Съдържание

IAO 2004, Всички кръгове — Задача 15. β7. Stars

Оригинал на условието (PDF)Съобщи за грешка

Всички материали от IAO 2004

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

Attached is a table with some data about bright stars in our sky.

№	Name of the star / Название звезды: Star	Parallax (arcsec.) / Параллакс (угл.сек.): P	Visible stellar magnitude / Видимая звёздная величина: m	Galactic longitude (degrees) / Галактическая долгота (градусы): l	Galactic latitude (degrees) / Галактическая широта (градусы): b
1	α CMa	0.376	-1.46	227	-9
2	α Car	0.018	-0.72	261	-25
3	α Cen	0.751	-0,27	316	+1
4	α Boo	0.009	-0.04	15	+69
5	α Lyr	0.123	+0.03	67	+19
6	α Aur	0.073	+0.08	163	+5
7	β Ori	0.003	+0.12	209	-25
8	α CMi	0.288	+0.38	214	+13
9	α Eri	0.032	+0.46	291	-59
10	α Ori	0.005	+0.50	200	-9
11	β Cen	0.016	+0.61	312	+1
12	α Aql	0.198	+0.77	48	-9
13	α Tau	0.048	+0.85	181	-20
14	α Cru	0.008	+0.87	300	0
15	α Sco	0.019	+0.96	352	+15
16	α Vir	0.021	+0.98	316	+51
17	B Gem	0.093	+1.14	192	+23
18	α PsA	0.144	+1.16	20	-65
19	α Cyg	0.004	+1.25	84	+2
20	β Cru	0.007	+1.25	302	+3
21	α Leo	0.039	+1.35	226	+49

Scale of circle sizes for the drawing: five dots of increasing size labelled 1m, -1m and -3m.

7.1. Using these data calculate for each star: the absolute stellar magnitude (M) and the projection of the distance from the Sun on the plane of the galactic equator (R). Fill the results into the table:

	Name of the star	Absolute stellar magnitude	Projection on the plane of the galactic equator of the distance from the Sun to the star (in light years)
№	Star	M	R
1
..
..

Arrange the stars in the table in order of decreasing absolute stellar magnitude.

7.2. For the stars with R not larger than 50 light years draw in your copybook positions of the nearest stars in projection to a plane of galactic equator in scale 1 cm – 10 light years. The sizes of the circles have to be M dependent (see fig under the table given). 0° direction of galactic longitude has to be horizontally to the right. Mark the stars with the numbers given in the table of conditions for the problem.

Решение

Stars. Звёзды.

7.1.

№	Name of the star / Название звезды: Star	Absolute stellar magnitude / Абсолютная звёздная величина: M	Projection on the plane of the galactic equator of the distance from the Sun to the star (in light years) / Проекция расстояния от Солнца на плоскость галактического экватора (световых лет): R (two digits – две значащие цифры)
1	β Ori	-7,49	980
3	α Ori	-6,01	640
3	α Cyg	-5,74	810
4	α Boo	-5,26	130
5	α Cru	-4,61	410
6	β Cru	-4,52	470
7	α Car	-4,44	149
8	β Cen	-3,37	204
9	α Sco	-2,65	166
10	α Vir	-2,41	98
11	α Eri	-2,01	52
12	α Tau	-0,74	64
13	α Leo	-0,69	55
14	α Aur	-0,60	44
15	α Lyr	0,47	25
16	β Gem	0,98	32
17	α CMa	1,41	8,3
18	α PsA	1,95	9,6
19	α Aql	2,25	16,3
20	α CMi	2,68	11,0
21	α Cen	4,10	4,3

7.2. See figure. См. чертёж.

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, $10^{24}$ kg	Av. density, g/cm $^3$	Grav. acceler. at surf., m/s $^2$	Max. magn. from Earth **)	Albedo
Солнце Sun	$1{,}6\cdot10^{9}$	$2{,}5\cdot10^{11}$	$2{,}2\cdot10^{8}$	$8\cdot10^{10}$		1392000	1989000	1,409		$-26{,}8^{m}$
Меркурий Mercury	0,387	57,9	0,241	87,97	0,206	4 879	0,3302	5,43	3,70	$-2{,}2^{m}$	0,06
Венера Venus	0,723	108,2	0,615	224,70	0,007	12 104	4,8690	5,24	8,87	$-4{,}7^{m}$	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	$-12{,}7^{m}$	0,07

**) Для внешних планет и Луны – в среднем противостоянии.
**) For outer planets and Moon – in mean opposition.

Оригинал в Архива: iao2004.pdf