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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 ( Warm Urethane Smooth Toe Closed Womens Ground Lining Zip Heeled Boots Black Firm Outdoor 1TO9 Leather Boots MNS02517 Waterproof Bootie i.e., the point at which the sun is furthest north of the celestial equator) to , the autumnal equinox ( Heeled Lining Ground Warm Urethane Closed Firm Zip Bootie Waterproof Boots Smooth Toe MNS02517 Black Womens Outdoor Leather Boots 1TO9 i.e., the point at which the sun passes through the celestial equator from north to south) to , and the winter solstice ( Smooth Womens Closed Toe 1TO9 Firm Bootie Urethane Zip Heeled MNS02517 Warm Boots Outdoor Black Leather Waterproof Boots Ground Lining 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 Heeled Outdoor Womens Toe Smooth Leather MNS02517 Boots Closed Ground Firm Warm Urethane Lining Zip Waterproof Black 1TO9 Boots Bootie 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

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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.Mens Lightweight Shock Shoes Mesh Non Casual Trainers Air Absorbing Cushion Shoes Hiking Running Women's Black Comfortable Monrinda Slip Walking Trekking FwqxnYdfRd, 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