SLOAA Problems (2007-2011)

Srilankan Olympiad on Astronomy and Astrophysics Problems

Please furnish the following information before the commencement of the examination Full Name of the Candidate: Colombo/Peradeniya/Kelaniya/Ruhuna/Batticaloa?Jaffna Date of Birth:

Signature of the Candidate :

INSTITUTE OF PHYSICS, SRI LANKA jointly with ARTHUR C. CLARKE INSTITUTE FOR MODERN TECHNOLOGIES THE 1ST NATIONAL OLYMPIAD ON ASTRONOMY AND ASTROPHYSICS - 2007 (Duration : One Hour) Answer all the questions and submit this paper to the supervisor at the end of the examination. This paper consists of 24 questions in two parts(A &B) printed in Four (04) pages. Electronic calculators are allowed. PART A (Answers to Part A should be made by circling or underlining the correct answer on the question paper) 1.

Solar atmosphere can be divided into three major parts based on temperature. They are photosphere, chromosphere and corona. The most suitable answer for the average temperature of the corona is a) 6000 K

b) 10000 K

c) above 100000 K

d) 3500 K

2.

The sidereal day is 3 minutes and 56 seconds less than a solar day. This time difference is due to a) Earth’s rotation b) Sun’s rotation c) Sun’s motion around the galactic center d) Earth’s revolution around the Sun

3.

The Polaris will not always be the North star due to a) The sidereal day being shorter than the solar day b) Due to the precession of the Earth’s axis. c) The Earth's period being slightly longer than 365 days. d) The Solar wind blowing the Earth away from the sun.

4.

o

An observer standing 30 north from equator observes a star at zenith (right above the head). If o

the observer moves along the same longitude, 90 to the south from where he is, what could be the new altitude of the star? o

a) 0

b) 30

o

o

c) 60

o

d) 90

1/4

5.

Red shift of the spectral lines show the distance galaxies are moving away from us. The    C . A spectrum of certain galaxy is observed in the H receding speed is given by V      region and found wavelength of H absorption line is 6564.64 oA. If the laboratory wavelength (  ) of H is 6563 oA and the speed of light (C) is 300,000 km s-1 find the receding speed of the galaxy. a) 35 km s-1 b) 50 km s-1 c) 65 km s-1 d) 75 km s-1

6.

The different bands of electromagnetic radiation consist of little packets of energy, called photons traveling through space. The amount of energy this packet possess is directly proportionate to their frequency. Find energy of such electromagnetic wave which has the wavelength of 5000A (5x10-7 m). The speed of light 3x108 m s-1 and Plank constant 6.625x10-34 J s . a) 39.75x1038 J

7.

b) 39.75x10-20 J c) 39.75x10-20 J s d) 30.34x1030 J s

The hydrogen in interstellar medium is generally quite cold (if it is not in the vicinity of warm stars) and found in its atomic or neutral ground state. Such clouds are called HI regions. Cold interstellar hydrogen emits radiation in radio region at the wavelength of a) 26 cm

b) 21 cm

c) 5910 A0

d) 1000 nm

8.

The term “Hot Jupiters” is a commonly used word among the planetary scientists in the world. This explains a) The Jupiter formed much closed to the Sun few billions years ago. b) Volcanic eruptions heat up the Jupiter’s surface. c) Discovered some Jupiter size extra-solar planets are closer to the parent star than the distance between the Sun and Jupiter. d) The Jupiter becomes a star in the future.

9.

Stars are born, evolve and die. The primary mass of the star decides the way it destroys. A star which is comparable to the Sun’s mass destroys as a) Supernovae b) Novae c) Planetary nebulae d) X-ray burst

10. A, B, and C are three stars with temperatures of 6000K, 24000K, and 3500K, respectively.

What is the possible colour sequence of those stars A, B and C, respectively. a) Yellowish, Bluish, Reddish b) Reddish, Bluish, Yellowish c) Bluish, Yellowish, Reddish d) Yellowish, Reddish, Bluish 11. The brightest star of the Scorpion constellation is

a) Sirius b) Regulus

c) Antares

d) Polaris

12. There a two stars A and B with apparent magnitudes 1 and 3, respectively. The correct

expression about their apparent brightness is a). Star A is 6 times brighter than the star B. b). Star A is 6 times fainter than the star B. c). Star A is 6.310 times brighter than the star B. d). Star A is 2.512 times brighter than the star B. 13. The weight of a man on Earth’s surface is 60 kg. If he goes to the planet Mars, his weight at the

