IAO 2005, Теория, практически тур и наблюдения — Задача 5. α5. Cluster.
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
Astronomers find a "star" which position in the Hertzsprung-Russell diagram is about higher than the corresponding stars of the main sequence. Assume that the "star" is a cluster of similar stars and estimate the number of stars in the cluster.
Отговори
about 1600 stars
The native solution explicitly rejects an exact 1585-star answer and preserves its printed magnitude-difference sign.
Решение
Let us consider that the absolute stellar magnitude and lightness of the cluster are and , of a star in the cluster is and . Initial relationship is:
So
As it done
So
Answer: about 1600 stars.
Note: Answer "1585 stars" is not correct! There is data "about ", so it is approximate value. For example, by varying this value only by only we will get range of formal answers from 1445 to 1738, and by : from 1000 to 2512.
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 · Звезди · Звездни величини · Поток и светимост · Диаграма на Херцшпрунг–Ръсел
Предпоставки: Гимназиална подготовка, Разширена олимпиадна подготовка
Оригинал в Архива: iao2005.pdf · официални решения: iao2005.pdf