IAO 2023, Теория — Задача 5 (αβγ). Метеоры / Meteors

XXVII International Astronomy Olympiad — Theoretical round / Задачи теоретического тура · 8 т.

Только для перевода. / For translation only.

Напоминание. Большинство задач составлены таким образом, что при написании решений от участника требуется минимальное использование какого-либо языка. Таким образом, допускается минимум текстов в решениях задач (ни на родном языке, ни на одном из официальных языков IAO). Уделяйте больше внимания формулам, рисункам и графикам. Разрешается употреблять несколько ключевых слов на английском языке (например, “Yes”, “No”, “Assume”, “Answer”, “Average”, “Minimum”, “Maximum”, “Impossible situation” и т.д.), а также термины, содержащиеся в прилагаемых таблицах, и названия объектов.

Reminding. Most of the problems are compiled in such a way that when writing solutions, minimal use of any language is required from the participant. So minimum texts is allowed in solutions of the problems (neither in the native language, nor in one of the official languages of the IAO). Pay more attention to formulas, drawings and graphs. It is permitted to write a few keywords in English (for example, “Yes”, “No”, “Assume”, “Answer”, “Average”, “Minimum”, “Maximum”, “Impossible situation”, etc.), as well as terms contained in the accompanying tables and names of objects.

Source notes / Примечания к источнику

The scan repeats the Russian second statement page. Russian and English versions are retained as sections of the same seven tasks. The note after 6.6 prints 8.3/8.5/8.6; the English scan has a handwritten correction. The solution’s final magnitude for task 2 prints +5 rather than −5, the eclipse expression prints L₁−L₂, and the redshift relation prints a(tₑ)/a(tₒ); these source expressions are preserved. The criteria for 6.5/6.6 have unrelated white-dwarf text crossed out without replacement. Reference data are also present within the question PDF and are not extra tasks.

Условие

Русский

Двое наблюдателей метеорного потока Леониды, начало которого приходится примерно на сегодняшнюю дату, визуально наблюдают метеоры в одной и той же области неба. За первые два часа наблюдений один из них заметил 28 метеоров, второй – 38, причём 18 из этих метеоров были замечены обоими наблюдателями. Все метеоры были примерно одной яркости.

5.1. Каково наиболее вероятное общее число метеоров, появившихся за время наблюдений на данном участке неба?

5.2. Решение сопроводите художественным рисунком ситуации, при которой в конце данных наблюдений к наблюдателям внезапно присоединился бурый медведь-астроном.

English

Two observers of the Leonid meteor shower, the beginning of which falls approximately on today's date, visually observe meteors in the same area of the sky. During the first two hours of observations, one of them noticed 28 meteors and the other one 38, and 18 of these meteors were noticed by both observers. All the meteors were about the same brightness.

5.1. What is the most probable total number of meteors that appeared during the observations in this area of the sky?

5.2. Accompany the solution with an artistic picture of the situation, in which the brown bear-astronomer suddenly joined the observers at the end of these observations.

Решение

Theoretical round. Sketches for solutions. For jury job ONLY

These solutions are written for jury members, so they contain a lot of explanations in the form of text. Students are instructed to minimize text, mostly use formulas, calculations, drawings and graphs, writing extra tests is not encouraged in the solutions. It is permitted to write a few keywords in English (for example, “Yes”, “No”, “Assume”, “Answer”, “Average”, “Minimum”, “Maximum”, “Impossible situation”, etc.), as well as terms contained in the accompanying tables and names of objects.

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.

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.

Theoretical round. Basic criteria. For work of Jury

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 use these positions. (For example, except the final conclusion, all the points in solution of problem 2 may be in only one common formula.)

Note. Jury members should elaborate more detailed criteria, and also create criteria for other correct ways of the student’s solutions.

Note. Everywhere “formula” means “correct formula”, “calculation” means “correct calculation”, “picture” means “correct picture”, etc., and in all cases: based on correct facts and intermediate formulae or calculations.

Note. Everywhere final calculation means also using correct number of significant digits. Extra significant digits, especially in estimational problems, will lead to subtraction of the points.

Note. Solutions with absurd or almost absurd answers should be rated lower (maybe ignoring the scoring schemes below, and maybe down to zero).

Everywhere – excessive number of significant digits in the answer – minus 1–2 points.

Теми и трудност

Трудност: неоценена.

Слънчева система · Астероиди, комети и метеори

Предпоставки: Разширена олимпиадна подготовка

Оригинал в Архива: theo.pdf · официални решения: theosol.pdf · допълнителни данни: data.pdf