Martian surface would be a) 20 kg b) 10 kg c) 60 kg

d) 120 kg 2/4

14. The escape velocity (V) of an object (at its surface) depends on its mass (M) and radius (R), and

is given by V = (2GM/R). (Here, universal gravitational constant G = 6.67 x 10-11 m3 kg-1 s-2). Suppose a star with a escape velocity of 1800 km s-1 subsequently becomes a neutron star having a radius 105 times smaller than the original star, the escape velocity of the neutron star would be a) 200,000 km s-1

b) 180,000 km s-1

c) 180,000 m s-1

d) 569210 km s-1

15. An observer who is on the 150 northern latitude observed a star in the Ursa Minor constellation

at 9.00 p.m. local time. The star has 250 angular separations with bottom star of the pointer stars of the Ursa Major constellation. What would be the altitude of the observed star after a time lapse of 3 hours. a) 37.50

b) 120

c) 250

d) 150

16. A comet orbiting around the Sun has a perihelion distance of 2.0 A.U. and an aphelion distance

of 6.0 A.U. Eccentricity (e) of its elliptical orbit is a) 0.4 b) 0.5 c) 0.7

d) 1.0.

17. Using the Kepler’s third law compute the period of an asteroid orbiting around the Sun having

a semi-major axis of 4.0 AU (astronomical Units). The answer in Earth years is a) 3 b) 4 c) 8 d) 76 18. If the orbital speed of earth as 30 km/s and distance between the Earth and the Sun as 1.5 x 10 11

m, the mass of the Sun would be (Useful information: Universal gravitational constant G = 6.67 x 10-11 m3 kg-1 s-2). a) 1.9 x 10 30 kg, b) 2.0 x 10 30 kg, c) 2.1 x 10 30 kg, d) Non of the above answers are correct. 19. If the focal length of the objective of a telescope is 1 m and the focal length of its eye piece is 10 mm, the magnification of the telescope is a) 10 b) 100 c) 200 d) 1000. 20. A star gives a parallax of 0.29” when observed from the earth with a time gap of 6 months. The distance to that star in light years is a) 3.26 b) 5.62 c) 11.24 d) 22.48. PART B (Please provide your answers to this part in the space provided in page 4) 21.Describe the Titius Bode law and estimate the distance to planet Saturn from the Sun in Astronomical Units (AU). 22. Draw a sketch of the celestial sphere and label i) ecliptic, ii) celestial equator, iii) Vernal and Autumnal equinoxes. On the same diagram or a separate diagram indicate the equatorial coordinate system: Right Ascension and Declination. 23. Draw the H-R diagram and indicate the regions where you could find main sequence stars, red giants, blue giants, white dwarfs and red dwarfs. 24. Draw a sketch of Saturn and label the main belts and zones of the Saturnian southern

hemisphere, its ring system and divisions . **** 3/4

Name of the candidate : Please use the following space to provide answers to the questions 21 to 24.

(21)

(22)

(23)

(24)

4/4

Please furnish the following information before the commencement of the examination Full Name of the Candidate: Examination Centre: Colombo/Peradeniya/Ruhuna/ Jaffna (underline) IColombo/Peradeniya/Kelaniya/Ruhuna/Batticaloa?Jaffna Date of Birth: Signature of the Candidate :

Index Number:

XYW lAk` @x_wQk vQq&` a`ywny – INSTITUTE OF PHYSICS, SRI LANKA w`rk` vQq&`v h` w`rk` @x_wQk vQq&`v pQLQb[ @qvn olQmp | Qy`d| wrM`vlQy-2008 THE 2ND NATIONAL OLYMPIAD ON ASTRONOMY AND ASTROPHYSICS - 2008 (k`ly p#y 1 vQn`dQ 30)(Duration : 1 hour and 30 minutes) sQyUm pYX~n vlt @mm pYX~n pwY@y~m pQLQwSr# spy` vQx`gy avs`n@y~qW vQx`g X`l`{QpwQ wSm` @vw x`r @qn~n Answer all the questions and submit this paper to the supervisor at the end of the examination. @mm pYX~n pwYy pYX~n A h` B @k`ts~ @qkkQn~ yEwS pYX~n 25 kQn~ sh mEqYQw pQtE 5 kQn~ sm~vQwy This paper consists of 25 questions in two parts(A & B) printed in Five (05) pages. gNk yn~wY x`vQw kl h#k/Electronic calculators are allowed. (pY@y`~jnvw~ qw~w / Useful information : a`@l`~k@y~ @v|gy / Speed of light c = 3 x 105 km/s, sr~vwY gSr#w~v`kr~Xn nQywy / Universal gravitational constant G = 6.67 x 10-11 m3 kg-1 s-2). sQAhl pr~vrwn@yhQ g#tU mwSvEv@h`w~ iAgWYsQ bsQn~ a#wQ pYXn ~ y bl` pQLQwSr# spyn~n.

