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EURO­ASIAN ASTRONOMICAL SOCIETY

R o u n d

Prac

XI XI International Astronomy Olympiad
­ - 12 ­ 2 1 . X . 2 0 1 4 Bishkek ­ Cholpon-Ata

G r o u p
language





English

Practical round. Problems to solve
7. Jupiter. In 2009, a nucleus of unknown comet or an asteroid crashed into Jupiter's atmosphere. A powerful explosion formed a dark cloud, which gradually stretched parallel to equator due to zonal flow in the atmosphere. Hubble Space Telescope was able to take a few pictures of Jupiter during this period. Determine the rate at which the dark cloud on the surface of Jupiter increased its length after the impact with the comet or asteroid by measuring the length of image fragments on the set of the 3 top images displayed on the right. The photos were taken in the same position of the cloud relative to the central meridian. The scale is determined from the image of Jupiter and position of the fragment marked on it. The equatorial diameter of Jupiter is 143842 km. 8. A new variable star. During late winter ­ early spring, 2014, a recently discovered variable star GSC 4560-02157, in the constellation of Ursa Minor, was observed at the Tien Shan Observatory of the Kazakhstan Astrophysical Institute, located in the mountains to the south of Almaty city, approximately in 60 km to the north of Cholpon-Ata (Kyrgyzstan). The star features complex physical variability along with regular eclipses. During the night of February 28 ­ March 1, the star was observed non-stop for almost 9 hours. The table (right) presents the most important data points derived from these observations. The time in the table is the mean solar time for the Almaty time zone. At times of the primary minimum, the star's properties correspond to the K0 spectral type. Plot the light curve. At the time axis, mark times of minimal brightness in the primary minima and in the secondary minimum. Knowing that the Julian date 2456949.000 begins at today's (October 18) Greenwich noon, label the times of minimal brightness with their Julian dates, with three digits after the decimal point. One of simplified models describing the event assumes that the process involves two stars only. From your analysis of the light curve in the frame of such a model, determine the spectral types (for example, that of the Sun is G2) of the larger (1) and smaller (2) components as well as the ratio of the radii of the larger (R1) and smaller (R2) components. Illustrate the solution with necessary figures. Almaty and Cholpon-Ata are in the same time zone.
, ­ - 2014

22 22 22 22 22 23 23 23 00 00 00 01 01 01 02 02 03 03 04 04 04 05 05 05 05 05 06 06

T h 00 h 12 h 24 h 36 h 48 h 00 h 12 h 30 h 00 h 18 h 42 h 00 h 24 h 48 h 12 h 30 h 12 h 36 h 15 h 25 h 36 h 00 h 12 h 24 h 36 h 48 h 12 h 48

m (February 28) m m m m m m m m (March 1) m m m m m m m m m m m m m m m m m m m

m 14.92 15.08 15.41 15.44 15.37 15.12 14.92 14.89 14.80 14.78 14.80 14.82 14.85 14.96 14.72 14.72 14.63 14.65 14.77 14.84 15.10 15.43 15.32 15.05 14.90 14.75 14.73 14.70

Bishkek ­ Cholpon-Ata, Kyrgyzstan