its annual revolution. That motion is called precession. It is, in essence, an almost imperceptibly slow wobble that creates a subtle and intriguing wrinkle in time. To visualize precession, imagine a top slowing down as it spins on the floor. Before it stops spinning entirely, it begins to wobble, its rotation axis rolling in various directions. As the axis changes direction, it sweeps out the shape of an upside-down cone, perpendicular to the floor; that motion is precession. There is, of course, one big difference between the top and the Earth: the precession of the top can take less than a second; the precession of the Earth takes almost 26,000 years.

Compared with twenty-six millennia, time scales measured in decades or even in centuries are so brief that for most practical purposes, the Earth's axis continues to point in the same direction. Today, north in any season can be determined by noting the position of Polaris. In the long run, however, the spatial orientation of the Earth's rotation axis does change. Every 26,000 years (more accurately, every 25,785 years), the two points on the sky directly above the Earth's North and South Poles--the extended ends of the axis of rotation--trace out complete circles on the background of stars. The radius of each circle is equal to the tilt of the rotation axis, 23.5 degrees. Thus the rotation axis changes only its orientation, while maintaining a constant angle to the Earth's orbital plane [see diagram on this page], as it sweeps out an inverted cone in space.

In spite of the, glacial rate of precession, you can't fully understand ancient history or archaeology without taking account of the fact that Polaris has not always pointed the way north. Four-and-a-half millennia ago, when the Egyptian pharaoh Khufu built the Great Pyramid, Polaris was nowhere near the "north celestial pole," the point that lies directly above the Earth's north pole at any particular time. In those days, astronomical observers relied on a much fainter star, Thuban, in the constellation Draco, the dragon, to serve as the north star; they may even have oriented the galleries of the pyramid on the basis of Thuban's position.

One and a half millennia later, at the time Homer composed the Odyssey, precession had left Thuban relatively useless as a north star. Homer's wandering hero Odysseus had to do his best with the Big Dipper--the seven bright stars of the constellation Ursa Major, or big bear, which then, as now, lay relatively close to the north celestial pole: "For so Kalypso, bright among goddesses, had told him to make his way over the sea, keeping the Bear on his left hand." In fact, the constellation would have moved around the sky quite a bit during the night, making Odysseus's navigational task considerably more difficult than Kalypso's directions imply. Still, the Big Dipper was a rough-and-ready indicator of the way north [see illustration above].

The discovery of precession, like Homer's great poem, was a signal achievement of ancient Greek culture. The Greek astronomer Hipparchus, who lived during the second century B.C., is justly famous for being the first to note its effects. Hipparchus made his breakthrough not by observing the position of the north celestial pole, but rather by noting some of the other changes caused by precession. High among them are the times of the year when the Sun reaches particular points on the sky, as it seems to move among the constellations, blocking some of them from view. (Astronomers now realize, of course, that it is the Earth that moves.)

Even as the orientation of the Earth's rotation axis wobbles, or precesses, the Sun continues to take its yearly lap around the sky, along the path called the ecliptic. Although ancient astronomers could not see the stars that happened to lie behind the Sun at various times of year, their excellent record keeping enabled them to accurately reconstruct which constellations provided a "house" for the Sun at any given moment.

There were twelve such houses, which match the familiar constellations, or signs, of the zodiac; together they form a band around the sky that includes the ecliptic. In the zodiacal system for keeping track of the year, created by astronomers in ancient Mesopotamia, each time the Sun entered a new house heralded the beginning of a new month. Every new year, moreover, began on the spring equinox when, as the Mesopotamians had determined, the Sun blocked the constellation Aries from sight.

But Hipparchus noted that something had happened during the two millennia since the Mesopotamian system had been codified: the Sun no longer occupied its specified position on the first day of spring. Instead, he determined, the Sun was reaching its marks along the ecliptic progressively earlier, by one day every seventy-two years. Because precession changes the times of the year of the spring and fall equinoxes--which we also measure by the visible seasonal changes on Earth--the effect acquired its full title: "precession of the equinoxes." If you could wait for 365 times seventy-two years--approximately 26,000 years--you would find that the equinoxes take place once again at their original times of the year, because one full cycle of precession had finished. Nowadays on the spring equinox, the Sun is near the first point in the constellation Aquarius, which leads some astrologers to refer to our epoch as the "Age of Aquarius."

How seriously do you read your horoscope? If you think the Sun's position in a particular constellation has important effects in determining birth signs, yours is wrong! Astrologers codified their basic principles roughly three millennia ago, and so precession has slipped the Sun's location at any particular time of year by about one and a half zodiacal constellations. If the horoscope column says that you are a Libra, for instance, you are actually a Virgo or even a Leo (assuming you judge by the Sun's actual position along the ecliptic at the time of your birth).

Conventional astrologers deal with that awkward fact by arguing that astrology has codified the meaning of the times of the year, not the location of the Sun against the backdrop of constellations in the zodiac. A minority sect, known as "new age astrologers," insists that conventional astrology requires wholesale revision, precisely because of precession. Both groups agree, however, that in the 230th century, more or less, the two systems will once again coincide in their predictions and their accuracy.