A @k`ts / PART A A @k`tst aq`l pYX~n vlt @h`[m pQLQwSr @w`~r` rvEmk~ a#qWm @h`~ ytQn~ irk~ a#[Wm sQqEkrn~n (Answers to Part A should be made by circling or underlining the correct answer on the question paper)

1.

wr#vk wQY@k`~NmQwQk asm|p`wy vQkl` 0.04 @ls mnQn lq~@q~ nm| wr#vt a#wQ qEr p`@sk~ vlQn~ vnE@y~ For a star, the trigonometric parallax was measured to be 0.04 arc seconds. What is the distance to the star in parsec? a) 20 pc

2.

b) 25 pc

c) 30 pc

d) 35 pc

bE{ sh bYhs~pwW gYhyn~@g~ k’]vl ar~{-mh` a] pQL@Q vlQn~ n]wY e~kk 0.387 sh 5.203 @v|. bYhs~pwQ gYhy`@g~ prQbYmN k`l`vr~wy avEr#qE 11.862 nm|, bE{ gYhy`@g~ prbYmN k`l`vr~wy vr~”;vln~ vnE@y~ If the semi-major axes of the orbits of Mercury and Jupiter are 0.387 and 5.203 astronomical units, respectively and Jupiter’s orbital period is 11.862 years, the orbital period of Mercury in years would be a) 2.106

3.

b) 0.937

c) 0.402

d) 0.241

p”’”^}QvQ@y~ sQt sQkSr# gYhy` nrW]Ny krn vQt sQkSr# gYhy` sRr~yy` sm”M qk~vn uprQm @vn~vWm aAXk 46 nm|, sRr~yy` sh sQkSr# gYhy` awr qEr n]wY e~kk vlQn~ vnE@y~ (p”’”^}QvQy h` sRr~yy` awr qEr n]wY e~kk 1 kQ.) If the maximum elongation of Venus from the sun is 46 o , the Sun – Venus distance in astronomical units would be (the distance between the Sun and the Earth is 1 AU) a) 0.71

4.

b) 0.72

c) 0.73

d) 0.93

hbl~ nQywy (H0 ), 70 km/s/Mpc @ls s#lkS vQt vQXv ~ @y~ vys a`sn~n vX@yn~ avEr#qE bQlQyn Using the value for Hubble's constant H0 as 70 km/s/Mpc, the age of the universe can be computed approximately as (in billion years) a) 12.1

b) 13.6

c) 14.0

d) 15.0 1/5

5.

vQv{ u’;~Nw~v shQw wr# hwrk ekm wrAg a`y`m pr`s@y~ lb`gw~ vr~N`vlQ hwrk~ phw r$p@y~ q#k~@v|. @mm vr~N`vlW hw@r~ ek~ ek~ wr#@v| s`@p~] wWv|rw` anEv sh e~v`@y~ av@X`~”;N @r~K` anEv w`rk` vl nQv#rqQ u’”’;~Nw~v vr~gWkrNy vnE@y~ The four spectra shown in the figures are taken in the same wavelength range from four stars which have different type of spectral classes. According to the maximum relative flux and the line absorptions in the given wavelength range, identify the spectral classes of the four spectra.

a) 1- O type, 2- A type, 3- M type, 4- G type b) 1- A type, 2- O type, 3- M type, 4- G type c) 1- G type, 2- O type, 3- A type, 4- M type d) 1- M type, 2- A type, 3- O type, 4- G type

6.

