Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.issp.ac.ru/iao/apao/2014/problems/pages03-04_ap14_t_en_b.pdf Дата изменения: Tue Dec 2 20:29:52 2014 Дата индексирования: Sun Apr 10 05:42:13 2016 Кодировка: Поисковые слова: apollo 13

EURO­ASIAN AST RONOMICAL SOCIET Y

R o u n d

Theo

- X As i a n - P a c i f i c As t r o n o m y O l ym p i a d
, - 24. X I . ­ 2. X I I . 2014 Irkutsk-Listvyanka, Russia

G r o u p





language

English

Theoretical round
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 Russ ian): «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» have to be written in English or Russian.



1. Footstep of babr. Babr is a local representative of the biological family of cats (felidae) depicted on the coat of arms of Irkutsk, and the emblem of the X APAO (with a telescope in his mouth). On June 6, 2012, Irkutsk astronomers have phot ographed the transit of the planet Venus passing across the solar disk (fig. 1). And on November 19, 2014, they saw a sunspot, like a paw print of babr, and named this spot "footstep of babr" (fig. 2). The surface of the Sun is shown in the same scale in both images.



1.1. Estimate the typical size of the sunspot "footstep of babr". 1.2. Estimate, at what magnitude the sunspot "footstep of babr" would shine (calculating without the emission of the rest solar surface). W ith the magnitude of what celestial body can the result be compared? 2. LSVT and babr. The Large Solar Vacuum Telescope (LSVT) of the Institute of Solar Terrestrial Physics, located in Listvyanka, has the main mirror 760 mm in diameter and focal length 40 m. One of the main activities of the scientists observing with the LSVT is the research of active features in solar atmosphere. Scientists regularly observe sunspots. 2.1. Draw in real scale a picture of image of the sunspot "footstep of babr" (see picture and condition of the previous problem) obtained in the focal plane of the LSVT. 2.2. W hen observing the Sun during sunset scientists have seen a running animal on the hill on the opposite side of the Angara river (approximately 5 km away). Scientists have suggested it is a babr, cat's like animal (felidae) about the size of a tiger. Estimate how far you need to
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X APAO 2014

Theoretical round. Problems to solve. Group



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move the screen on which the animal. 2.3. Draw in actual scale in something else) that will be 2.4. W ill the resolving power of («-yes» or «-no»).

the Sun was recorded to clearly see on it the silhouette image of your notebook something (a point, spot, silhouette, image or visible on the screen. LSVT be enough to understand what kind of animal is observed?

3. Orion's Belt. The Babr decided to join company of astronomy animals-observers and came to Listvyanka to the X APAO to take photos of stars of Orion's Belt near the horizon. W ill this be possible? («-yes» or «-no»). W hen is it better to take the photos: on rising, culmination or setting of Orion? At approximately what time (use time of Irkutsk) should the photos be taken? The solution has to include an artistic picture with an image of the B abrobserver taking photos of Orion's Belt. 4. Fourth star of Orion's Belt. As you know, there is a Penguin among animals-observers, and he is a great joker. The Penguin decided that something is missing for artistic perception of Orion, and one must "put" a fourth star on the B abr's picture of Orion's Belt. For this, he found a photoflash lamp and, sitting somewhere in the field of view of the camera during the exposure, flashed once (sent one light pulse) to the camera during the exposure. Estimate at what distance from the Babr the Penguin was, if the shining of the "fourth star of Orion's Belt" approximately corresponds to that of the three others in the picture. W hen photographing, the Babr-observer used an exposure time of the order of 10 seconds. Take into account the parameters of the flash pulse. The photographic conditions (sensitivity of CCD, diaphragm) while photographing objects with the flash at the distance of 1 meters (from both flash and camera) should be the same as while photographing the same objects on a sunny day with an exposure time of about 1/1000 second. The solution has to include a picture with artistic images of the Penguin and his flash lamp. 5. Eclipses. Our Moon is moving away from Earth at a rate of 3.8 cm per year. Estimate how many years the habitants of Earth will have a possibility to see total solar eclipses. 6. ISS near Zenith. On the day of the beginning of the X APAO, November 24, 2014, at 05 h 01 min (Irkutsk time) the spacecraft Soyuz-TMA-15M was launched. At 10 h 48 min it was docked with the ISS. It is interesting to note that sometimes ISS flies very close to Zenith for an observer in Listvyanka. At what minimum zenith distance can ISS be seen from Listvyanka? November 24, 2014, the main parameters of the orbit of the ISS are: Inclination of the orbit: i = 51.648°. Mean motion (revolutions per day): n = 15.5142. The shape of the Earth can be considered as spherical (with radius equal to the distance from Listvyanka to the center of the Earth), and the ISS orbit as circular. Note: It is not a problem to estimate. Precise calculations may be necessary to get correct result.





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