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IAO 1999 Problems

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International Astronomy Olympiad 1999
  IV International Astronomy Olympiad  Crimean Laboratory of SAI MSU and Crimean Astrophysical Observatory, s. Nachny!, September # $ October , %&&&.   'roblems to solve(heoretical rond Text of these problems is available also in other languages. To solve every problem you may use constants and well-known values you know by heart. )rop A *!niors, + % years old-.   %.  The apparent diameter of the Moon, as seen from the Earth, is 31'. hat is the ima!e diameter in the ob ective focal plane if its focal len!th is #$% cm and the ob ective diameter is %& cm (raw a fi!ure )a few fi!ures* to e+plain your calculations. .   photometer is mounted on a 1#$ cm )focal len!th* telescope. an you observe a star with ma!nitude a.$ m   b.1& m  c.1$ m  in a cluster if a count from a star of a similar spectral type with ma!nitude  m  !ives %&&& counts/second The level of white noise of the photometer )instrumental noise* is $&& counts/second0 the upper limitin! value for observations is #&&&&& counts/second. E+plain your calculations. )rop  *seniors, / % years old-.   %.  ne star peaks at #&&& . nother peaks at 1&&&& . hich one emits more radiation at #&&&  hich one emits more radiation at 1&&&&  hat is the ratio of the total radiation emitted by the two stars onsider the stars as black bodies. .  En!ineers from the 2imferopol niversity describe a new method to utili4e old military ships5 to construct very small black holes from their material )patent y4arc-&%6*. Estimate the diameter of a black hole constructed usin! this patent from a ship with the mass of $&&& tn )1 tn 7 1&&& k!*. hat physical ob ect has a si4e of the same order of ma!nitude (escribe propa!ation of visible li!ht near this black hole. Other problems *0$&- are for the both *A and - 1rops2   (heoretical rond 0.  here )on the Earth* and when is it possible to observe the sunrise with the lon!est duration Estimate its duration. 3.  sually we consider that there are about 8&&& stars in the whole sky which are visible  by our eyes. Estimate, how many visible stars are circumpolar )which means that they never set*5 a.if you are placed 1 °  from the 9orth :ole.  b.if you are placed 1 °  from the E;uator )to the 9orth*. 1   9ote5 formula for sphere's area calculation5 2 7 % π <  # . #.  n airship started from a cosmodrome located near the e;uator of the earth at the moment of a sunset.  pilot of the airship wants to continue to observe the sun on the hori4on. hat should the speed of movin! of the airship be (escribe in detail the motion of the air ship. .  2uppose that a total solar eclipse is observed from a place at the e;uator when the sun is in 4enith. lso, suppose that the shadow of the moon moves alon! the e;uator. alculate the speed of the shadow relative to the observer. 'ractical rond 4.  rite the observational pro!ram for this ni!ht on a %&-cm telescope. hat stars would you observe this ni!th rite se;uence of the observations. 2tars to observe5   V (mag)  δ  (1950) 1  η  Aql 3 m .519 h  49 m .90 °  53 ′  2   Per 2.13 04.940 463  χ  Cyg 14.219 48.632 474 R Aqr 12.423 41.2-15 345   Ori 1.35 52.47 246 RW Vir 6.712 04.7-6 29 Moon rise5 #15165#8, phase &.66 2ideral time for & h  s &  7 &5315&% =ou may use all observational time )since #&h till $h 3& min*. >ocal time >T7T?3 oordinates of observatory λ  7 # h 18 m   ϕ  7 %% ° %3 ′  :ut your result into the table5 StarInterval of obervation  2tars that could not be included in the pro!ram5 E+planations and notes5 #  5.   li!th curve of eclipsin! binary is shown in the fi!ure. Estimate the ratio of </r in assumin! that the eclipse is central and the small component is fainter. Observational rond &.%.  9ame the distance between the Moon and @upiter in de!ree. 2how how did you find the result. &. .  Aind and name the five bri!htesr stars of autumn sky. hich one is the bri!htest &.0.  (efine the period since new moon for today.3


Jul 23, 2017
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