IAO 2016, Теория, Група β — Задача 3. Heaven omen. Two comets.

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.

Do not forget that in clean copy you should write solutions only on even (left) pages. The odd (right) pages will be used by your team leader to translate solutions into English and make emphasizing of your thoughts in solutions.

Общее замечание. Не исключено, что не во всех задачах вопросы поставлены корректно. Некоторые вопросы (возможно, главный вопрос задачи, возможно – подвопрос) могут не иметь смысла. В этом случае следует написать в ответе (по-русски или по-английски): «ситуация невозможна – impossible situation». Естественно, ответ должен быть подкреплён вычислениями или логическими рассуждениями.

Данные из таблиц (Солнечная система, звёзды, константы) могут быть использованы в любой задаче.

Ответы «Да-Yes» или «Нет-No» должны быть написаны по-русски или по-английски.

Не забудьте, что в чистовике вы должны писать решения только на чётных (левых) страницах. Нечётные (правые) страницы предназначены для того, чтобы руководитель вашей команды перевёл решения на английский язык и подчеркнул основные мысли решения.

On June 22, 813 A.D., after 15 days of standing opposite to each other, Bulgarian Khan Krum defeated the Byzantine army of Emperor Michael I Rhangabe near Adrianople (currently Edirne, Turkey) and took over the city. After this victory, the Bulgarian army marched on Constantinople and besieged the capital of the Byzantine Empire. It is possible that the outcome of the battle was affected by superstitious generals. Fear of astronomical events is described in the Byzantine chronicles: “When the two armies, Bulgarian in north-west and Greek in south-east, converged, a terrible celestial omen was the gaze of warriors: two comets, bright as moons, separated from one another”. Some historians of astronomy believe that it is one of the first descriptions of a cometary nucleus fragmentation. However, there are also other options.

**) Для внешних планет и Луны – в среднем противостоянии. / For outer planets and Moon – in mean opposition.

Данные о некоторых звёздах / Data of some stars

The official preliminary solution is retained in its original Russian; English general and applicable beta or joint alpha/beta jury criteria are provided separately. Alpha-only grading sheets are excluded.

The official PDF ends after the second factor in solution 5. Its solution 2 graph is clipped at the original page boundary. The printed dates “17 июня 613 г.” and “16 июня” in solution 4.5 are retained, as are the inconsistent sub-point allocations in general criteria 4.1 and 4.2.

Note. The given sketches are not full; the team leaders have to give more detailed explanations to students. But the correct solutions in the students’ papers (enough for 8 pts) may be shorter.

Note. Jury members should evaluate the student’s solutions in essence, and not by looking on formal existence the mentioned sentences or formulae. The formal presence of the mentioned positions in the text is not necessary to give the respective points. Points should be done if the following steps de facto using these positions.