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EURO­ASIAN ASTRONOMICAL SOCIETY

Round Group

Theo

XVI
X V I I n te r na t i o na l A s t ro no m y O l y m pi a d
, - 22 ­ 30. IX. 2011 Alm aty , Kazakhsta n

English

language

Theoretical round. Problems to solve
General note. Maybe not all problems have correct questions. Some questions (maybe the main question of the problem, maybe one of the subquestions) may make no real sense. In this case you have to write in your answer (in English or Russian): «impossible situation ­ ». Of course, this answer has to be explained numerically or logically. Data from the tables (Planetary data, stars, constants, etc.) may be used for solving every problem. The answers «-Yes» or «-No» has to be written in English or Russian.

1. Observation of a star. Observations were done by the naked eye on June 16, 2008, Universal time was used. An observer has registered that a star passed zenith at 0 h18m, and at 8h17m its height above the horizon was 87°12'. Find the latitude of the observations. 2. Planetarium. Classical devices "planetaria" are arranged so that each group of stars is projected on a dome by a small optical system. Foils with hole-stars of the corresponding sizes are often used as these "slides" of constellations which are projected on the dome, so that most of the light is blocked by the foil (the black sky appears), and only light through the holes are transmitted (so stars appear). For example, images of 0m stars on the foil have the size l 0 = 0.1 mm, and stars up to 6m are demonstrated, the focal length of the projecting system is f = 25 cm, and the device has 16 separate projecting systems for every hemisphere. The dome of the planetarium of the observatory "Bobek" has a diameter of 2R = 10 m. Let's suppose that all slides have been removed for replacement by more perfect ones, and the whole light began to be projected on the dome. What would the total stellar magnitude of the illuminated dome be (the artificial gray sky)? Would it be possible to read a newspaper in such an illuminance? The answer has to include a list of the necessary parameters with formulae and numerical values. 3. Sunrise on Mars. The Polar Bear (whom was already met in the texts of many International Astronomy Olympiads) was tired to make astronomical observations on Earth. He made a fascinating journey to the North Pole of Mars, and decided to observe a sunrise there. Calculate how long this sunrise lasts. The solution has to include a picture with an image of the Bear on the North Pole of Mars. Necessary sizes or angular sizes should be in the picture. Assume that Mars is spherical and its orbit may be considered circular. Recollect for yourself the necessary information about the Polar Bear. 4. Photo of Jupiter. In the photo of Jupiter that was taken on October 19, 2009, one of the Galilean moons and its shadow on the disc of the planet can be seen. Jupiter was near the middle of Capricornus constellation when the photo was taken. Find the orbital distance from the moon to the surface of the planet. Determine the name of the moon. The solution should be illustrated by drawings. The name of the moon in the solution and in the drawings should be written (or duplicated) in English. 5. Jupiter disappeared. Let us suppose that Jupiter suddenly disappeared. The moons of Jupiter became independent bodies. 5.1. Which former Galileo moon(s) and in what case may leave the Solar system? 5.2. Which former Galileo moon(s) and in what case may fall into the Sun? The answers "which moon" and "in what case" (configurations at the moment of Jupiter disappearance) have to be given in the form of drawings, and calculations should be the base for the answers. The names of the moons in the solution and in the drawings should be written in English. Consider the orbit of Jupiter (before its disappearance) to be circular.
, - 2011 Almaty , Kazakhstan