IAO 2005, Теория, практически тур и наблюдения — Задача 3. Andromeda nebula. · 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
We hope that you are familiar with the object Andromeda nebula (M31, NGC 224). Its stellar magnitude is and its distance from us is . To what distance from this object should we move, if it were to shine as the full Moon? What would the (approximate) angular size of this object be in that case?
Отговори
situation is impossible - ситуация невозможна
The native sketch prints N = exp(17.1/5) = 2630; that printed expression is retained without scientific correction.
Решение
The full Moon stellar magnitude is . So we should come nearer to the Andromeda nebula so that the stellar magnitude changes from to , i.e. for . The formal calculation gives us times. . Taking into account that the angular size of the Andromeda nebula in our sky is about –, i.e. the linear size is about , we see that the formal answer has no real sense. There is no real sense for the question about the angular size as well (formal answer is 130 radians).
Answer: «situation is impossible - ситуация невозможна».
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: 3/5.
Светлина и астрономически измервания · Галактики и космология · Звездни величини · Определяне на разстояния · Ъглов размер · Галактики
Предпоставки: Гимназиална подготовка, Разширена олимпиадна подготовка
Оригинал в Архива: iao2005.pdf · официални решения: iao2005.pdf