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2.10 The Tropics

 

Frank L. Preuss

 

The following table gives information about the Tropics.

The two striking things there are once that there are two summers and two winters and then also that the days of the short winter are longer than those of the summer, and that, despite the sun not standing that high as in summer.

Also the fact is notable that the two winter high points coincide with the solstices, but not the two summer high points. The high points of the winter are always on the 21. June and 22. December. But the two summer high points are not fixed, as it is the case outside of the tropics. Only for places being directly on the equator, are the two summer high points also the two solstices; there exists no difference between the northern and the southern hemisphere.

In the following table the equator is the center. Then places were chosen, which are about 10 degrees and 20 degrees away from the equator. But near the two tropics a narrower distance than 10 degrees was chosen, to highlight the course of the data there and also the transition from the tropics to the subtropical area; therefore the transition from two summers and two winters to one summer and one winter.

When the sun is near the equator, then the vertical component of its daily wandering is the greater and when it is near a solstice, then the horizontal wandering is the greater and the vertical becomes smaller and smaller and the difference of the lengths of the days wanders against zero.

In the table the horizontal center is the equator; the vertical center is the first solstice, the one of the 21.06., therefore the summer solstice for the northern hemisphere. Since now the seasons in the tropics are of different lengths and the high points of summers and winters are different for different parallels, they can therefore be on different days and also months, one cannot assign them so, as it can be done outside of the tropics.

For that reason the 6 columns for the seasons were also not provided with names, but only the ones in the center, that one for 21. June and the one to the very right, the one for 22. December; therefore those for the solstices.

 

The seasons in the tropics
123456789101112131415161718192021222324252627282930313233
Parallel Seasons.
Yellow is the summer high point; blue is the winter high point
"dd" means days after the previous date, therefore length of the season in days
Des-crip-tion φ Place 1. Solstice, on the 21.06. 2. Solstice, on the 22.12.
De-gree Name Date dd Length of day An-gle of sun in de-grees Date dd Length of day An-gle of sun in de-grees Date dd Length of day An-gle of sun in de-grees Date dd Length of day An-gle of sun in de-grees Date dd Length of day An-gle of sun in de-grees Date dd Length of day An-gle of sun in de-grees
Length in hh:mmDif-fer-rence in mm:ss Length in hh:mmDif-fer-rence in mm:ss Length in hh:mmDif-fer-rence in mm:ss Length in hh:mmDif-fer-rence in mm:ss Length in hh:mmDif-fer-rence in mm:ss Length in hh:mmDif-fer-rence in mm:ss
 23.6Dhaka 20.03.8812:06+1:2366.0 21.06.93 13:35+0:01 89.7 23.09.9412:06-1:2166.2 22.12.90 10:40< 1s 42.9
Tro-pic of can-cer 23.2Bhopal 20.03.8812:06+1:2166.5 14.06.86 13:33+0:13 90.0 21.06.7 13:34+0:01 89.8 28.06.7 13:33-0:10 90.0 23.09.8712:06-1:2066.7 22.12.90 10:42< 1s 43.3
 23.0La Havana 20.03.8812:06+1:2066.8 11.06.83 13:32+0:18 90.0 21.06.10 13:33< 1s 89.7 30.06.9 13:32-0:14 90.0 23.09.8512:06-1:1966.6 22.12.90 10:42< 1s 43.4
 22.2Cal-cutta 20.03.8812:10+1:1868.3 06.06.78 13:27+0:26 90.0 21.06.15 13:31+0:01 89.1 07.07.30 13:27-0:24 90.0 23.09.6412:06-1:1767.4 22.12.90 10:45< 1s 44.0
 19.2Mexico 20.03.8812:06+1:0670.5 17.05.58 13:04+0:44 90.0 21.06.35 13:18< 1s 86.0 25.07.34 13:04-0:43 89.9 23.09.6012:06-1:0570.3 22.12.90 10:57< 1s 47.2
 10.2Cara-cas 20.03.8812:06+0:3579.4 17.04.28 12:22+0:33 90.0 21.06.65 12:06< 1s 66.4 25.08.65 12:22-0:32 89.9 23.09.2912:06-0:3479.3 22.12.90 13:20< 1s 86.5
Equa-tor  -0.4Quito 20.03.88 12:06< 1s 89.9 21.06.93 12:06< 1s 66.4 23.09.94 12:06< 1s 89.9 22.12.90 12:08< 1s 66.8
 -9.3Port Mores-by 25.02.65 12:19-0:31 89.8 20.03.2312:07-0:3180.9 21.06.93 11:34< 1s 57.1 23.09.9412:06+0:3180.6 18.10.25 12:19+0:30 89.9 22.12.65 12:40< 1s 76.0
-19.6Beira 22.01.31 13:07-0:45 89.9 20.03.5712:07-1:0870.4 21.06.93 10:55-0:01 46.7 23.09.9412:07+1:0770.3 21.11.59 13:08+0:44 89.9 22.12.31 13:20< 1s 86.4
-19.9Belo Hori-zonte 21.01.30 13:07-0:44 89.9 20.03.5812:07-1:0970.2 21.06.93 10:55< 1s 46.7 23.09.9412:07+1:0770.2 22.11.60 13:08+0:44 89.8 22.12.30 13:20< 1s 86.5
-20.3Bula-wayo 20.01.29 13:09-0:44 90.0 20.03.5912:07-1:0970.0 21.06.93 10:54-0:01 46.4 23.09.9412:07+1:0870.0 22.11.60 13:09+0:44 90.0 22.12.30 13:21< 1s 86.7
-22.5Wind-hoek 05.01.14 13:27-0:26 90.0 20.03.7412:07-1:1867.6 21.06.93 10:44-0:01 44.0 23.09.9412:07+1:1767.6 07.12.75 13:28+0:28 90.0 22.12.15 13:31< 1s 89.1
-23.0Rio de Janei-ro 02.01.11 13:30-0:21 90.0 20.03.7712:06-1:2066.9 21.06.93 10:43< 1s 43.7 23.09.9412:07+1:1867.2 10.12.78 13:30+0:23 90.0 22.12.12 13:32< 1s 89.5
Tro-pic of Ca-pri-corn-23.3Reho-both 27.12.5 13:33-0:10 90.0 20.03.8312:07-1:2166.9 21.06.93 10:41-0:01 43.3 23.09.9412:07+1:2066.7 16.12.84 13:34+0:12 90.0 22.12.6 13:34< 1s 89.9
-23.5Sao Paulo 20.03.8812:07-1:2266.6 21.06.93 10:40< 1s 43.0 23.09.9412:07+1:2166.7 22.12.90 13:35< 1s 89.9