For astronomers, the chief effect of precession appears in star charts, which record the coordinates of celestial objects. Those coordinate systems usually designate a particular position on the sky--say, the Sun's position at the time of the spring equinox--as their primary reference point. But precession continuously slides that point along the ecliptic, and--since most coordinate systems depend on the orientation of the Earth in space--it also changes the orientation of the coordinates that astronomers measure from that point. As a result, astronomers must attach a particular "epoch" to the coordinates they use; today the standard epoch is January 1, 2000 (before that, it was January 1, 1950). Computers can readily make the small adjustments needed to update an object's coordinates from the current epoch to the present time; once fed into a telescope's tracking system, the updated coordinates enable astronomers to work unfettered by precessional effects.

Even in less meticulous circles, though, precession still rears its wobbly head. It affects the calendar, which must correct for the slippage in time that Hipparchus first noted. Our Gregorian calendar incorporates precession by changing the usual rule for leap years: It omits the leap day in every century year, such as 2100, that is not evenly divisible by 400.

What causes precession? The answers are gravity, angular momentum, and the fact that the Earth has a bit of a belly around its midsection, a bulge at the equator. The bulge itself arises from the Earth's rotation, which tends to fling the planet's central regions outward. The gravity of the Sun and the Moon attract the bulge, and tend to make the Earth "stand up straight," attempting to make its rotation axis perpendicular to the plane of its orbit. (The plane of the Moon's orbit around the Earth happens to nearly coincide with the plane of the Earth's orbit around the Sun, so both the Moon and the Sun act in nearly the same way on the bulge.)

If the Earth did not rotate, or if it rotated extremely slowly, the two objects would indeed set the Earth's rotation axis nearly upright. But because the Earth rotates rapidly, the net effect of the Sun's and Moon's gravity on the Earth's bulge drives precession. Draw the vectors, do the math, and you find that the forces give rise to a 26,000--year circle, never changing the amount of tilt but continuously varying the Earth's orientation in space.

Polaris, which has acted as the north star since the time of Columbus, will continue to serve us well for many more centuries; in fact, the north celestial pole on the sky will move even closer to Polaris during the next 150 years. Eventually, however, the celestial pole will wander on, and Polaris will no longer work as a good north star. Our descendants will labor under virtually the same handicap that our brethren in the Southern Hemisphere have for centuries. Bereft of a south star, they have been forced to compensate by using the Southern Cross as a pointer toward the south celestial pole.

In about 11,800 years, just over halfway through the cycle of precession from now, the northern end of the Earth's rotation axis will point almost directly at the extremely bright star Vega. In those navigationally favorable times, from the 130th through the 150th centuries (more or less), no one will have trouble finding the way north on a clear starry night [see illustration on page 22].

Do other planets precess? Certainly, provided they, too, are not spinning perpendicularly to their orbital planes, and provided they have equatorial bulges gravitationally affected in the same way that the Sun's gravity affects the Earth. Although astronomers have never directly measured the precession of any planet except our own, an observer on, say, Mars could detect the same kind of precessional changes that we find for Earth.

But the rotation axis of a tilted spinning object is not the only thing that precesses. If an orbit is not perfectly circular, its long axis can change its orientation in space, giving rise to a precession of the entire orbit. For example, the Moon's orbit around the Earth undergoes just such a precession, historically called the "regression of the Moon's nodes." The full cycle of precession lasts 18.6 years, which explains why eclipse "seasons" also vary over an 18.6-year cycle.

Another important example of orbital precession affects the elliptical orbit of Mercury. Astronomers who studied the orbit during the nineteenth century observed a relatively large precessional effect. They calculated that the gravity of the other planets could account for more than 90 percent of the observed precession. But try as they might, a small fraction of the total remained unexplained--forty-three seconds of arc per century. Since each of the 360 degrees in a full circle is equal to 3,600 seconds of arc, the unexplained precession of Mercury's orbit seemed trivial.

But that "trivial" amount turned into a key piece of confirming evidence for Einstein's general theory of relativity. Einstein's theory makes a precise prediction of the amount of precession of Mercury's orbit, by calculating how much the Sun bends space (and time) in the neighborhood of the planet. The theory's prediction corresponded almost exactly with the observed precession, and played a crucial role in gaining rapid acceptance among scientists for Einstein's revolutionary hypothesis.

So if anyone asks you why you should care about precession, be prepared to answer with confidence and pride. Not for any reason linked to daily life, for eclipses and star charts remain the provinces of astronomers. Rather, precession turns out to describe a deep truth about the cosmos, worth understanding in its own right.

If your questioner demands more than that, ask him or her to consider what the discovery of precession could have meant to earlier civilizations. In their book Hamlet's Mill, two historians of science, Giorgio de Santillana and Hertha von Dechend, speculated that precession was known not only to Hipparchus in the second century B.C., but also to the Babylonians, many centuries earlier. Such a discovery must have been mind-boggling:

[Precession] became the vast impenetrable pattern of fate itself, with one world-age succeeding another, as the invisible pointer of the equinox slid along the signs, each age bringing with it the rise and downfall of astral configurations and rulerships, with their earthly consequences.

Then ask: Could precession really have seemed so impressive to our ancestors? Have we become so indifferent to the cosmos since they looked to the skies and expounded a host of explanations that we have lost our sense of wonder? And if so, are we better or worse off than they were, adrift in space on our rotating, revolving, precessing planet?

DONALD GOLDSMITH is the author of twenty books on astronomy, including Connecting with the Cosmos (published by Sourcebooks in 2002). He is the co-author, with Neil deGrasse Tyson, of Origins: Fourteen Billion Years of Cosmic Evolution (Norton, 2004).

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