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2.6 Angle of sun orbit


Frank L. Preuss


The following image shows the influence of the inclination of the earth axis by 23.5 degrees.

It shows the summer solstice on the northern hemisphere, on the 21. June, and the winter solstice on the southern hemisphere, also on the 21. June.


The horizontal lines are rays of the sun. In the north the most outer line is the one, which is tangent to the far side of northern polar circle and therefore goes on further beyond it. In the south the most outer line is the one, which is tangent to the near side of the southern polar circle, and also goes beyond it.

In these two tangent points the inclination of the rays of the sun is 90 degrees, measured to the vertical, therefore horizontal.

At the Tropic of Cancer the rays of the sun hit the steepest way. There the inclination to the vertical is 0 degree. The rays of the sun come directly vertically from above.

The angle, under which the rays of the sun at a certain degree of latitude hit at the time of the summer solstice at midday, one can calculate with this formula: Alpha is equal to the degree of the latitude minus 23.5 degrees, for the 21. June, and plus 23.5 degrees for the 22. December.

The following table gives the inclination to the vertical of the course of the sun, and that for certain degrees of latitude. For the better power of imagination also places on these latitudes are given as examples.

These angles are at the same time also angles, which the rays of sun have at midday, also measured against the vertical.

Not the angle measured to the horizontal was used, but the angle measured to the vertical, to portray the direct relationship between the given angles and the number of the degree of latitude.

At the equinox, therefore on 20. March and on 23. September, the angle is directly that angle, which names the angle of latitude.

At solstice on 21. June the angle is obtained by subtracting 23.5 degrees from the angle of latitude, and at the solstice on 22. December it is added.

The smaller the angle therefore is, the higher does the sun stand, and the warmer it is. That is therefore exactly as with the degrees of latitude. The smaller the number of the degree of latitude is, the warmer it is.

High numbers of angles mean high cold.

The sun always shines on one half of the globe, the far half in not shone on. This also applies to the two areas between the polar circles and the poles. But after the equinox in spring it is also started to shine on the half being far from the sun, until then in high summer the whole area is shone on.

This results in that for example on the degree of latitude 75 at midday in high summer the sun has a degree to the vertical of 75. It therefore stands 15 degrees above the horizon. But on the far side from the sun it also shines; there the angle is 89,5 degrees to the vertical, therefore also there the sun is above the horizon, though only 0.5 degrees.

What therefore would be midnight normally, is there not midnight, but day.

And this again causes that the "day" then becomes up to half a year long.

On the following table an angle of 0 degree therefore means that the sun shines vertically from above at midday. And an angle of 90 degrees means that the sun is horizontal, therefore is tangent to earth.


