IAO 2005, Теория, практически тур и наблюдения — Задача 2. Sun. · Groups α β
X Международная астрономическая олимпиада · X International Astronomy Olympiad · 25.X. – 2.XI.2005 · Beijing, China · Китай, Пекин · 25 октомври 2005 г. · 8 т.
Внимание: Бележка към темата
This photographed English/Russian mixed-round booklet includes nine distinct theory tasks with native solution sketches, practical αβ7 and β8 without keys, and three bilingual observational tasks without keys. The α practical task 8, planetary data table, observational sky map and refraction drawing grid referenced in the source are absent. The Sun sketch provides only methods and no calculated distance or magnitude. Jury-result companions print 8 points per theory task, 10 per practical task and 20 for the observational round together, with 88 per cohort; those two cohort totals are not a total for this combined 14-task edition. The 12-minute allowance applies only to all observational jobs. Printed source errors are preserved: the Andromeda sketch uses exp(17.1/5)=2630; the α5 magnitude-difference sign is positive; β4 switches to Δα in one sentence; β5 refers to α2; the refraction formula prints 273°; the planetary-nebula question describes an explosion. Native diagram lines and spectrum peaks are faint in the original photograph.
Theoretical round. Problems to solve · General note
Groups α β
General note. Maybe not all problems have correct questions. Some questions (maybe the main question of the problem, maybe one of the subquestions) may have no real sense. In this case you have to write in your answer (in English or Russian): «situation is impossible - ситуация невозможна». Of course, this answer has to be explained numerically or logically.
При решении каждой задачи можно использовать данные прилагаемой “Таблицы данных о планетах”
Data from the “Table of planetary data” may be used for solving every problem.
Theoretical round. Sketches for solutions · Тезисы решений задач теоретического тура
Русский · English
Условие
In one of the ancient models of the Universe the centre of solar system is the Earth rotating around its own axis. The stars are not moving around the Earth. The Moon and the Sun are orbiting the Earth. Mercury and Venus are orbiting the Sun. Mars, Jupiter and Saturn moves around invisible objects which are orbiting the Earth.
Consider the explanation of the system Earth-Moon to be correct in this model and the mass of Sun to be negligible in comparison with the mass of the Earth-Moon system and find (by two different ways of solution) the distance between the Earth and the Sun in such a model.
Find the absolute stellar magnitude of such a Sun.
Решение
Внимание: Непълно решение
The native sketch supplies only the two Kepler-law comparisons. It prints no calculated distance or absolute stellar magnitude, so no missing numerical results are invented.
The both ways are to use the III General Kepler's law. The first way is to compare the system Earth-SunInModel (365.25 days) with system Earth-Moon (27.37 days) taking into account the same total mass of system. The second way is to compare the system Earth-SunInModel (total mass of system is mass of Earth+Moon) with real system Earth-Sun (total mass of system is mass of Sun+Earth+Moon ≈ mass of Sun).
Observational round. Problems · Задачи наблюдательного тура · Groups α, β
English
Maximum total time for all jobs is 12 minutes.
Русский
Максимальное время выполнения задания – 12 минут.
Теми и трудност
Оценена трудност: 4/5.
Небесна механика · Светлина и астрономически измервания · Закони на Кеплер · Гравитационни системи · Звездни величини
Предпоставки: Гимназиална подготовка, Разширена олимпиадна подготовка
Оригинал в Архива: iao2005.pdf · официални решения: iao2005.pdf