iao 2011 problems

8/10/2019 IAO 2011 Problems

1/22

IAO2011QUESTION PAPERS


2/22

THEORYQUESTION PAPERS


3/22

EUROASIAN

ASTRONOMICAL SOCIETY R ound The

GroupXVI

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95eoreti:al ro8n%0 ;roeneral note0Maybe 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

ussian)! "i!$oior e%ample,

images of 6!stars on the foil have the si:e l/B 6.3 mm, an& stars up to 4!are &emonstrate&, the focal

length of the proAecting system is f B 5C cm, an& the &evice has 34 separate proAecting systems for every

hemisphere. he &ome of the planetarium of the observatory DobekF has a &iameter of 5 B 36 m.

Get=s suppose that all sli&es have been remove& for replacement by more perfect ones, an& the wholelight began to be proAecte& on the &ome. Hhat woul& the total stellar magnitu&e of the illuminate& &ome

be (the artificial gray sky) Houl& it be possible to rea& a newspaper in such an illuminance

he answer has to inclu&e a list of the necessary parameters with formulae an& numerical values.

.0 B8nrie on Car0he olar ear (whom was alrea&y met in the te%ts of many International 9stronomy

$lympia&s) was tire& to make astronomical observations on Earth. Je ma&e a fascinating Aourney to the

1orth ole of Mars, an& &eci&e& to observe a sunrise there. ?alculate how long this sunrise lasts. he

solution has to inclu&e a picture with an image of the ear on the 1orth ole of Mars. 1ecessary si:es or

angular si:es shoul& be in the picture. 9ssume that Mars is spherical an& its orbit may be consi&ere&

circular. ecollect for yourself the necessary information about the olar ear.

D0 ;5oto oA E8$iter0 In the photo of 2upiter that was taken on $ctober 3K, 566K, one of the Lalilean moons

an& its sha&ow on the &isc of the planet can be seen. 2upiter was near the mi&&le of ?apricornus

constellation when the photo was taken.

>in& the orbital &istance from the moon to the surface of the planet. 'etermine the name of the moon.

he solution shoul& be illustrate& by &rawings. he name of the moon in the solution an& in the &rawings

shoul& be written (or &uplicate&) in English.

F0 E8$iter %ia$$eare%0 Get us suppose that 2upiter su&&enly &isappeare&. he moons of 2upiter became

in&epen&ent bo&ies.

C.3. Hhich former Lalileo moon(s) an& in what case may leave the Solar system

C.5. Hhich former Lalileo moon(s) an& in what case may fall into the Sunhe answers Dwhich moonF an& Din what caseF (configurations at the moment of 2upiter &isappearance)

have to be given in the form of &rawings, an& calculations shoul& be the base for the answers. he names

of the moons in the solution an& in the &rawings shoul& be written in English. ?onsi&er the orbit of 2upiter

(before its &isappearance) to be circular.

& ' ( ) * + * , / 1 1 A l ! a t " ) 2 a 3 a 4 5 t a n


4/22

EUROASIAN


Groups

XVI


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5/22

EUROASIAN


Groups

XVI


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6/22

EUROASIAN


Groups

XVI


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7/22

EUROASIAN


GroupXVI


&'() *+* ,, - ./0 IX0 ,/11 Al!at") 2a3a45tan

'6Englishlan 8a e

95eoreti:al ro8n%0 ;roeneral note0Maybe 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

ussian)! "i!$oi


8/22

EUROASIAN


Groups

XVI


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9/22

EUROASIAN


Groups

XVI


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4325 6'705

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4320-:;82.

0+.445. *?05 *5-

9532 03as!."nis

03#ln.$#

032'[email protected]

03 1402

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1024

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102

g/%#3

2 18A.