p”’”^}QvQ@y~ sQtQn nQrW]kykSt s$m vQtm cn~qYy`@g~ ek~ p#w~wk~ pmNk~ @p@nn~@n~ The reason that we see the same side of the moon always is

a) 5 degrees angle between the planes of the moon and earth. (cn~qYy`@g~ wlyw~ p”’”^}QvQ@y~ wlyw~ awr aAxk 5 k a`nwQy nQs`) b) Moon does not rotate at all . (cn~qYy` bYmNy @n`vn nQs`) c) Moon’s rotational speed is equal to the moon’s speed of revolution. (cn~qYy`@g~ bYmNy k`ly sh prQbYmN k`ly sm`n nQs`) d) Tidal effect of the moon on the earth. (cn~qYy`@gn~ p^}QvQy mw a#wQvn uqm| nQs`) 7.

p”’”^}QvQ@y~ sQt nQrW]Ny krn sRr~yy` @g~ vr~N`vlQy av@X`~’;N vr~N`vlQykQ. nmEw~ o|n$m k^;~N vs~wSvkQn~ l#@bn vr~N`vlQy vQ@m`~ck vr~N`vlQyk~ @v|. sRr~yy` @gn~ l#@bn vr~N`vlQy av@X;k vr~N`vlQyk~ vWmt @h~wSv vn~@n~ The solar spectrum observes in ground based telescope is an absorption spectrum. The spectrum of any black body is usually an emission spectrum. The reason/s for the solar spectrum becomes an absorption is

a) The gases around the solar atmosphere (sRr~yy` vt` a#wQ v`yE @g`~l@y~ v`yRn~) b) The Earth’s atmosphere ( p^}QvQ v`yE @g`~ly) c) The convection current in the solar convection zone (sRr~yy` @g~ sAvhn kl`p@y~ a#wQvn sAvhn {`r`) d) Both (a) and (b) (a sh b @qkm) 8. aynWkrny vR k#l~sQym| (Ca) vl pr~@y~’;N`g`r wrAg a`y`my 393.3 nm @v|. mn~q`kQNQykQn~ l#@bn @mm k#l~sQym| @r~K`v nQrW]Ny klvQt ekW wrAg a`y`my 401.8 nm @ls q#k~@v|. mn~q`kQNQyt a#wQ qEr~ a`sn~n vX@yn~ @qnE lbn~@n~ (pY@y`~jnvw~ qw~w: H0=70 km/s/Mpc, rk~w vQs~}`pny sh aRw~vW@m| @v|gy awr adE @v|g sm|bn~{w`vy up@y`~gW krgn~n.) When measured in a laboratory on Earth, ionized Ca is found to have a wavelength of 393.3 nm. When you observe the spectrum of a galaxy you find this spectral line at 401.8nm. What is the approximate distance of the galaxy? (Useful information: H0 = 70 km/s/Mpc, use low speed relationship between recessional speed(v) and red shift (z) ) a) 93 Mpc

b) 60 Mpc

c) 120 Mpc

d) 205 Kpc

2/5

9. bYhs~pwW@g~ q^X& vQX`lw~vy a`sn~n vX@yn~ -4 pmN @v|. pQ@yvQ a#st @p@nn qWp~wQ@yn~ adEm wr#@v| q^X& vQx`lw~vy +6 nm|, bYhs~pwW @mm wr#vt vd` @k`pmN gSNyk~ qWp~wQmw~q? Jupiter has a magnitude of about -4. Roughly, how many times brighter is the Jupiter than the dimmest stars visible to the naked eye, with magnitude of + 6 ? a) 100

b) 1000

d) 105

c) 10000

10. mn~q`kQNQyk a#wQ vQcl& w`rk`vk~ vn RR lyQ@r~ wr#vk~~ a`vr~wWy @ls ehQ pYx`vy @qgSN kryQ. evQt ehQ q^X& vQX`lw~vy @k`pmN pYm`NykQn~ @vns ~@v|q?. A RR Lyrae variable in a galaxy periodically doubles its light out put. By how much does its apparent magnitude change? a) 0.50 b) 0.75 c) 4.00 d) Does not change (@vns~ @n`@v|).

11. w`rk`vn~ vQv{ @prhn~ @y`q` nQrW]Ny krnE l#@b|. phw vgS@v| q#k~@vn~@n~ B sh V @prhn~ x`vQw` kr @s`y`gw~ wr# hwrk vQX`lw~v agyn~y. @mm wr# hw@rn~ pY}m@yn~m vQk`Xy vWm a`rm|x krn wr#v kSmk~q ? The stars are observed through various filters. The following table shows 4 stars and their magnitudes observed through B and V filters. Of those four stars which one will evolve first? Star E F G H a) E 12.

b) F

B 0.56 0.78 0.29 0.45

V 0.34 0.58 0.89 0.54

c) G

d) H

qE@r~]yk av@n@whQ n`xQ qERr 1m sh ehQ up@n@w hQ n`xQ qEr 20 mm nm|, qE@r~]@y~ vQX`lny vnE@y~ If the focal length of the objective of a telescope is 1 m and the focal length of its eye piece is 20 mm, the magnification of the telescope is a) 10 b) 50 c) 100 d) 200.

