NIGHT and DAY

ELLIPTICAL ORBIT

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T

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 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.


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.

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