#/s2

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783 B,CDBEJ F,GDBE11 F,FDBEK HDBE1/ BIJFEEE BJHJEEE B,KEJ

!%=48 E,IHL GL,J E,FKB HL,JL E,FEC K HLJ E,IIEF G,KI I,LE E,EBM E,EC

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10/22

EUROASIAN


Groups

XVI


&'() *+* ,, - ./0 IX0 ,/11 Al!at") 2a3a45tan

'6lan 8a e

'6

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L6 6 M6

Fo!e Eontant an% Cor!8lae

%%, 4 (_) FJJ LJF KGH 79 'A 50/@2 03 +488


11/22

OBSERVATION

QUESTION PAPERS


12/22

EUROASIAN

ASTRONOMICAL SOCIETY R ound Obs

Groups

XVI


&'() *+* ,, - ./0 IX0 ,/11 Al!at") 2a3a45tan

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13/22

PRACTICALQUESTION PAPERS


14/22

EUROASIAN

ASTRONOMICAL SOCIETY R ound Pr!

GroupXVI


&'() *+* ,, - ./0 IX0 ,/11 Al!at") 2a3a45tan

'6Englishlan 8a e

9ra:ti:al ro8n%0 9ro;le! to olat8rn ,/1/0

You are provided with a series of Saturn images. Find the rotational period for Saturn, and the velocity and

the direction of the movement of unique formation in the atmosphere of Saturn Great Northern

Disturance !GND", which appeared on Decemer #, $%&%.

=010'se measurements of two images on Saturn on &( Decemer $%&% to determine the rotational period

) for Saturn from the angular change of the GND position during the time interval etween two images.

=0,0*lot from all measurements of the GND core a graph showing how the core longitude + depends on

time t. )he time should e epressed in hours and parts of hours. Set the time of the first image as -ero

time !%.%5". )he inclination of the graph must show the direction and the angular velocity of GND.=0.0Determine the value of radius /!a0"1$ at the GND latitude in 2ilometers and determine the linear

velocity of the G3D core latitude in 2ilometers using the graph that shows + vs t.

You may neglect the tilt of the equator to the line of sight !the direction 4arth5Saturn". 6n the images

north is up. Saturn7s equatorial radius // 8%$88 2m. )he planet is rotating countercloc2wise if you loo2

from the north pole, or from left to right in the images. )he longitude of the central meridian of the planet

increases following the planet7s rotation. 6t means that + increases from right to left in the images.

Data on the images9 date !$%&%, Decemer, day", time ') !h, m", and +:3, the longitude of the central

meridian !in degrees" in system of coordinates of planet.

;n the aove drawing you can see the scheme !a view from the North", is the radius on the GND

latitude. 4vidently < /.

& ' ( ) * + * , / 1 1 A l ! a t " ) 2 a 3 a 4 5 t a n


15/22

EUROASIAN


Group

XVI


&'() *+* ,, - ./0 IX0 ,/11 Al!at") 2a3a45tan

'6lan 8a e

'6

Englishlan 8a e

90 : ,/1/0

90 ;at8rn ,/1/0


16/22

& ' ( ) * + * , / 1 1 A l ! a t " ) 2 a 3 a 4 5 t a n


17/22

EUROASIAN


GroupXVI


&'() *+* ,, - ./0 IX0 ,/11 Al!at") 2a3a45tan

'6Englishlan 8a e

9ra:ti:al ro8n%0 9ro;le! to ol?o$lanet0

Recently astronomers discovered an exoplanet that practically reflects no light and belongs to the class ofhot Jupiters. Its mass corresponds to 12 Jupiter's masses, the average orbit radius is 0.0! "# and the

period is 2.$% days. &he given data about the exoplanet has been obtained ith the help of the data from

the ()epler( telescope hich continuously monitors the s*y region beteen the constellations +ygnus and

yra. &he device as launched in -arch 200 and is capable of seeing not only gas giants, but also planets

ith the si/e of arth. Recently scientists have discovered that exoplanets are capable of causing huge

tidal aves in the stars that have a significant influence on the spectral parameters of the emitted light

from the star. In fact, ith the help of this effect scientists have been able to prove that the planet moves

around a star in a circular orbit.

In the graph see separate sheet the flux of radiation from the system vs. the phase phase given in

radians can be seen, normali/ed to the radiation flux from the star.=0103uring the transit there are four (contacts( hen the contour of the smaller ob4ect touches the contour

of the larger ob4ect at one point. &he contacts ta*e place in the folloing order5

6irst contact5 &he smaller body is completely outside of the larger and moving inside.

