IAO 2003, Теория, Група B — Задача 5
VIII International Astronomy Olympiad, Stockholm, Sweden, 2–8.10.2003 — Theoretical round. Problems to solve — Group B · 2 октомври 2003 г.
Внимание: Бележка към темата
Solutions for problems 1-3 are shared 'Group A,B' solutions as printed in the source; they were matched to the Group B problem statements which are identical in content for these three problems.
Бележка
Data from the "Table of planetary data" may be used for solving of every problem.
Условие
Every day an astronomer makes observations at the same moment of the Local Sidereal Time, and always notices the Sun just on the mathematical horizon. Where and when the observations are carried out? Your answer must contain both explanations and explicit figures (possible coordinates, etc.)
Отговори
- Arctic Circle at 18ʰ Local Sidereal Time, or Antarctic Circle at 6ʰ Local Sidereal Time.
Решение
Because Sidereal Time is fixed, the ecliptic orientation is fixed too. Because the Sun moves along ecliptic, the mathematical horizon line coincides with ecliptic at the moment of sunrise (or sunset). This applies only on the Arctic or Antarctic Circles. At what time? It is easy to understand if we take into account that on June 22 on the Arctic Circle the situation is possible only at midnight (at Local Sidereal Time) or on December 22 only at midday (at of the Local Sidereal Time too). Analogous considerations give us that on the Antarctic Circle it is possible at Local Sidereal Time.
Answer: The location can only be on the Arctic Circle at or on the Antarctic Circle at Local Sidereal Time.
Note: the term «mathematical horizon» has been used to avoid effects of atmospheric refraction and horizon depression (the main effects in the problem about the White Bear and the Penguin).
Оригинал в Архива: theo.doc · официални решения: theosol.doc