IAO 2004, Всички кръгове — Задача 7. β1. Distance between galaxies
IX International Astronomy Olympiad · 1 октомври 2004 г.
Внимание: Бележка към темата
Old photocopy scan. Two short passages of the official solutions are lost where the photocopied pages join (problem 4 between pages 4 and 5, the Sunrise solution between pages 13 and 14). The sky maps of the observational round are not in the archive file.
Условие
There are about 100 galaxies in the cluster of galaxies in the constellation of Virgo. The region in our sky covered by this cluster is about . The distance to the cluster is equal to 15 Mpc. Estimate the average distance between the galaxies in this cluster.
Отговори
0.3 Mpc
The official solution: "about 0,3 megaparsecs" or "about 1/3 megaparsecs".
Решение
Note at first, that the precision up to three and even up to two significant figures here is inappropriate, therefore the calculations will be yielded to within two significant figures, and in the answer one figure is pertinent only. The linear size of the cluster is approximately equal to 1.5 Mpc (6° is about 1/10 radian. Accordingly the linear size is approximately 10 times less than the distance to the cluster). Thus, the volume for these 100 galaxies is equal to cubic megaparsecs. So the volume for 1 galaxy in the cluster is equal to 0.034 cubic megaparsecs. The reference linear size of this volume of space is megaparsecs. It is also the average distance between galaxies. Since only one significant digit is appropriate, the correct answers are: "about 0,3 megaparsecs" or "about 1/3 megaparsecs".
Group α, theoretical round
Data from the “Table of planetary data” may be used for the solving of every problem.
And the White Bear and Penguin are waiting for you on the practical round.
Group β, theoretical round
Data from the “Table of planetary data” may be used for the solving of every problem.
And the White Bear and Penguin are waiting for you in the practical round.
Parameters of orbits. Physical characteristics of some planets, Moon and Sun
Элементы орбит. Физические характеристики некоторых планет, Луны и Солнца
| Body, planet | Average distance to central body, in astr. units | Average distance to central body, in mln. km | Sidereal (or analogous) period, in trop. years | Sidereal (or analogous) period, in days | Eccentricity e | Equat. diameter, km | Mass, kg | Av. density, g/cm | Grav. acceler. at surf., m/s | Max. magn. from Earth **) | Albedo |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Солнце Sun | 1392000 | 1989000 | 1,409 | ||||||||
| Меркурий Mercury | 0,387 | 57,9 | 0,241 | 87,97 | 0,206 | 4 879 | 0,3302 | 5,43 | 3,70 | 0,06 | |
| Венера Venus | 0,723 | 108,2 | 0,615 | 224,70 | 0,007 | 12 104 | 4,8690 | 5,24 | 8,87 | 0,78 | |
| Земля Earth | 1,000 | 149,6 | 1,000 | 365,26 | 0,017 | 12 756 | 5,9742 | 5,515 | 9,81 | 0,36 | |
| Луна Moon | 0,00257 | 0,38440 | 0,0748 | 27,3217 | 0,055 | 3 475 | 0,0735 | 3,34 | 1,62 | 0,07 |
**) Для внешних планет и Луны – в среднем противостоянии.
**) For outer planets and Moon – in mean opposition.
Оригинал в Архива: iao2004.pdf