IAO 2004, Всички кръгове — Задача 9. β3. Cometary bodies

IX International Astronomy Olympiad · 1 октомври 2004 г.

Условие

During an observation of a solar eclipse the observers discovered two cometary bodies in the constellation of Aries near the solar corona at an angular distance of $\alpha = 9''$ from each other. Further researches have shown that these two bodies are moving along exactly the same path, at the detection time they were in the aphelion of their orbit (distance from the Sun $A = 8.85$ a.u.), and in perihelion the distance from the Sun is equal to $P = 1.63$ a.u.

What will thus be (or would thus be) the angular distance β between them as seen from the Earth?

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