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he second reason for the yearly variation of the Equation of Time has to do with the fact that the Earth's equator is inclined to the plane of the Earth's orbit around the Sun.

2. Inclination of the Ecliptic. Another element enters the scene, causing the sundial to vary from the clock. This effect is purely a geometrical one. The axis of rotation of the Earth is not perpendicular to the plane of its orbit around the Sun, but is tilted by an angle of 23 o . So, as the Earth revolves around the Sun, the north pole is tilted 23 o toward the Sun on June 21, and 23 o away from the Sun on December 21, as illustrated in Fig. 3. These are the dates of the summer and winter solstices as recognized in the northern hemisphere. The result, as seen from the northern hemisphere, is that the Sun crosses the sky at noon much higher in June than in December, and if one were to plot the path of the Sun during the year, as seen against the background of the stars, it would appear as a line crossing over the celestial equator on March 21 and September 21 the vernal and autumnal equinoxes. The annual apparent path of the Sun against the background of the stars, called the ecliptic, is shown in Fig. 4, along with the celestial equator. The celestial equator is an imaginary line in the sky directly above the Earth's equator. Thus, when the Sun is on the celestial equator, it stands directly above the Earth's equator We see that the path extends north and south > of the equator by 23 o.

Figure 3. Inclination of the Earth's axis with respect to the plane of its orbit.

Figure 4. The annual apparent path of the Sun, the ecliptic, reaches 23 o north and south of the celestial equator.

Ignoring the change
of speed of the Earth in its elliptical orbit (effect number one above), the true eastward motion of the Sun is greatest when all of its motion is due eastward. This occurs in June and December. In March and September, part of the Sun's motion is northward or southward, and the eastward part of its motion is reduced. This makes the sundial fall behind the standard clock at the solstices and move ahead of the clock at the equinoxes. Fig. 5 illustrates this geometrical effect upon the equation of time.

Figure 5. Equation of Time component due to the obliquity of the ecliptic. (obliquity = 23 o).


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