List of Problems
Russian Open School Astronomical Olympiad by Correspondence 2005
2. The artificial satellite is rotating around the Earth along an elliptical orbit lying in the ecliptic plane. When it is in perigee point, the distances from Earth to the satellite and to Moon are the same. Estimate the maximum possible eccentricity of the satellite's orbit. Please don't consider the gravitation of the Moon.
3. The distant star is situated in the summer solstice point of the sky. During the passing of ascending node of lunar orbit near this star the lunar occultations of this star will be visible on the Earth every revolution of the Moon. How many occultations will this sequence contain? At what latitude and in what place of the sky will the first and the last occultation of the sequence be seen? The orbit of the Moon can be considered as circular.
4. The path of total solar eclipse consistently passed the following cities: Oslo (Norway), Warsaw (Poland), Constantsa (Romania), Ankara (Turkey), Baghdad (Iraq), Kerman (Iran) and Islamabad (Pakistan). What astronomical season (winter, spring, summer or autumn) the eclipse was observed in?
5. The astronomical azimuths of the rise and the following set of the planet in the city of Saint-Petersburg (latitude +60o) were equal to -90.0o and +90.4o. The duration of the planet disk set was equal to 3.2 seconds. What the planet is it and can it be said anything about the season, when it was happened?
6. Being in the maximum eastern elongation point, Mercury came to the conjunction with Venus. The angular diameter of Mercury was more than 5 times less than the angular diameter of Venus. What planet will be the first to come to the inferior conjunction with Sun? What time will it be earlier than another planet? The orbits of Mercury, Venus and Earth can be considered as circular.
7. Two meteor streams are moving around the Sun by the same orbit, but in opposite directions. One moment both streams meet each other and the Earth. In the same moment two meteor showers are visible on the Earth, their radiant points have the coordinates a=6h, d=-66.6o and a=18h, d=0o. Please find the eccentricity of the meteors' orbit. What date did the streams meet the Earth? The orbit of Earth can be considered a circular one.
8. While using the Giant Optical Cosmic telescope with ultra-high resolution astronomers of the future succeeded to see the disk of Betelgeuse (a Orionis). What object - Betelgeuse or Venus - will have higher surface brightness (the brightness of angular square unit)? What will the ratio of surface brightness of these objects be?
9. The globular stellar cluster has the magnitude equal to 4.5m and angular diameter equal to 25 angular minutes. The distance to the cluster is equal to 3 kpc. Having assumed that the cluster consists of the stars, which are like the Sun and their density is the same over the whole ball volume, so estimate the brightness of the night sky of the planet rotating around the star in the center of cluster. Compare it with the moonlit sky on the Earth. The absorption of light in the interstellar medium and planet's atmosphere can be ignored.
10. The radius of the Galaxy is equal to 15 kpc, the thickness of its disk being many times less. The mass of the galaxy is equal to 1011 solar masses and it is distributed uniformly in the volume of the galaxy. Two stars are rotating around the center of the galaxy in the same direction by the circular orbits with radii equal to 5 kpc and 10 kpc. Please find the synodic period of the first star while observing from the vicinity of the second star.
All Problems written by Oleg S. Ugolnikov
See Olympiad Index Page and General Rules.