Angle of sun orbit
Location Angle of sun orbit in degrees to the vertical
Description Line of latitude - parallel Examples De-tails 20th March 21st June 23rd Sep-tem-ber 22nd Decem-ber
De-grees of north lati-tude De-grees of south lati-tude
o N o S
North-ern Hemis-phereNorth-pole90  Arctic Ocean90  66.590  no sun-shine
75   Kotelnyy, on Islands Novosibirskiye Ostrova, in Russia.
Nordvik, in Russia.
Islands Novaya Zemlya, in Russia.
Bjørnøya, Island.
Uummannaq, on Greenland.
Devon, island in Canada.
Bathurst, island in Canada,
Melville, island in Canada.
near side75  51.575  no sun-shine
far sideno sun-shine89.5no sun-shineno sun-shine
Arctic circle 66.5 Zhigansk, in Russia.
Salekhard, in Russia.
Rovaniemi, in Finland.
Mount Forel, on Greenland.
Fort Good Hope, in Canada.
Fort Yukon, in Alaska, USA.
Uelen, in Russia.
near side66.543  66.590  
far sideno sun-shine90  no sun-shineno sun-shine
60  Magadan, in Russia.
St Petersburg, in Russia.
Uppsala, in Sweden.
Oslo, in Norway.
Southern tip of Greenland.
Hudson Bay.
60  36.560  83.5
45  Hokkaido.
Aral See.
Belgrad, in Serbia.
Peninsula Istra.
Turin, in Italy.
Bordeaux, in Frankreich.
Minneapolis, in Minnesota, USA.
45  21.545  68.5
30   Shanghai, in China.
Mount Everest.
Delhi, in Indien.
Eilat in Israel.
Cairo, in Egypt.
Agadier in Marokko.
Kanary Islands.
New Orleans, in Louisiana, USA.
Houston, in Texas, USA.
30   6.530  53.5
Tropic of cancer23.5 Taiwan (Formosa).
Guangzhon, in China.
Dhaka, in Bangladesh.
Bhopal, in India.
Masqat, in Oman.
Assuan Damm, in Egypt.
Havana, in Cuba.
Mazatlan, in Mexico.
23.50  23.547  
15  Manila, on the Philippines.
Sana, in Yemen.
Asmera, in Eritrea.
Khartoum, in Sudan.
Dakar, in Senegal.
Dominica, on Guadeloupe.
Guatemala, in Guatemala.
15  -8.515  38.5
Equator0  0  Pontianak, on Borneo.
Mount Kenya, in Kenya.
Kampala, in Uganda.
Libreville, in Gabon.
Sao Paulo, Island in Atlantic (Brasil).
Macapa, in Brasil.
Quito, in Ecuador.
Galapagos Islands, Ecuador.
0  -23.50  23.5
South-ern Hemis-phere-15  Espiritu Santo, Vanuatu, New Hebrides.
Cooktown, in Australia.
Antalaha, on Madagascar.
Mocambique, in Mozambique.
Lusaka, in Zambia.
Namibe, in Angola.
St. Helena, Island, in Atlantic, U.K.
Brasilia, in Brasil.
La Paz, in Bolivia.
Apia, on Island Upolu, Samoa.
-15  -38.5-15  8.5
Tropic of Capri-corn-23.5Rockhampton, in Australia.
Alice Springs, in Australia.
Newman, in Australia.
Toliara, on Madagascar.
Soekmekaar, in South Africa.
Parr's Halt, in Botswana.
Leonardville, in Namibia.
Rehoboth, in Namibia.
Sao Paulo, in Brazil.
Londrina, in Brazil.
Concepcion, in Paraguay.
Embaracion, in Argentina.
Antofagasta, in Chile.
Henderson Island, in Pacific Ocean, U.K.
Tonga Trench, in the Pacific Ocean.
-23.5-47  -23.50  
-30  Norfolk Island, in Pacific Ocean, Australia.
Bourke, in Australia.
Durban, in South Africa.
Molisana, in Lesotho.
Vanderkloof, in South Africa.
Porto Alegre, in Brasil.
Coquimbo, in Chile.
Kermadec Islands, in Pacific Ocean, New Zealand.
-30  -53.5-30  -6.5
-45  Queenstown, in New Zealand.
Prince Edward Island, in the Southern Ocean, South Africa.
Comodoro Rivadavia, in Argentina.
Chatham Island, in the Pacific Ocean, New Zealand.
-45  -68.5-45  -21.5
-60  South Sandwich Islands, in the Atlantic Ocean, U.K.
South Orkney Islands, in the Atlantic Ocean.
Drake Passage, between Atlantic Ocean and Pacific Ocean, and between Argentina and Antarctic Peninsula.
-60  -83.5-60  -36.5
Ant-arctic circle -66.5 South Magnetic Pole.
Antarctic Peninsula.
Casey, on the Antarctic, Australia, permanent base.
Dumont d'Urville, on the Antarctic, France, permanent base.
near side-66.5-90  -66.5-43  
far sideno sun-shineno sun-shineno sun-shine-90  
-75   Prince Charles Mountains, on Antartica.
Prince Albert Mountains, on Antartica.
Ross Sea.
Amundsen Sea.
Cape Dart, on Antarctica.
Siple, on Antarctica, USA, permanent base.
Halley, on Antarctica, U.K., permanent base
near side-75  no sun-shine-75  -51.5
far sideno sun-shineno sun-shineno sun-shine-89.5
South-pole-90  Amundsen-Scott, on the Antarctic, USA, permanent base. -90  no sun-shine-90  -66.5
Location Angle of sun orbit in degrees to the vertical
Description Line of latitude - parallel Examples De-tails 20th March 21st June 23rd Sep-tem-ber 22nd Decem-ber
De-grees of north lati-tude De-grees of south lati-tude
o N o S


This is the end of "2.6 Angle of sun orbit"
To the German version of this chapter: 2.6 Winkel der Sonnenumlaufbahn



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