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Old International Astronomy Olympiad Papers
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  IAO final papers – Problem Sets Theory Tests Cat Question   J1 1.   Why is it sometimes better to use a small telescope in orbit around the Earth than it is to use a large telescope on a mountain top? J1 2.   A thick black fly has dotten onto the object lens of a 5 cm telescope. What will an observer looking to the Moon through the telescope see? J1 3.   Explain why we see more meteors from midnight to dawn than from evening to midnight. J1 4.   The 12 Zodiacal signs are equally extended on the ecliptic. In which of them does the Sun lie in for the shortest period? J1 5.   On 1 cm 2  of Pluto's surface fall approximately 10,000 photons per second from a star of the fifth magnitude. How many photons would fall on a detector from a star of 20 m  during half an hour, if BTA at the Earth is used (the diameter of the main mirror is 6 m)? J1 6.   The sun has a parallax of p s  = 8 .8, and a star with the same absolute brightness – p *  = 0 .022. Is it  possible to observe the star at night sky visually? J1 7.   The moon set in St. Petersburg (60° North, 30° East) yesterday just at midnight. In what region of the Earth will there be an opportunity to observe a total solar eclipse sometime next week? J1 8.   A spaceship landed on an asteroid 2.2 km in diameter with an average density of 2.2 g/cm 3 . The asteroid is slowly rotating. The cosmonauts decided to travel along the equator of the asteroid in a rover in 2.2 hours. Will it be possible for them to do such a thing? If the answer is negative, why? If the answer is positive, what do they take into account? S1 9.   Why might some stars appear double in blue light through they could not be resolved in red light? S1 10.   Why can radio astronomers observe during the day, whereas optical astronomers are (for the most  part) limited to nighttime observing? S1 11.   Why is it better for some purposes to use a medium size telescope on a mountain instead of a telescope on a spaceship at low orbit near the Earth? S1 12.   What are the reasons why the Hubble Space Telescope is able to observe fainter objects than we can study from the ground? S1 13.   The moon set in St.Petersburg (60° North, 30° East) yesterday just at midnight. In what region of the Earth will there be an opportunity to observe a total solar eclipse sometime next week? S1 14.   Altair (a Aquila) has a parallax of p = 0 .198, proper motion µ = 0 .658/year, radial velocity Vr = -26 km/s and visible brightness m = 0m.89. When and what would be the minimum distance of Altair to the Sun? Also find the brightness of Altair at that point. S1 15.   Recently the Ten-meter Keck telescope began to operate on Mauna Kea (Hawaii), where the diameter of stellar images may be as small as 0 .3. Can you evaluate the limiting stellar magnitude for visual observation with this telescope? J2 16.   Two stars have the same absolute magnitude. One is thousand times farther away than the other. What is the difference in apparent magnitudes? Which magnitude larger?  J2 17.   What would an observer have seen sitting on the Moon and looking at the Earth, when the total eclipse of the Sun took place on the Solovetz Islands (34°45' East, 65°01' North) at 5 a.m. July 22, 1990? Illustrate your answer with a drawing. J2 18.   The duration of the day on Mars is only approximately 2.5 % longer than on Earth. The orbital  period of Mars is 687 days. Find (approximately) the difference between the duration of the sidereal day and the mean solar day on Mars. J2 19.   On the day of the all-the-world holiday (fortieth anniversary of the launch of the first satellite), October 4, 1997, Venus was not far from its Eastern elongation, its coordinates were approximately a = 15h20m, d = -22°. Using the above data, estimate its coordinates and position relative to the Sun on the day of the launch of the first satellite, October 4, 1957. The orbital period of Venus is 0.61521 of the tropical year. J2 20.   Let us consider that observer is sitting on a planet of Sirius. Which object is brighter one in his sky : either our Sun or the stars of the Big Dipper? J2 21.   Let us say that the Sun is in Zenith, if it covers the Zenith by its disc. Where is it possible to see such an event more often - in Quito (latitude = 0°) or in San-Paulo (latitude = -23.5°)? Explain. S2 22.   If a star is moving away from the Earth at very high speed, will the star have a continuous spectrum that appears hotter or cooler than it would if the star were at rest? Explain S2 23.   In the course of star war one crazy civilization cut a star in two halfs (without varying substance density and its temperature). How did this lofty deed change the star's magnitude? What is the magnitude of the resulting double star compared to that of the srcinal star S2 24.   What limits the resolving power of the 6-meter telescope BTA in SAO? Calculate it. Explain your calculations J3 25.   What can one see in the Moon's sky more often – the Sun or the Earth? J3 26.   In a new postal service a huge cannon shots a postal shell from England to New Zealand. Can you estimate the duration of the shells flight? J3 27.   It is known that the equatorial coordinates of vernal equinox are 0 hr and 0 deg. Which are the  North Ecliptic Pole coordinates? J3 28.   Suppose that the Sun collapsed suddenly to a black hole. How would the orbital period of the Earth be affected? J3 29.   Can we distinguish the lunar Mare Crisium, which diameter is 520 km, by a naked eye? J3 30.   There are about of 250 millions of stars in the elliptical galaxy M32 (a satellite of Andromeda galaxy). The visual magnitude of this galaxy is 9m. If luminosities of all stars are equal, what is the visual magnitude of one star in this galaxy? S3 31.   Is it possible to observe solar eclipses, meteors, comets, auroras, rainbows, noctilucent clouds and artificial satellites on the Moon? S3 32.   There are Cepheids variables in our own Galaxy as well as in other galaxies. Why was the period-luminosity relation first recognized for Cepheids in the Magellanic Clouds? S3 33.   Because precession, the vernal equinox point moves slowly (50 per year) in the sky. Along what celestial circle does it move – the equator or the ecliptic? S3 34.   