Earth Sun Geometry
Solar Insolation Effects
Obliquity refers to the tilt of the
Earth's axis. Over time, the angle of Earth's tilt varies between 22.2
and 24.5 degrees (currently the tilt is 23.5 and decreasing). These
variations, discovered by French astronomer Urbain Leverrier in the
1840s, are caused by the gravitational pull of large planets, including
Jupiter. Earth's obliquity varies cyclically with a period of 41,000
obliquity cycle animated! The
tilt is exaggerated by about 10x in this animation. However, the phasing
What is the effect of variations in
obliquity? Changes in obliquity amplify or suppress the seasons. A larger
tilt means that the summer hemisphere will receive more solar radiation,
while the winter hemisphere will receive less.
The Earth's orbit around the Sun is
described by its eccentricity. Eccentricity is expressed mathematically
e = (a2
where a and b are the major and minor
axes of the ellipse, respectively. What is the eccentricity of a
circular orbit? Earth's eccentricity has varied over time between values
of 0.005 and 0.0607 (currently the eccentricity is 0.0167). Eccentricity
has a period of about 100,000 years (see below).
Changes in insolation due to the
eccentricity cycle are very slight, at most 0.2%. Eccentricity is
important because it modulates the amplitude of the precession cycle
eccentricity cycle animated! The
eccentricity is exaggerated. Without this exaggeration, the changes
would be nearly imperceptible.
Precession of the equinoxes
The position of the solstices and
equinoxes are not fixed. Instead, they shift with respect to Earth's
eccentric orbit and with respect to aphelion (point in Earth's orbit
farthest from Sun) and perihelion (point in Earth's orbit closest to the
The best way to imagine the axial precession is to think of the Earth
as a spinning top. As a spinning top slows, it begins to wobble.
Similarly, the Earth has a slow wobbling motion, called the
axial precession. This wobbling motion does
not affect the tilt angle of the Earth, but the direction in which the
Earth is tilting (see the diagram above). The axial
precession is caused by the gravitational pull of the Sun and the Moon
on the Earth's equatorial bulge.
precession causes the solstices and equinoxes to move
around Earth's orbit, completing a full orbit around the Sun every
A second motion also affects the
position of the equinoxes and solstices and is known as the precession of the ellipse.
This motion describes the rotation of the Earth's elliptical orbit (see
below). This motion is even slower than the wobbling motion of the axial
The combined effect of the axial
precession and precession of the ellipse is referred to as the
precessional cycle with a cyclicity of 3,000 and 19,000 years (for an
average of 21,700 years).
See the precessional cycle animated!
This animation demonstrates the changing winter time position of the
Earth in its orbit around the Sun.
(above figure from http://en.wikipedia.org/wiki/Precession)
The complete effect of the precession
on solar radiation must take into account both the eccentricity of the
Earth's orbit and the precession. Compare the unmodulated (above) and
modulated (below) precessional cycles.
What is the effect of the precessional
cycle? The precession cycle modifies where the equinoxes and solstices
occur in the Earth's, influencing the seasonal cycle. Currently, the
Earth's axis points toward Polaris. In 12,000 years, the axis will be
tilted toward Vega, and the orbital positions at which winter and summer
solstices occur will be reversed. Consequently, the Northern hemisphere
will experience winter near aphelion and summer will occur near
perihelion. Thus, seasonal contrasts will be greater than they are
Insolation changes on Earth
The diagram below shows the long-term
June and December insolation variations. Changes in low- and
middle-latitude insolation are the result of precession. Solar
insolation changes at high middle-latitudes are due predominantly to the
Figure. June and December insolation at
various latitudes (from Earth's Climate Past and Future by W.F.
Also note that the phasing of the
insolation maxima and minima differ for the obliquity and precession
cycles. The tilt causes in-phase changes in insolation. If the tilt
increases, both hemispheres receives more insolation during summer and
less during winter (see the top panel below). In contrast, precession
causes out-of-phase changes in insolation. When the Northern Hemisphere
summer solstice is at aphelion (as it is now), the summer insolation is
at a minima. On the other hand, the Southern Hemisphere summer solistice
is at perihelion and summer insolation is at a maxima (see the bottom