APAO 2014, Теория, Група α — Задача 1. Footstep of babr

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

Babr is a local representative of the biological family of cats (felidae) depicted on the coat of arms of Irkutsk, and the emblem of the X APAO (with a telescope in his mouth). On June 6, 2012, Irkutsk astronomers have photographed the transit of the planet Venus passing across the solar disk (fig. 1). And on November 19, 2014, they saw a sunspot, like a paw print of babr, and named this spot “footstep of babr” (fig. 2). The surface of the Sun is shown in the same scale in both images.

Fig. 1 (no printed caption): grey photograph of a patch of the solar surface with the round dark disk of Venus in the middle during the transit of June 6, 2012. No lettering.
Fig. 2 (no printed caption): grey photograph of a patch of the solar surface, same scale as fig. 1, showing the sunspot group “footstep of babr” shaped like a paw print — several small dark toe spots above a larger dark pad, surrounded by a grey penumbra. No lettering.

1.1 Find which is larger and how much larger: the area of a sunspot “footstep of babr” or the area of the Earth's surface.

1.2 Estimate, what mass would a felid have, which may print footsteps of such size on the solar surface. Consider the structure of the space felid to be similar to one of the Siberian felidae. With the mass of what cosmic body can the result be compared? Recollect for yourself the required information about the felidae.

Решение

Внимание: Непълно решение

В архива няма официално решение на тази задача.

Оригинал в Архива: alphatheo.pdf