The Seasons and the Earth's Orbit
Milankovitch Cycles
Astronomical Applications Dept. Astronomical Applications Dept.
 
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The Tilt of the Earth's Axis and Its Elliptical Orbit

We have all been taught that the seasons are caused by the 23.4° angular offset between the Earth's axis of rotation and the perpendicular to the Earth's orbital plane with the Sun (see obliquity below). The Earth's rotational axis stays nearly fixed in space, even as the Earth orbits the Sun once each year. As a result, when the Earth is at a certain place in its orbit, the northern hemisphere is tilted toward the Sun and experiences summer. Six months later, when the Earth is on the opposite side of the Sun, the northern hemisphere is tilted away from the Sun and experiences winter. The seasons are, of course, reversed for the southern hemisphere.

The solstices mark the two dates during the year on which the Earth's position in its orbit is such that its axis of rotation is most tilted toward or away from the Sun. These are the dates when the days are longest for the hemisphere tilted toward the Sun (where it is summer) and shortest for the opposite hemisphere (where it is winter).

However, there is a complication. The Earth's orbit is very close to being a perfect circle, but not quite. It is somewhat elliptical, which means that the distance between the Earth and the Sun varies over the course of the year. This effect is too weak to cause the seasons, but it might have some influence over their severity. The remainder of this page explains this possibility.

The Earth reaches perihelion - the point in its orbit closest to the Sun - in early January, only about two weeks after the December solstice. Thus winter begins in the northern hemisphere at about the time that the Earth is nearest the Sun. Is this important? Is there a reason why the times of solstice and perihelion are so close? It turns out that the proximity of the two dates is a coincidence of the particular century we live in. The date of perihelion does not remain fixed, but, over very long periods of time, slowly regresses (moves later) within the year. There is some evidence that this long-term change in the date of perihelion influences the Earth's climate.

The Length of the Year

We can measure the length of the year in several different ways. The length of the year from equinox to equinox (equivalently, solstice to solstice) is called the tropical year, and its length is the basis for our Gregorian (civil) calendar. Basically, the tropical year is the year of a complete cycle of seasons, so it is natural that we use it for ordinary purposes. But we can also measure the length of the year from perihelion to perihelion, which is called the anomalistic year. On average, the anomalistic year is about 25 minutes longer than the tropical year, so the date of perihelion slowly shifts over time, regressing by about 1 full day every 58 years. The date of perihelion thus moves completely through the tropical year in about 21,000 years.

It is important to note that we are talking about long-term trends here. There are small year-to-year variations in the dates and times of solstice and perihelion due to our leap-year cycle and the effect of the Moon on the motion of the Earth. See our page on Earth's Seasons for the exact dates and times of these events for current years.

Milankovitch Cycles
Precession

Most of the difference in the average lengths of the two kinds of year is due to the very slight change in the direction of the Earth's axis of rotation in space from one year to another. We usually think of the Earth's axis of rotation as being fixed in direction - after all, it always seems to point toward Polaris, the North Star. But the direction is not quite constant: the axis does move, at a rate of a little more than a half-degree per century. So Polaris has not always been, and will not always be, the pole star. For example, when the pyramids were built, around 2500 BCE, the pole was near the star Thuban (Alpha Draconis). This gradual change in the direction of the Earth's axis, called precession, is caused by gravitational torques exerted by the Moon and Sun on the spinning, slightly oblate Earth.

Because the direction of the Earth's axis of rotation determines at which point in the Earth's orbit the seasons will occur, precession will cause a particular season (for example, northern hemisphere winter) to occur at a slightly different place from year to year. At the same time, the orbit itself is subject to small changes, called perturbations. The Earth's orbit is an ellipse, and there is a slow change in its orientation, which gradually shifts the point of perihelion in space. The two effects - the precession of the axis of rotation and the change in the orbit's orientation - work together to shift the seasons with respect to perihelion. Thus, since we use a calendar year that is aligned to the occurrence of the seasons, the date of perihelion gradually regresses through the year. It takes 21,000 years to make a complete cycle of dates.

We would not expect the 21,000-year cycle to be very important climatologically because the Earth's orbit is almost circular - the distance to the Sun at perihelion is only about 3% less than its distance at aphelion. That is, whether perihelion occurs in January or July, it seems unlikely that our seasons would be much affected. At least, that is the case now; but the eccentricity of the Earth's orbit (how elliptical it is) also changes over very long periods of time, from almost zero (circular orbit) to about three times its current value. The eccentricity of the orbit varies periodically with a time scale of about 100,000 years. So, it would be reasonable to suppose that if the 21,000-year perihelion shift cycle were to have any effect on climate at all, it would only be during the more widely-spaced epochs when the orbital eccentricity was relatively large. That is, climatologically, the 100,000-year cycle of eccentricity should modulate the 21,000-year cycle of perihelion.

In fact, Mars has an orbit much more eccentric than the Earth's, and its perihelion cycle (which has a period of 51,000 years) does apparently have a significant effect on climate and prevailing wind direction there.

Change in Obliquity

There is another important cycle that has the potential to affect the Earth's climate; it is a 41,000-year variation in obliquity, the tilt of the Earth's axis of rotation with respect to the perpendicular to its orbital plane. This variation is different from precession - the two motions are at right angles to each other - and astronomically is a much smaller effect. The obliquity varies by only a few degrees back and forth, and the current value of 23.4 is near the middle of the range. However, climatologically, the obliquity variation has the potential to have a fairly direct effect on seasonal extremes. After all, it is the obliquity that causes our seasons in the first place - if the Earth's axis were perpendicular to its orbital plane, there would be no seasons at all.

The astronomical cycles described above are called Milankovitch cycles after Milutin Milankovitch, a Serbian scientist who provided a detailed theory of their potential influence over climate in the 1920s. Milankovitch's work was an attempt at explaining the ice ages, and it built upon previous astronomical theories of climate variation postulated by Joseph Adhemar and James Croll in the 19th century. Although the Milankovitch theory is well-grounded astronomically, it remains controversial. The theory predicts different effects at different latitudes, and thus its use as a predictor of global (or at least hemispheric) climate change is not unambiguous. The exact mechanisms by which the relatively modest variations in the Earth's orbit and axis direction might result in such large effects as the ice ages are not well established. The theory's popularity has tended to vary depending on the type of long-term climatological data that has been available and the method used to establish a time scale for the data.

The 21,000-year perihelion cycle and the 41,000-year obliquity cycle do in fact appear to be present in the climatological record. But the dominant climate cycle that is seen has a period of about 100,000 years. Although this coincides with the period of change in the eccentricity of the Earth's orbit, the theory outlined above does not predict that we should see this period directly - the effect of eccentricity should appear only as a modulation of the 21,000-year perihelion cycle. The mechanism by which the Earth's orbital eccentricity could affect the climate in such a direct and important way is not known, although recent evidence (published in 2000) indicates that atmospheric carbon dioxide may play a leading role in amplifying the orbital effect. However, some researchers still have doubts about the association between the 100,000-year climate cycle and orbital variations. Thus, many questions remain about long-term climate variations and their relationship, if any, to astronomical causes.

A very readable book on the whole subject of ice ages and the development of the astronomical theories for their origin is Ice Ages: Solving the Mystery by John Imbrie and Katherine Palmer Imbrie (1979, Enslow Publishers, New Jersey). The book obviously does not cover the latest research, but provides an excellent background and historical context.