7econd contact5 &he smaller body is completely inside of the larger and continues to move

inards.

&hird contact5 &he smaller body is completely inside of the larger and moves outards.

6ourth contact5 &he smaller body is completely outside of the larger and starts to move aay.

In the given graph mar* the points of the first, second, third and the fourth contacts. 8rite in the copyboo*

the value of the phase for each contact.

=0,03etermine the duration of the transit duration of the passage of the dis* of planet over the dis* of the

star.

=0.03etermine the inclination of the orbit for exoplanets and binary stars the reference plane is assumed

to be the (image plane( 9 the plane that is perpendicular to the line of sight.

=0@0+alculate the radius of the star.

=0A0+alculate the radius of the planet.

& ' ( ) * + * , / 1 1 A l ! a t " ) 2 a 3 a 4 5 t a n


18/22

EUROASIAN


Groups

XVI


&'() *+* ,, - ./0 IX0 ,/11 Al!at") 2a3a45tan

'6lan 8a e

'6

Englishlan 8a e

90 :'0

90 ;


19/22

EUROASIAN


GroupXVI


&'() *+* ,, - ./0 IX0 ,/11 Al!at") 2a3a45tan

'6Englishlan 8a e

9ra:ti:al ro8n%0 9ro;le! to ol


20/22

EUROASIAN


Group

XVI


&'() *+* ,, - ./0 IX0 ,/11 Al!at") 2a3a45tan

'6lan 8a e

'6

Englishlan 8a e

90 : ;0

90


21/22

EUROASIAN


GroupXVI


&'() *+* ,, - ./0 IX0 ,/11 Al!at") 2a3a45tan

'6Englishlan 8a e

9ra:ti:al ro8n%0 9ro;le! to ol?o$lanet0

Recently astronomers discovered an exoplanet that practically reflects no light and belongs to the class ofhot Jupiters. Its mass corresponds to 12 Jupiter's masses, the average orbit radius is 0.0! "# and the

period is 2.$% days. &he given data about the exoplanet has been obtained ith the help of the data from

the ()epler( telescope hich continuously monitors the s*y region beteen the constellations +ygnus and

yra. &he device as launched in -arch 200 and is capable of seeing not only gas giants, but also planets

ith the si/e of arth. Recently scientists have discovered that exoplanets are capable of causing huge

tidal aves in the stars that have a significant influence on the spectral parameters of the emitted light

from the star. In fact, ith the help of this effect scientists have been able to prove that the planet moves

around a star in a circular orbit.

In the graph see separate sheet the flux of radiation from the system vs. the phase phase given in

radians can be seen, normali/ed to the radiation flux from the star.=0103uring the transit there are four (contacts( hen the contour of the smaller ob4ect touches the contour

of the larger ob4ect at one point. &he contacts ta*e place in the folloing order5

6irst contact5 &he smaller body is completely outside of the larger and moving inside.

7econd contact5 &he smaller body is completely inside of the larger and continues to move

inards.

&hird contact5 &he smaller body is completely inside of the larger and moves outards.

6ourth contact5 &he smaller body is completely outside of the larger and starts to move aay.

In the given graph mar* the points of the first, second, third and the fourth contacts. 8rite in the copyboo*

the value of the phase for each contact.

=0,03etermine the duration of the transit duration of the passage of the dis* of planet over the dis* of the

star.

=0.03etermine the inclination of the orbit for exoplanets and binary stars the reference plane is assumed

to be the (image plane( 9 the plane that is perpendicular to the line of sight.

=0@0+alculate the radius of the star.

=0A0+alculate the radius of the planet.

& ' ( ) * + * , / 1 1 A l ! a t " ) 2 a 3 a 4 5 t a n


22/22

EUROASIAN


Groups

XVI


&'() *+* ,, - ./0 IX0 ,/11 Al!at") 2a3a45tan

'6lan 8a e

'6

Englishlan 8a e

90 :'0

90 ;

iao 2011 problems

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