13.

ek~wr` ps@l`s~vk qQnk r`wQY@y~ cn~qYy` vQsQn~ nQrW]k@ykS@g~ a#@shQ aAXk 0.49 k @k`~Nyk~ a`p`wny kryQ. em r`wY@Q y~qW nQrW]ky` sh cn~qYy` awr qEr vnE@y~ (cn~qYy`@g~ vQ’;~km|xy 3476 km). One night during a full Moon, the Moon subtends an angle of 0.49 degree to an observer. The observer’s distance to the Moon on that night is (the diameter of the moon is 3476 km) a)

14.

432,947 km

b) 203,223 km

c) 406,446 km

d) 384,400 km

hQr# vt` gmn~ gn~n` a`vr~wW {Rm@k~wSvk hQr#t a$wQn~m pQhQtn vQt qEr n]wY e~kk 31 vn awr hQr#t lgQn~m pQhQtn vQt qEr n]wY e~kk 1 @v|. {Rm@k~wS@v| k]@y~ a`vr~w k`ly p^}QvQ vr~; vlQn~ A Sun-orbiting periodic comet is the farthest at 31 A.U. and the closest at 1 A.U. The orbital period of this comet (in earth years) is a) 8

15.

b) 16

c) 64

d) 76

mwSpQt u;~Nw~vy 5000 K vn wr#vk~ uprQm Xk~wQy pQtkrnE lbn~@n~ kSmn wrAg a`y`m@y~qWq ? (wr#v k^;~N vs~wSvk~ @s~ slk` vWn~@g~ nQymy x`vQw` krn~n, vWn~ nQywy = 2.898 x 10-3 m K) At what wavelength does a star with the surface temperature of 5000 K radiate most intensely. (Consider the star as a blackbody and use the Wien’s law, Wien constant = 2.898 x 10-3 m K) a) 0.58 µm

16.

b) 0.75 µm

c) 0.49 µm

d) 0.63 µm

cn~qYy` mwSpQt a#wQ a`v`tyk vQ;~km|xy 80 km @v|. ap@g~ a#@shQ krNQk`@v| vQ;~km|xy 5 mm @ls upkl~pny krmQn~ @mm a`v`ty pQyvQ a#sQn~ h[En`gw h#kQq#yQ qk~vn~n. A crater on the surface of the Moon has a diameter of 80 km. Is it possible to resolve this crater with naked eyes, assuming the eye pupil aperture is 5 mm ? a) Yes (h#kQy) b) No(@n`h#kQy) c) Depend on country of observation(nQrW]ny krn rt d) Data provided is insufficient to answer (pQLQwSr# s#pyWmt wrm| qw~w pYm`N`vw~ @n`@v|.)

mw wWrny @v|) 3/5

17.

p^}QvQy mwSpQtqW 60 kg brk~ a#wQ mQnQskS h[t gQ@y~ nm|, h[ mwSpQtqW ohE@g~ br vnE@y~ The weight of a man on Earth’s surface is 60 kg. If he goes to the moon, his weight at the lunar surface would be a) 10 kg b) 20 kg c) 60 kg d) 120 kg

18.

sRr~yy`@g~ s~kn~{y 1.9891 x 10 30 kg q, p^}QvQ@y~ sQt sRr~yy`t a#wQ qEr 1.5 x 1011 m q nm| p^}QvQy wm k]@y~ gmn~ gn~n` @v|gy vnE@y~ (v^w`k`r k]yk~ slkn~n) If the mass of the Sun is 1.9891 x 10 30 kg, and the distance between the Earth and the Sun is 1.5 x 1011 m, the orbital velocity of the earth would be (assume a circular orbit) a) 28 km/s b) 30 km/s c) 32 km/s d) None of the above answers are correct. (ihw pQLQwSr# kQsQvk~ @n`@v|).

