(pages 134-136)

For the last million years, the peaks of ice ages have been spaced about 100,000 years apart, with smaller wiggles spaced about 41,000 years, or 23,000 years, or 19,000 years apart.
Remarkably, this spacing of the ice-age wiggles was predicted decades before it was observed. {11/6} Building on important earlier work, the Serbian mathematician Milutin Milankovitch had spent much of the early 20th century calculating changes in the distribution of sunshine on the planet in response to features of Earth’s orbit, and had found just those timings.
To see what Milankovitch calculated, imagine a spinning child’s top. (Better yet, go get one—they’re fun! And, this is a lot easier if you have something to look at.) The “spin axis”—the north pole, or the red handle sticking up out of the middle—will be tracing a small circle in the air, even if the “south pole” isn’t moving where it touches the table. This circle-tracing is the precession of the top. The Earth’s precession isn’t quite a perfect cycle, but repeats roughly every 19,000 or 23,000 years. {11/7}
Keep watching and you’ll see this small circle getting bigger as the top begins to fall over. The angle between the top’s north pole and the vertical is called the obliquity, or tilt. For the Earth, the obliquity cycles from about 22o to 24.5o and back over 41,000 years, without falling over. {11/8}
The Earth’s orbit about the sun is a non-circular ellipse, with the sun off-center at one of the foci, so our distance from the sun changes a little during a year. The eccentricity, or out-of-roundness, of the elliptical orbit increases and decreases over about 100,000 years, increasing and decreasing the changes in our distance from the sun during a year. {11/9}
If the obliquity were zero, sunshine would always just graze the poles while shining down straight on the equator. Increasing obliquity tilts the equator slightly away from the sun so it receives less sunshine, but exposes the poles to a lot of sunshine during their summers so that they get more during a year.
Today, the Earth is near its greatest distance from the sun during northern summer, but 10,000 years ago precession had reversed this with the Earth closest to the sun during northern summer. Thus, midsummer sunshine has dropped in the north while increasing in the south over the last 10,000 years.
Eccentricity primarily controls how much effect the precession has on summer sunshine. If the orbit were perfectly circular, then our distance from the sun would never change and precession wouldn’t matter.
So, features of the orbit serve primarily to move sunshine around on the planet, north to south to north, or poles to equator to poles, affecting how much sunshine a latitude gets and how it is distributed through a year. The changes can be large—midsummer sunshine may increase by more than 25% over 10,000 years at the poles before decreasing again—even though the total sunshine received by the whole globe in a year is almost unchanged. Milankovitch calculated all of this, without a computer, in a couple of decades of serious work before WWII, and hypothesized that the changing sunshine had controlled ice ages. And, decades later, the climate-change spacings he predicted were discovered in histories of ice ages.
11/6 Milankovitch, M., 1941, Canon of Insolation and the Ice Age Problem. Belgrade; Imbrie, J. and K.P. Imbrie, 1979, Ice Ages: Solving the Mystery, Harvard University Press; Broecker, W.S., 2002, The Glacial World According to Wally, Eldigio Press, Columbia University, Lamont-Doherty Earth Observatory, Palisades, NY; Alley, R.B. 2000, The Two-Mile Time Machine, Princeton University Press.
11/7 More accurately, the precession takes a bit over 26,000 years, but it interacts with a pivoting of the whole orbit to cause the changing distribution of sunshine to repeat roughly every 19,000 or 23,000 years.
11/8 Note that under very special conditions, it might just be possible to roll a planet over; Williams, D.M., J.F. Kasting and L.A. Frakes, 1998, Low-latitude glaciation and rapid changes in the Earth’s obliquity explained by obliquity-oblateness feedback, Nature 396, 453-455. For recent times and behavior, this doesn’t matter.
11/9 Eccentricity changes primarily from the slight tug of Jupiter’s gravity as we pass it in our respective orbits, and varies with a 400,000-year cycle as well as the better-known 100,000-year cycle. Eccentricity is calculated as the difference between the maximum and minimum distances of the Earth from the sun, divided by the sum of these distances, and ranges from 0.0034 (virtually circular) to 0.058 (still pretty close to circular). Modern eccentricity is fairly low (0.0167) and decreasing slowly. The precession and obliquity of the child’s top change as the Earth’s gravity tugs on it; for the Earth, the precession and obliquity vary as the gravity of the moon and sun act on the slight bulge at the equator caused by the planet’s rotation. Today, our obliquity is about 23.4o and roughly halfway through a decrease. Precession has little effect on the total sunshine for a year at a place, because more-intense summers caused by closer approach to the sun are also shorter; with a non-circular orbit around an off-center sun, the Earth spends less time close to the sun and more time far from the sun during a year. The trade-off between distance and time spent at that distance also means that variations in eccentricity cause the total sunshine received by the planet in a year to change a tiny bit—less than 0.1%. Changes in the obliquity and precession have vanishingly small influence on the total sunshine received by the planet in a year.