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he reasons for this yearly variation in the
apparent motion of the Sun are twofold. The first reason
has to do with the fact that the Earth's orbit is not a
perfect circle, but is elliptical with the Sun being nearer
one end of the ellipse. The speed of the Earth in this
elliptical orbit varies from a minimum at the farthest
distance to a maximum at the closest distance of the Earth
to the Sun. The second reason for the yearly variation
has to do with the fact that the Earth's equator is inclined
to the plane of the Earth's orbit around the Sun. These
two effects are explained in the following paragraphs.
1. Elliptical Orbit. While the Earth is rotating
upon its axis, it is also moving around the Sun in the same
sense, or direction, as its rotation. If we select a spot
on the Earth where the Sun is directly overhead, in order for that
spot to rotate with the Earth and come back so that the Sun is
overhead again, it must turn a little extra because of
the Earth's motion around the Sun. The Earth turns a little
more than once with respect to the stars in order to
complete one rotation with respect to the Sun. The
"little extra" is just the angle through which the Earth has
moved around the Sun in a day's time. On the average, this
angle amounts to a little less than one degree per day
(360 degrees/ 365 ¼ days) and is illustrated in Figure 1.
Figure 1. The Earth must rotate 360 degrees plus a, a very small angle,
for observer at A to return to the same position relative to the Sun at B.
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The time for the Earth to turn this small angle is about
four minutes. This little difference would cause no concern
if it were always the same, but it is not! Recalling that
the Earth moves in an elliptical path (much exaggerated in
Fig. 1) around the Sun, rather than a circular path, it turns out
that the Earth is nearer to the Sun in January than in July.
The difference is about three million miles (out of an
average distance of ninety-three million miles). The speed
of the Earth in its orbit increases as it gets nearer to the
Sun. Since the Earth is closest to the Sun in January and
furthest in July, it follows that the Earth is moving more
rapidly in its orbit in January than in July! Thus, the
Earth must rotate a little more each day from October to
April to return to a chosen spot to face the Sun again.
This small amount each day accumulates until it amounts to
a difference of 7.7 minutes on April 2. Having to
turn a little more each day means the sundial lags behind
the standard clock and so the sundial time minus standard
time on April 2 is -7.7 minutes. From April 2 on, the Earth
rotates a little less each day to return to a chosen spot
to face the Sun again, and this decrease accumulates from
April to October until it amounts to a difference of +7.7
minutes on October 2. The difference between sundial time
and clock time resulting from the varying speed of the Earth
in its orbit is graphically illustrated in Figure 2
Figure 2. (top) The Earth moves slowest at A and fastest at B.
(bottom) Equation of Time component due to the eccentricity of
the Earth's orbit.