19.

sRr~yy`@g~ pYx`v 3.9 X 1026 J/s vn awr ehQ a`sn~n vX@yn~ prm`NE 1057 pmN a#Ew. sRr~yy`@g~ pYwQky YQ ` mgQn~ nQkSw~ vn Xk~wQ pYm`Ny 10-19 J/atom @s~ slk` ehQ smQpRrN prm`NE pYm`Ny x`vQw vWmt gwvn k`ly @s`yn~n. The luminosity of the Sun is 3.9 X 1026 J/s and Sun contains roughly 1057 atoms. The reactions in the Sun involved in burning release roughly 10-19 J/atom. What is the length of time required to consume the entire Sun by burning? b) 2.6 x1012 years.

a) 3.9 trillion years. 20.

c) 3.9x1011 seconds

d) 0.26x1012 seconds

sRr~yy` ]Wrp}y mn~q`kQN@y~ m{&@y~ sQt d = 8500 pc qErQn~ pQhQt` a#w~nm| sh ehQ k]@y~ @v|gy v=220 km/s, nm|, k]@y~ a`vr~} k`ly P= 2πd/v smWkrNy x`vQw`kr avEr#qE mQlQyn vlQn~ gnny krn~n. If the Sun is at a distance (d )of 8500 pc from the centre of the Milky Way Galaxy and the Sun’s orbital speed ( v ) is 220 km/s, using the equation for period P= 2πd/v, calculate the orbital period of the sun about the centre of the Galaxy. The answer is (in million years) a) 225

b) 230

c) 400

d) 850

___________________________________________________________________________________________ B @k`ts / PART B

awQ@r~k @k`l @yq`gnQmQn~ phw pYX~nvlt pQLQwSr# spyn~n. s$m awQ@r~k pQLQwSr# pwYykm ihlQn~ oB@g~ nm sh vQx`g aAky s[hn~ krn~n. (Please provide your answers to this part using additional sheets. Write your name and index number on top of each and every additional sheet)

21.

vr~; 2006 a@g`~s~wS ms 24 qQn an~wr~ j`wQk w`rk` vQq&` sm|@m|lny mgQn~ sm|mw krgw~ prQq Q phw s[hn~ vs~wSn~ s[h` @qnlq nQr~vcnyn~ qk~vn~n. (a) gYh@l`~kyk~, (a`) v`mn gYh@l`~kyk~, (a#) kSd` @s_rgYh mN~dl vs~wSn~. Based on the International Astronomical Union resolution passed on 24th August 2006 give the definitions of (a) a planet, (b) a dwarf planet, and (c) Small Solar-System Bodies.

22.

CCD k#mr`vk a`@l`~k sQA@v|qW pQk~sl @k`tsk pYm`Ny 9x10-6m @v|. @mm CCD k#mr`v 45 cm vQ;~km|xyk~ sh F aAky f/12 vn k#s@g~Yn~ vrg@y~ qE@r~]ykt svQklvQt em k#mr`@v| pQk~sl ekk~ mw ahs mgQn~ a`p`wny krn @k`~Ny vQkl`(a`k~ww~pr) vlQn~ @s`yn~n. A CCD (Charge Coupled Device) camera with pixel dimensions 9x10 -6m is attached to the Cassegrain focus of the 45cm, f/12 telescope. Find the angle subtended by a pixel in the sky in units of arcseconds.

23.

ap sRr~yy` pY{`n anEkYmN@y~ sQtQn vQt wm s~kn~{@yn~ 10% ehQ hr@y~ qW n&;tQk pYwQkYQy` mgQn~ qhny kryQ. n&;tQk pYwQky YQ `@v|qW s~kn~{@yn~ 0.7% Xk~wQy bvt prQvr~wny @v|. ww~pr ekkqW sRr~yy`@gn~ pQtvn xk~wQy L= 3.845x1026 J @v|. sRr~yy`@g~ skn~{y M= 1.9891x1030 Kg @v|. ayQn~s~tyQn~@g~ Xk~wQy h` s~kn~{y awr pYsQq~{ smWkrNyk~ vn E=mc2 x`vQw` kr sRr~yy` pY{`n aNEkYm@yhQ gw krn k`ly avErEqE bQlQyn vlQn~ gnny krn~n. Our sun in the Main Sequence(MS) burns 10% of its total mass in the core. In the nuclear fusion reaction 0.7% of mass is converted in to energy. The total energy output of the Sun in one second is L= 3.845x1026 J. The mass of the Sun M= 1.9891x1030 Kg. Using the Einstein’s famous equation for energy and mass, E=mc 2 find the life time of the Sun in the main sequence in billions of years.