 

Summer high point Equinox Winter high point

 

The equator is the only place in the tropics, where the high point of summer, of both summers, falls on the equinoxes; at all the other places in the tropics the summers do not fall on the equinoxes, but always on other days. The high point of the winters always fall on solstices, exactly as in the rest of the world, only that there are two winters in the tropics.

We want to reconstruct the seasons in the tropics at the example of Windhoek.

On 23. September is equinox and the sun stands above the equator and in Windhoek the day is 12:07:29 long and the sun stands 67.6o high. It is equinox and the day and the night are about the same length, therefore about 12 hours long, and 5 days before, on the 18. September they were quite exactly 12 hours long. And the angle of the sun at midday is equal to the number of degrees of the parallel and that are 22.5 degrees against the vertical and that are 67.5 degrees against the horizontal.

After that the length of the day becomes longer and the angle of the rays of the sun at midday to the horizontal becomes greater. It goes towards the summer.

The high point is reached on 7. December. The length of the day is 13:28:00 and the angle is 90,0o. The sun stands directly vertically at midday in Windhoek. It is the high point of the first summer.

The angle from now on becomes again smaller, but the days are not getting shorter, on the contrary.

On 22. December is solstice. The sun has reached the Tropic of Capricorn. It is the high point of the first winter, but which is only a theoretical winter. The length of the day has, despite being winter, reached its maximum, 13:31:21, but the angle its minimum, 89,1o. From now on the days become again shorter, but the angle will again rise. It goes towards the high point of the second summer.

It comes on 5. January, therefore 14 days after that. The time period from the high point of the first summer to the solstice was 15 days, therefore quite symmetry. On the 5. January is the day 13:27:59 long and the sun has again taken its highest possible stand, 90,0o, therefore stands again vertically above Windhoek.

Therefore, within one month, the city has had summer, winter, and again summer.

Now it goes again towards equinox, the second. From now on the length of the day decreases and also he angle, until not only equinox is reached, but also the second winter, which is a real winter.

The equinox is then on 20. March. Then the day is 12:07:39 long and the angle of the sun to the vertical is 67.6o, has therefore values as on the previous equinox. Windhoek’s southern parallel is 22.5o and at equinox that is also the angle of the rays of the sun to the vertical and to the horizontal that are then 67.5o. And equinox means that both, day and night, are about 12 hours long; and that is then also so, but 6 days later, on 26. March.

The sun wanders further towards the north and with it away from Windhoek and the high point of the second winter is then reached on 21. June, when the sun stands on the Tropic of Cancer. Both, the length of the day and also the angle of the sun now reach their minimum: 10:44:57 and 44,0o. It is solstice; the sun stops wandering north and will from now on again return to the south.

From now on the days become again longer and the sun rises up. It is again going towards the equinox, on the 23. September, there where we started, only just one year later.

At the column "Length of the day - Difference in mm:ss" it is about the time, how long it is light during day, and that is about the change of this length from day to day. When the sun is in the area of equinox, it is in the area of the equator, and there it moves fast, the change of its position in the sky from day to day is great. But the closer it comes to the tropic, the smaller is the change and directly at the tropic almost zero.

And that is also the reason, why in the areas of the tropics near the tropics and in the areas of the subtropics near the tropics, it is often hotter than at the equator, because the sun stays there longer. At the equator it is in a hurry, but at the tropics it turns around and therefore has more time to heat up the area. The Persian Gulf is outside of the tropics, but it is one of the areas in the world, where it can become the hottest.

That is also the time, where the two summers lie quite close together and the winter in-between is just a theoretical winter, which is practically exactly as hot as the two neighbouring summers. There the shining of the sun concentrates time wise.

At the time of the equinox, therefore when the sun is at the equator, the difference is great, more than one minute, but at solstice it often smaller than one second.

 

^

 

This is the end of "2.10 The Tropics"
To the German version of this chapter: 2.10 Die Tropen

 

 

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