APAO 2006 Theory Problems

E u ro- As i an As t r on omi cal S oci et y The I nt e rn at i onal A st r on omy Ol ym pi ad

I I Азиатско-Тихоокеанская астрономическая олимпиада I I Asian-Pacific Astronomy Olympiad Россия, Владивосток

4–11. XII. 2006

Vladivostok, Russia

Theoretical round English Groups

µαβ

1. Where is Vladivostok? You see a figure from the book of a Russian popular astronomy writer M.V.Shevchenko, which explains the elliptic character of the Earth’s orbit. Redraw this figure into your answer sheet and point approximately the position of Vladivostok on the image of the Earth, where it is winter midday in Vladivostok. Give the reasons of your answer.

2. Meteor. The meteor is seen from the point A at the altitude 30° over the horizon, the magnitude of the meteor is equal to 0m. The same meteor is seen at a zenith from the point B. What is the magnitude of the meteor at this point? The atmosphere extinction can be neglected. 3. A queer orbit. XXIII century. Midnight. A recently discovered planet in a remote solar type star system (its parallax is equal to 0.003200959") is observed. It is found out, that the circle of the visual motion of the planet in the sky has the radius equal to exactly 0.003200959", however the star is not in the center of this circle but on a half-radius distance from the center. In the first newspaper article devoted to the discovery, the daring assumption has been stated, that high level (in the techniques and law) civilization lives on the planet, which has learned how to break the I Kepler law. Do you have any other assumptions? Find the period of rotation of the planet around the star. Whether the planet (territory outside artificial constructions) is suitable for human’s life if the size and mass of the planet are approximately equal to ones of the Earth? 4. Satellite. It is required to launch an artificial satellite in circular polar orbit around the Earth so that it exactly once (neither more, nor less) a sidereal day would appear at a zenith of the point with geographical coordinates in the latitude of 0° and longitude of 0°. What are the possible periods of revolution of the satellite? Put down the answer as XXHYYM within 1 minute accuracy. 5. 60°. The problem is devoted to the 60-th Moscow astronomical olympiad. The Moscow astronomy amateur observes a star with declination +60° by the telescope with the magnification factor 60 and the field of view 1° (60'). Because of incorrect adjustment the clockwork of the telescope goes in (1/60) faster, than it is required. How long is it possible to observe the star without correction of the telescope? 6. N'N'N. The problem is devoted to the Moscow astronomical Olympiad. Moscow astronomical olympiad carried out annually, the first Olympiad (I MAO) took place in 1947. Let us assume, that the following problem is given at this Olympiad annually: «Massive spherical cluster has the radius N pc and consists of N millions stars similar to the Sun. One of the stars is moving at the edge of the cluster with the speed N km/s. Whether this star will leave the cluster?». Every year N is equal to the number of the Olympiad. In what years the star could leave the cluster? In what years it can’t leave it? Maximum total time for all jobs is 4 hours.