IAO 2005, Теория, практически тур и наблюдения — Задача 8. β5. 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" of the spectral class A0 which position at the Hertzsprung-Russell diagram is about – ! (I.e. it is very much higher than the main sequence). Assume that the "star" is a cluster that consists of many similar stars and estimate the possible number of stars in the cluster.
Отговори
about from 600 to 1600 stars
The native solution explicitly rejects exact endpoints 631 and 1585 and refers to α2 as printed.
Решение
Stars of A0 spectral class have absolute stellar magnitude about . So the problem is analogous to α2 with the difference in magnitude of "about – ". Analogous to α2 solution we can find approximate boundaries of number of stars in the claster.
Answer: about from 600 to 1600 stars.
Note once more: Answer about "from 631 to 1585 stars" is not correct! There is data "about – ", so we have approximate values.
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 · Свойства на звездите
Предпоставки: Гимназиална подготовка, Разширена олимпиадна подготовка
Оригинал в Архива: iao2005.pdf · официални решения: iao2005.pdf