Съдържание

IAO 2004, Всички кръгове — Задача 5. α5. Cats in space

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

Exactly 47 years ago, on October 4, 1957, the first artificial satellite of the Earth, "Sputnik I", was launched. Soon after animals went to space. At first there were Russian dogs, then American monkeys... And the French government planned to send cats into space, and not simply one or two cats, but a whole crew of 5 cats! You can see the squad of French cat astronauts (five members of the main crew and one doubler (reserved astronaut)) on the photo. In one of the experiments the cats were illuminated by a strong floodlight located on the Eiffel tower and the data were analyzed. The experiments with the doubler located 10 km from Eiffel tower, have shown, that each of its eyes when hit by this floodlight sparkles as a star of $7^{m}$ (while observed from Eiffel tower).

Calculate approximately the visible stellar magnitude of the total constellation of the eyes of the crew, if the satellite flies above Paris at an altitude of 250 km.

Estimate roughly from what maximum distance the members of the main crew could determine that the light of the eyes of the cat-doubler is not simply a single star but a binary star?

Consider all the crew members and doubler to be identical to each another. The height of the Eiffel tower is $h = 300$ m.

Faded photocopy of a photograph: several cats sitting in narrow box-like enclosures that simulate spacesuits. — Photo. Cats train for space travel planned by the French government in 1973. The enclosures are meant to simulate spacesuit confinement.

Отговори

Решение

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