IAO 2004, Всички кръгове — Задача 16. β8. Sunrise

IX International Astronomy Olympiad · 1 октомври 2004 г.

Условие

The White Bear and Penguin (whom was already met in the texts of the VII and VIII International Astronomy Olympiads) decided to meet each other. For this purpose they arrived to Crimea a few days before the IX Olympiad and they decided to observe sunrise at the day of the autumnal equinox. «I shall go to the Eastern point of Crimea and see the sunrise before others», – the Penguin has said. «No, I shall see the sunrise earlier, because I’ll climb to the highest mountain in Crimea – Roman-Kosh», – the Bear parried. Who is right? On how many minutes or seconds earlier will he see the sunrise? Make a table with all data, which you have found or recollected and used in solving the problem. The solution has to include a picture with an image of the Bear on the mountain Roman-Kosh and the Penguin at the coast of the Kerch channel; the necessary linear or angular sizes should be in the picture. Assume that the Earth is spherical. Recollect for yourself the necessary information about the White Bear and the Penguin.
A map of Crimea is attached.
(Note: the answer «Медведь / Bear» or «Пингвин / Penguin» has to be written in English or Russian.)

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.

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Оригинал в Архива: iao2004.pdf