Artificial Earth satellite moves with a speed of 6.9 km/sec along the circular equatorial orbit in the direction of the Earth rotation. What is the period of the satellite appearance above any fixed  equatorial point? S3 35.   Can we distinguish the lunar Mare Crisium, which diameter is 520 km, by a naked eye? S3 36.   There are about of 250 millions of stars in the elliptical galaxy M32 (a satellite of Andromeda galaxy). The visual magnitude of this galaxy is 9m. If luminosities of all stars are equal, what is the visual magnitude of one star in this galaxy? J4 37.   The apparent diameter of the Moon, as seen from the Earth, is 31'. What is the image diameter in the objective focal plane if its focal length is 254 cm and the objective diameter is 40 cm? Draw a figure (a few figures) to explain your calculations. J4 38.   A photometer is mounted on a 125 cm (focal length) telescope. Can you observe a star with magnitude - 5m, 10m, 15m in a cluster if a count from a star of a similar spectral type with magnitude 8m gives 4000 counts/second? The level of white noise of the photometer (instrumental noise) is 500 counts/second; the upper limiting value for observations is 200000 counts/second. Explain your calculations. JS4 39.   Where (on the Earth) and when is it possible to observe the sunrise with the longest duration? Estimate its duration. JS4 40.   Usually we consider that there are about 6000 stars in the whole sky which are visible by our eyes. Estimate, how many visible stars are circumpolar (which means that they never set): Note: formula for sphere's area calculation: S = 4pR2. a.   if you are placed 1° from the North Pole.  b.   if you are placed 1° from the Equator (to the North). JS4 41.   An airship started from a cosmodrome located near the equator of the earth at the moment of a sunset. A pilot of the airship wants to continue to observe the sun on the horizon. What should the speed of moving of the airship be? Describe in detail the motion of the air ship JS4 42.   Suppose that a total solar eclipse is observed from a place at the equator when the sun is in zenith. Also, suppose that the shadow of the moon moves along the equator. Calculate the speed of the shadow relative to the observer. S4 43.   One star peaks at 2000 A. Another peaks at 10000 A. Which one emits more radiation at 2000 A? Which one emits more radiation at 10000 A? What is the ratio of the total radiation emitted by the two stars? Consider the stars as black bodies. S4 44.   Engineers from the Simferopol University describe a new method to utilize old military ships: to construct very small black holes from their material (patent yzarc-048UA7). Estimate the diameter of a black hole constructed using this patent from a ship with the mass of 5000 tn (1 tn = 1000 kg). What physical object has a size of the same order of magnitude? Describe propagation of visible light near this black hole. J5 45.   As you know, the most widely used calendar in the middle centuries was Julian. Just now most countries use the Gregorian calendar and the difference between Julian and Gregorian calendars is 13 days: for the same days dates in the Julian calendar fall behind the dates in the Gregorian calendar by 13. Last time the dates in these calendars coincided were in the 3rd century. Calculate in what century such a difference will be 1 year and the 22nd of October (for example) in Gregorian calendar will coincide with the 22nd of October in the Julian once again. J5 46.   Two stars have the same apparent magnitude and are of the same spectral type. One is twice as far away as the other. What is the relative size of the two stars? JS5 47.   There are two photos of the Moon taken by the same camera mounted on the same telescope (the  (the telescope is placed on the Earth). The first photo has been made while the Moon was near its perigee and the second one – near the apogee. Find from these data the value of the Moon's orbit eccentricity. Estimate the minimal period between the moments at which these two  photos could be taken. JS5 48.   A cosmonaut in a spacecraft is moving over the Moon surface through the Mare Frigoris at an altitude of 100 km. An astronaut is walking on the Moon's surface at Mare Frigoris and it is daytime at that place (the Sun is shining). Can the cosmonaut register the astronaut using  binoculars with a magnification of 20x. Take into account all the possibilities. JS5 49.   There is a radio source placed on a satellite of some planet named Olympia . The radio source is working all the time but an observer does not register the signal all the time due to eclipses. The figure shows the level of the receiving signal by the observer vs time. Find from these data the average density of the planet. Take into account that the orbit of the satellite is circular, the observer is in the plane of the satellite's orbit and Olympia is far away from the observer. (Picture Missing!!!) JS5 50.   An 1.2-meter Schmidt camera has a 6° ´ 6° field of view. Estimate how many photographs you would have to take to cover the whole sky. (Please, make an estimation of the maximum and minimum number of photos.) Explain your calculations. Where do you have to place your telescope to be able to do this? S5 51.   A quasar is observed and it is found that a line whose rest wavelenght is 3000 Ao is observed at 15000 Ao. Estimate: a.   How fast is the quasar receding?  b.   How far away is it if its distance is given by the Hubble relation (The Hubble constant is H = 75 km/s/Mpc)? Both answers may be done with an accuracy of 30 %. S5 52.   Young scientists from the Komi-Republic territory (in the Russian Federation) registered a few days ago a new object looking like an eclipsing binary star. But the period of this star was not stable: the stellar magnitude of the object is usually equal to 24.32m. Once every 7-11 seconds it is rising to 24.52m for 0.2-0.3 seconds. After investigations it was clear that the shining object is eyes of a group of absolutely black cats sitting on a small absolutely black body in our Solar System and looking towards the Sun! And one of the cats is blinking! Calculate the number of cats in the group sitting on the small body and looking to the Sun. Draw a picture explaining your solution. Consider that all the cats are equal in size.
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