Every winter since 1947 competitions for young amateur astronomers are carried out in Moscow (Russia). They are called the Moscow Astronomical Olympic Games. Professional astronomers - professors of Moscow University and researchers of Sternberg Astronomical Institute - are heads of these competitions. The ages of participants range from 11 to 18. The aim of these competitions is to stimulate intellectual curiosity and identify clever young people orientated toward natural sciences.
We have collected 450 of the best problems of the Moscow Astronomical Olympic Games with comprehensive solutions and explanations. Practical astronomy, astrodynamics, astrophysics, planetology and astronautics are the general subjects of the problems. These problems consist of very different levels of difficulty: from simple questions for young amateurs to real problems for professionals. The book may be interesting for college and university teachers, for amateur and professional astronomers.
We are ready to collaborate with enthusiasts of the astronomical competitions all over the world. We are interested in information on international astronomical competitions.
Below is a collection of problems at different levels which you may like to try out. If there is sufficient interest, we will provide solutions and explanations.
Sternberg Astronomical Institute
13, Universitetskij Prospect
1. Why are the longest solar eclipses observed in tropical countries ?
2. A fly has gotten onto the object-lens of a telescope. What will an observer looking through the telescope see?
3. Explain why we see more meteors from midnight to dawn than from evening to midnight.
4. Air is pumped out of the tubes of some solar telescopes. Why is that so?
5. The 12 Zodiacal signs are equally extended on the ecliptic. In which of them does the Sun lie in for the shortest period?
6. Comet Halley and the planet Neptune revolve around the Sun with a period of 76 years and 165 years respectively. Which of them lies further away from the Sun at the aphelion point of their orbits?
7. Why is it that the sunlit surface of the new Moon can be seen well generally, but not during a solar eclipse ?
8. From a star of 0m on 1 cm2 of the Earth's surface fall approximately 106 photons per second. How many photons would fall on a photographic plate from a star of 20m per 1 hour, if the diameter of the objective of the telescope is 1 m ?
9. A spaceship landed on an asteriod 1 km in diameter with an average density of 2.5 g/cm3. The cosmonauts decided to travel along the equater of the asteriod in a rover in 2 hours. Is it possible for them to do such a thing?
10. Three stars of equal mass form an equilateral triangle with each side of L and revolve around their common centre of mass in circular orbits with periods of P. Find the mass of the stars.
11. Altair (Alpha Aquila) has a parallax of pi = 0.198 arcsec, proper motion mu = 0.658 arcsec/yr , radial velocity Vr = -26 km/s and brightness m = 0.89m. When and what would be the minimum distance of Altair to the Sun? Also find the brightness of Altair at that point.
12. What would be the form of spectral lines in the spectrum of a rotating planet if the slit of the spectrograph is directed along its equator ?
13. How many times in a year is the Moon at zenith on the equator ?
14. The Moon set in New York yesterday near midnight. In what region of the Earth will there be an opportunity to observe a total solar eclipse sometime next week?
15. Usually the path of a total solar eclipse on the Earth's surface is about 10,000 km and about 200 km width. As a rule, one total solar eclipse takes place during a year. Evaluate the characteristic timeinterval between total solar eclipses at a certain place of the Earth, for example, your town.
16. Astronautical experts suppose that some crews of perspective moonstations will be prefer to live by 25-hour, not 24-hour, day. Why?
17. The proverb say: "The grass is always greener on the otherside of fence". If the observation is true or not? And, if it is true, what reasons you can suggest to explanation this observation (naturally, except psychological reasons, such as envy)? Is there some analogy between the observation and the appearance of the Sun's surface?
18. Determine any point on the Earth surface from which a person can travel at first 100 miles to the South, then 100 miles to the East, and after that 100 miles to the North, and as a result return to his original point of departure. (Look for nontrivial solutions!)
19. Recently the 10-meter Keck telescope began to operate on Mauna Kea (Hawaii), where the diameter of stellar images may be as small as 0.3 arcsec. Can you evaluate the limiting stellar magnitude for visual observation with this telescope?