APAO 2014, Теория, Група α — Задача 4. Fourth star of Orion’s Belt

X Азиатско-Тихоокеанская астрономическая олимпиада / X Asian-Pacific Astronomy Olympiad — Theoretical round — Group α · 24 ноември 2014 г.

Бележка

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

As you know, there is a Penguin among animals-observers, and he is a great joker. The Penguin decided that something is missing for artistic perception of Orion, and one must “put” a fourth star on the Babr’s picture of Orion’s Belt. For this, he found a photoflash lamp and, sitting somewhere in the field of view of the camera during the exposure, flashed once (sent one light pulse) to the camera during the exposure. Estimate at what distance from the Babr the Penguin was, if the shining of the “fourth star of Orion’s Belt” approximately corresponds to that of the three others in the picture. When photographing, the Babr-observer used an exposure time of the order of 10 seconds.

Take into account the parameters of the flash pulse. The photographic conditions (sensitivity of CCD, diaphragm) while photographing objects with the flash at the distance of 1 meters (from both flash and camera) should be the same as while photographing the same objects on a sunny day with an exposure time of about 1/1000 second.

The solution has to include a picture with artistic images of the Penguin and his flash lamp.

Решение

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Оригинал в Архива: alphatheo.pdf