IAO 2006, Теория, Група β — Задача 3. Polar day and night.
Theoretical round. Problems to solve · 10 ноември 2006 г.
Бележка
Maybe not all problems have correct questions. Some questions (maybe the main question of the problem, maybe one of the subquestions) may have no real sense. In this case you have to write in your answer (in English or Russian): «situation is impossible – ситуация невозможна». Of course, this answer has to be explained numerically or logically.
Source annotations
Printed source inconsistencies are retained: the English telescope key repeats Δx_m on the right of its displacement identity; the galaxy key uses both1.89×10⁻³ and1.86×10⁻³rad; the alpha eccentricity ratio has a sign inconsistency before the later positive0.07 result. The English polar key prints71°06′N/72°48′S; the Russian copy has handwritten70°06′N/71°48′S. No scientific correction has been silently substituted.
Условие
Find the boundaries of the region of the polar day and the region of polar night at the dates when the Sun may be in Zenith in Mumbai, HBCSE. The latitude and longitude of HBCSE are , . Take as many effects as possible into account.
Решение
If the Sun is in zenith in any point, its declination is equal to the latitude of this point. Therefore those dates when the Sun can be in Bombay (HBCSE) in zenith, declination of the Sun is equal to . In this case (firstly refraction not taken into account) the center of the Sun during the current day never be under the horizon at northern latitudes above and also never be above the horizon at latitudes to the south from . Taking into account refraction ( at horizon) and radius of the Sun (), it is possible to receive, that the top edge of the Sun during the current day never set under the horizon at northern latitudes above and also never rise from the horizon at latitudes to the south from . These latitudes are the real boundaries of polar day and polar night. For HBCSE and the boundaries appear on N (polar day) and S (polar night).
Оригинал в Архива: theo1.jpg · официални решения: theosol1.jpg · допълнителни данни: theo2.jpg · допълнителни данни: theodata1.pdf · допълнителни данни: theodata2.jpg · допълнителни данни: constants.jpg · допълнителни данни: theosol2.jpg · допълнителни данни: theosol3.jpg · допълнителни данни: theosol4.jpg