IAO 2014, theory, α — Задача 4

*АСТРОНОМИЧЕСКОЕ ОБЩЕСТВО

EURO–ASIAN ASTRONOMICAL SOCIETY

Round Theo

Group α

язык language English

XIX Международная астрономическая олимпиада XIX International Astronomy Olympiad

Бишкек – Чолпон-Ата 12–21. X. 2014 Bishkek – Cholpon-Ata

Theoretical round. Problems to solve · 12 октомври 2014 г.*

General note

General note. Maybe not all problems have correct questions. Some questions (maybe the main question of the problem, maybe one of the subquestions) may make no real sense. In this case you have to write in your answer (in English or Russian): «impossible situation – ситуация невозможна». Of course, this answer has to be explained numerically or logically.

Data from the tables (Planetary data, stars, constants, etc.) may be used for solving every problem.

The answers «Да-Yes» or «Нет-No» have to be written in English or Russian.

Условие

4. Hydroplanet. Hydroplanet consists of a rocky “core” of radius $R$ and a thick layer of water surrounding it from all sides. Local humans live at the bottom of this world’s ocean (i.e., on the surface of the “core”), and hydrosphere is an analogue of our atmosphere for them. Local scientists observe astronomical objects from the bottom of the ocean. Like on our Earth, the duration of day-night period on Hydroplanet is $T = 24$ hours.

4.1. Find the minimum depth $H$ of the ocean, for which celestial bodies will be visible at the horizon.

4.2. What will be the duration of the day for inhabitants of the planet’s equator? The disk of the central star can be considered as a point source of light.

4.3. Calculate the value of “atmoshperical” refraction at the horizon on such a planet.

Points of your solution have to include drawings with all necessary sizes or angular sizes. The outer surface of the ocean is smooth, no waves or ripples.

Решение

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Киргизия, Бишкек – Чолпон-Ата 2014 Bishkek – Cholpon-Ata, Kyrgyzstan

Теми и трудност

Трудност: неоценена.

Небесна сфера и сферична астрономия · Атмосферни ефекти

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Оригинал в Архива: alphatheo.pdf