## Millions of Years

3.2. Gradual changes in the eccentricity ("out-of-roundness") of Earth's orbit around the Sun occur at a cycle of 100,000 years.

The second way to alter climate is by changing Earth's distance from the Sun. You can make this claim somewhat tangible by holding your hand a foot away from a typical light bulb and then holding it 3 inches away. Distance from a heat source clearly matters, and the amount of heat from a light bulb is in the general ballpark of the average amount coming from the Sun.

Two factors in Earth's present-day orbit combine to alter Earth's distance from the Sun during its annual revolution. The first is the eccentricity of its orbit. Although we generally think of the orbit as circular, in fact it is slightly out of round, or elliptical, in shape. As a result, Earth is about 5 million kilometers (3 million miles) closer to the Sun in one part of its orbital path than on the opposite side. These changes are small but significant departures from Earth's average distance to the Sun of 155 million kilometers (93 million miles).

Over long time scales, this elipticity, commonly called eccentricity, changes (fig. 3.2). French astronomer Leverrier is again credited with discovering that eccentricity varies at a cycle near 100,000 years. On rare occasions the eccentricity drops to zero and Earth's orbit around the Sun becomes perfectly circular. Most of the time the orbit is eccentric, with the amount of eccentricity constantly varying. These changes in eccentricity are more irregular than those of tilt: the peaks and valleys vary widely in size. Changes in eccentricity through time affect the Earth-Sun distance in different parts of Earth's orbit because they produce departures from circularity.

The second aspect of Earth's orbit that affects Earth-Sun distance is precession, a wobbling motion best understood by analogy to a spinning top. Like a top,

Earth spins (rotates) once per day on its tilted axis. Earth revolves around the Sun once a year, a motion also shown by most tops that slowly trace out a circular path on a flat surface. But tops often show a third kind of motion: they may wobble or change the direction in which they lean, first toward one direction, then another. These changes in the direction in which Earth leans on its tilted axis differ from the amount of lean, which is the tilt.

In the 1800s French mathematician Jean le Rond d'Alembert was the first to understand how precession affects Earth's orbit around the Sun. He found that it takes about 22,000 years for Earth's tilted axis to complete one slow wobble in its orbit, an interval far longer than its once-daily rotational spin or its once-yearly revolution. It takes 22,000 annual revolutions and over 8 million daily rotational spins for Earth to complete just one of these wobbles in its orbit. You would have to watch a top carefully for a long time to detect so slow a wobble.

At the start of a single precession cycle, Earth is tilted in a particular direction in space, and it keeps that same attitude throughout the year. But as the years pass, the direction of tilt slowly begins to shift, gradually tracing out a circle. After 11,000 years, Earth's tilt direction has shifted enough that it leans in exactly the opposite direction it did initially. Then, after another 11,000 years pass, the direction of tilt circles all the way around to the same position it had at the start, 22,000 years earlier. In trying to explain precession in the classroom, I usually ended up walking around in a circle with my body and arms tilting in one direction and then in the other, apparently doing some religious dance ritual (well, of course, a Sun dance!). Most of my students probably remembered my weird body English long after they forgot how precession works.

Eccentricity and precession work together to determine the amount of solar radiation actually arriving on Earth. In effect, changes in eccentricity (fig. 3.2) act as a multiplier on the cycles of precession. They make the precession cycles larger in amplitude when eccentricity is high and smaller when eccentricity is low. Each individual precession cycle stays nearly 22,000 years, but the multiplier effect from eccentricity determines whether the swings from peaks to valleys are large or small (fig. 3.3).

If Earth's orbit around the Sun were perfectly circular (with zero eccentricity), and if Earth did not slowly wobble (precess) in its orbit, the amount of solar radiation received every summer would be identical, and every winter as well. More radiation would arrive in summer than winter because of Earth's tilted position relative to the Sun, but the amounts of radiation received during each of the seasons would not change from millennium to millennium.

But because Earth's orbit is eccentric and also precesses, summers and winters do not remain identical through time. When Earth's orbit is highly eccentric, it can be as much as 6 percent closer to the Sun during part of its annual orbit and