The Seasons and the Earth's Orbit
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 (obliquity) between the Earth's axis of rotation and
a 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.
Long-Term Astronomical Cycles
Precession of the Seasons
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. Because we use a calendar
year that is aligned to the occurrence of the seasons, the date of
perihelion gradually regresses through the year. As mentioned above, it
takes 21,000 years to make a complete cycle of dates.
Eccentricity of the Earth's Orbit
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.
Changes 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.
Milankovitch Cycles:
Astronomically Induced Climate Change
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. (Note:
somewhat different periods for these cycles appear in some literature.) 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 has been debated for decades.
However, recent work with sophisticated computer models of climate and ice sheet
growth has led to a better understanding of how the effects of precession
and eccentricity might work together to produce the ice ages (see
paper
by Ayako Abe-Ouchi and collaborators in the
8 August 2013 edition of the journal Nature, and a less technical
review
of the work in the same issue). Given the long history
of controversy in this field, however, it seems unlikely that this will be
the final word.
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. An Internet search on
"Milankovitch cycles" will provide links to additional information.