4/5

24. H-R sthn a#[ ehQ sRr~yy` v#nQ wr#vk~ an~wrW] vl`vkQn~ a`rm|x vW wr#@v| avs`ny qk~v` vQk`Xy vn mr~gy a#[

qk~vn~n. Draw the Hertzsprung-Russel (H-R) diagram and indicate the track of a sun like star on the same diagram during its evolutionary history, i.e. birth from an interstellar cloud of gas and dust to its final demise.

25.

wr#vk wWv|rw`vy (I) em wr#vt a#wQ qE@rhQ vr~gyt (d2) pYwQ@l`~mv sm`nEp`w @v|. 1 I d2 enm| o|n$m wr#vk~ sRr~yy` @g~ sQt p`@sk~ 10 qErQn~ w#bRvQt @p@nn vQX`lw~vy em wr#@v| nQr@p~] vQX`lw~vy (M) @ls ar} qk~vnE l#@b|. wr#vk pYk`X pr`s@y~ nQr@p~] vQX`lw~vy (Mv) sh pYk`X pr`s@y~ q^X& vQX`lw~vy(mv) sh wWv|rw`vy (I)phw sm|bn~{y mgQn~ @qnE l#@b|. M  mv  2.5log I (10 pc)  log I (d ) v (a) ihw smWkrN @qk up@y`~gW krgnQmQn~ M v  mv  5 log d  5 bv @pn~vn~n. (a`) emgQn~ q^X& vQX`lw~vy (mv) vn wr#vk~ sRr`yy`@g~ sQt p`@sk~ 63 (d) a$wQn~ w#bRvQt ehQ nQr@p~] vQX`lw~vy (Mv) @syn~n. The intensity (I) of a star is inversely proportional to the square of the distance (d 2) of the star.

I

1 d2

The magnitudes which the stars would have if they were at distance of 10 parsec are called the absolute magnitudes ( M ). The absolute visual magnitude ( M V ), apparent visual magnitude ( mv ) and the intensity ( I ) are related as follows.

M  mv  2.5log I (10 pc)  log I (d ) v

a) Using above two relations show that

M v  mv  5 log d  5 b) For a star with mv

 3.0 , the distance (d) was measured to be 63 pc. Find the absolute magnitude ( M V ) of the star. *****

5/5

Please furnish the following information before the commencement of the examination Full Name of the Candidate: Examination Centre: Colombo/Batticaloa/Jaffna/Kelaniya/Peradeniya/Ruhuna (underline) IColombo/Peradeniya/Kelaniya/Ruhuna/Batticaloa?Jaffna Index Number: Date of Birth: Signature of the Candidate :

XYW lAk` @x_wQk vQq&` a`ywny – INSTITUTE OF PHYSICS, SRI LANKA w`rk` vQq&`v h` w`rk` @x_wQk vQq&`v pQLQb[ @wvn olQmp | Qy`d| wrM`vlQy-2009 THE 3RD NATIONAL OLYMPIAD ON ASTRONOMY AND ASTROPHYSICS - 2009 (k`ly p#y 1 vQn`dQ 30)(Duration : 1 hour and 30 minutes) @mm pYX~n pwYy pYX~n A h` B @k`ts~ @qkkQn~ yEwS pYX~n 25 kQn~ sh mEqYQw pQtE 5 kQn~ smn~vQwy This paper consists of 25 questions in two parts (A & B) printed in Five (05) pages. gNny kQrWm| s[h` sh B @k`tst pQLQwSr# s#pyWm s[h` amEN` a#wQ hQs~ kdq`sQ x`vQw` krn~n. Use the attached blank sheets for your calculations and also to answer the questions in Part-B. sQyUm pYX~n vlt @mm pYX~n pwY@y~m pQLQwSr# spy` sQyU kdq`sQ vQx`gy avs`n@y~qW vQx`g X`l`{QpwQ wSm` @vw x`r @qn~n Answer all the questions in this paper and submit all sheets to the supervisor at the end of the examination. gNk yn~wY x`vQw kl h#k/Electronic calculators are allowed. (pY@y`~jnvw~ qw~w / Useful information : a`@l`~k@y~ @v|gy / Speed of light c = 3 x 105 km/s, sr~vwY gSr#w~v`kr~Xn nQywy / Universal gravitational constant G = 6.67 x 10-11 m3 kg-1 s-2). sQAhl prQ~vr~wn@yhQ g#tU mwSvEv@h`w~ iAgWYsQ bsQn~ a#wQ pYXn ~ y bl` pQLQwSr# spyn~n.

