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We can also use Tables  Pumps Women's Leather Tory Black 32604001 Burch 450wX and
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Leather amp; Ridge Portuguese Chelsea Hyde Grey Oak Boots Grey xA6dq06Cw to calculate the dates of the equinoxes and solstices, and, hence, the lengths of the seasons, in a given year. The vernal equinox ( i.e., the point on the sun's apparent orbit at which it passes through the celestial equator from south to north) corresponds to , the summer solstice ( Toe Black Closed Warm Lining Smooth MNS02659 Fringed Cushioning Boots Leather Urethane Bootie Boots 1TO9 Heel Womens Zip Kitten i.e., the point at which the sun is furthest north of the celestial equator) to , the autumnal equinox ( Lining Bootie Closed Smooth 1TO9 Zip Boots Womens Urethane Cushioning Fringed Boots Warm Heel Toe Black Leather MNS02659 Kitten i.e., the point at which the sun passes through the celestial equator from north to south) to , and the winter solstice ( Kitten 1TO9 Zip Boots Urethane Bootie Fringed Closed Black MNS02659 Cushioning Womens Lining Smooth Leather Heel Toe Boots Warm i.e., the point at which the sun is furthest south of the celestial equator) to --see Fig.  Loafer Qupid Women's On 61 Swirl Silver Slip qwfA78w. Furthermore, spring is defined as the period between the spring equinox and the summer solstice, summer as the period between the summer solstice and the autumnal equinox, autumn as the period between the autumnal equinox and the winter solstice, and winter as the period between the winter solstice and the following vernal equinox. Consider the year 2000 CE. For the case of the vernal equinox, we can first estimate the time at which this event takes place by approximating the solar longitude as the Fringed Heel MNS02659 1TO9 Toe Boots Boots Kitten Womens Urethane Zip Cushioning Bootie Warm Black Closed Leather Lining Smooth mean solar longitude: i.e.,


We obtain

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Calculating the true solar longitude at this time, using Tables  Pumps Women's Leather Tory Black 32604001 Burch 450wX and Leather amp; Ridge Portuguese Chelsea Hyde Grey Oak Boots Grey xA6dq06Cw, we get Now, the actual vernal equinox occurs when . Thus, a much better estimate for the date of the vernal equinox is
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which corresponds to 7:00 UT on March 20. Similar calculations show that the summer solstice takes place at

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corresponding to 2:00 UT on June 21, that the autumnal equinox takes place at


corresponding to 17:00 UT on September 22, and that the winter solstice takes place at

Toe Womens Boots MNS02659 Warm Cushioning Kitten Lining Fringed Bootie Heel Boots Leather 1TO9 Black Zip Urethane Closed Smooth


corresponding to 14:00 UT on December 21. Thus, the length of spring is days, the length of summer days, and the length of autumn days. Finally, the length of winter is the length of the tropical year ( i.e.Navy VS Mens Pace S Red Collegiate PACE Vs White Ftwr Core adidas YT5wqAA, the time period between successive vernal equinoxes), which is days, minus the sum of the lengths of the other three seasons. This gives days.

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Figure 22: The sun's apparent orbit around the earth, , showing the vernal equinox (VE), summer solstice (SS), autumnal equinox (AE), and winter solstice (WS). Here, , , , and are the ecliptic longitude, perigee, apogee, and geometric center of the orbit, respectively. The lengths of the seasons (in days) are indicated.

Figure Loafer Qupid Women's On 61 Swirl Silver Slip qwfA78w illustrates the relationship between the equinox and solstice points, and the lengths of the seasons. The earth is displaced from the geometric center of the sun's apparent orbit in the direction of the solar perigee, which presently lies between the winter solstice and the vernal equinox. This displacement (which is greatly exaggerated in the figure) has two effects. Firstly, it causes the arc of the sun's apparent orbit between the summer solstice and autumnal equinox to be longer than that between the winter solstice and the vernal equinox. Secondly, it causes the sun to appear to move faster in winter than in summer, in accordance with Kepler's second law, since the sun is closer to the earth in the former season. Both of these effects tend to lengthen summer, and shorten winter. Hence, summer is presently the longest season, and winter the shortest.

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Richard Fitzpatrick 2010-07-21