Съдържание

Условие Решение

IOAA 2011, theory — Задача 3

Автор: Olympiads XYZ · транскрипция на официалните материали

Проверена срещу оригинала на 14.9.2026 от независим модел

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Съдържание

Условие Решение

Long theoretical questions

[Source note]

Instructions

You will receive in your envelope an English and native language version of the questions.
You have 5 hours to solve 15 short (tasks 1-15) and 3 long tasks.
You can use only the pen given on the desk.
The solutions of each task should be written on the answer sheets, starting each question on a new page. Only the answer sheets will be assessed.
You may use the blank sheets for additional working. These work sheets will not be assessed
At the top of each page you should put down your code and task number.
If solution exceeds one page, please number the pages for each task.
Draw a box around your final answer.
Numerical results should be given with appropriate number of significant digits with units.
You should use SI or units commonly used in astronomy. Points will be deducted if there is a lack of units or inappropriate number of significant digits.
At the end of test, all sheets of papers should be put into the envelope and left on the desk.
In your solution please write down each step and partial result.

[Source note]

Long theoretical questions (max 30 points each)

Условие

The planetarium program 'Guide' gives the following data for two solar mass stars:

Star	1	2
Right Ascension	$14^{\mathrm h}\ 29^{\mathrm m}\ 44.95^{\mathrm s}$	$14^{\mathrm h}\ 39^{\mathrm m}\ 39.39^{\mathrm s}$
Declination	$−62^{\circ}\ 40′\ 46.14″$	$−60\ 50′\ 22.10″$
Distance	1.2953 pc	1.3475 pc
Proper motion in R.A.	−3.776 arcsec / year	−3.600 arcsec / year
Proper motion in Dec.	0.95 arcsec / year	0.77 arcsec / year

Based on these data, determine whether these stars form a gravitationally bound system. Assume the stars are on the main sequence. Write YES of bound or NO if not bound alongside your final calculation.

Note: the proper motion in R.A. has been corrected for the declination of the stars.

Решение

Внимание: Непълно решение

В предоставените източници няма официално решение.

Теми и трудност

Трудност: неоценена.

Небесна сфера и сферична астрономия · Звезди · Небесна механика · Небесни координати · Свойства на звездите · Двойни звезди · Гравитационни системи

Оригинал в Архива: 2011_Long_Questions.pdf