A @k`ts / PART A A @k`tst aq`l pYX~n vlt @h`[m pQLQwSr @w`~r` rvEmk~ a#qWm @h`~ ytQn~ irk~ a#[Wm sQqEkrn~n (Answers to Part A should be made by circling or underlining the correct answer on the question paper) 1.

mwSpQt u;~Nw~vy 10000 K vn wr#vk~ uprQm Xk~wQy pQtkrnE lbn~@n~ kSmn wrAg a`y`m@y~qWq ? (wr#v k^;~N vs~wSvk~ @s~ slk` vWn~@g~ nQymy x`vQw` krn~n, vWn~ nQywy = 2.898 x 10-3 m K). At what wavelength does a star with the surface temperature of 3000 K radiate most intensely. (Consider the star as a blackbody and use the Wien’s law, Wien constant = 2.898 x 10-3 m K). a) 0.58 µm

b) 0.75 µm

c) 0.49 µm

d) 0.29 µm

2. wr#vk wQY@k`~NmQwQk asm|p`wy vQkl` 0.05 @ls mnQn lq~@q~ nm| wr#vt a#wQ qEr p`@sk~ vlQn~ vnE@y~ For a star, the trigonometric parallax was measured to be 0.05 arc seconds. What is the distance to the star in parsec? a) 20 pc

3.

b) 25 pc

c) 30 pc

d) 35 pc

a`wr~ sW k~l`k~ a`ywn@y~ a#wQ qE@r]@y~ av@n@whQ ary 45 cm @v|. ekQ@nkt 30 cm qErQn~ a#wQ @k`L p#h# ( = 5.4x10-4 cm) kSd` vs~wS @qkk~ qE@r~]y wSln Q ~ ekQ@nkQn~ yn~wm| vQ@x~qny @k`t q#kQy h#k~@k~ kSmn qErkqWq? qE@r~]y s[h` avm vQ@x~qn @k`~Ny phw smWkrN@yn~ qQy h#kQ bv upkl~pny krn~n. The objective of the Arthur C Clarke Institute telescope has a diameter 45 cm. At what distance would two small green ( = 5.4x10-4 cm) objects 30 cm, apart be barely resolved by the telescope, assuming the minimum angle of resolution for the telescope is given by

a)

20.6 km

b) 17.3 km

c) 24.8 km

d) 22.4 km

1/5

4.

cn~qYy` mwSpQt a#wQ a`v`tyk vQ;~km|xy 80 km @v|. ap@g~ a#@shQ krNQk`@v| vQ;~km|xy 5 mm @ls upkl~pny krmQn~ @mm a`v`ty pQyvQ a#sQn~ h[En`gw h#kQq#yQ qk~vn~n. A crater on the surface of the Moon has a diameter of 80 km. Is it possible to resolve this crater with naked eyes, assuming the eye pupil aperture is 5 mm ? a) Yes (h#kQy) b) No(@n`h#kQy) c) Depend on country of observation(nQrW]ny krn rt mw wWrny @v|) d) Data provided is insufficient to answer (pQLQwSr# s#pyWmt wrm| qw~w pYm`N`vw~ @n`@v|.)

5.

qE@r~]yk av@n@whQ n`xQ qERr 2 m sh ehQ up@n@w hQ n`xQ qEr 20 mm nm|, qE@r~]@y~ vQX`lny vnE@y~ If the focal length of the objective of a telescope is 1 m and the focal length of its eye piece is 20 mm, the magnification of the telescope is a) 10 b) 50 c) 100 d) 200.

6. pY{`n anEkYmn@y~ a#wQ K wr#vk qWp~wQy 0.4L @v|. @mm wr#@vhQ 6.23 x 10-34 W m-2 @]~wYyk~ a#wQ bv nQrW]ny kr a#w. @mm wr#vt a#wQ qEr @k`pmnq? obt V`yE@g`~lWy blp$m| @n`slk` h#rQy h#k. (sRr~yy`@g~ qWp~wQy L = 3.96 x 1026 J s-1@v|). A K star on the main sequence has the luminosity of 0.4L  . This star is observed to have a flux of 6.23 x 10 -34 W m-2. What is the distance to this star? You may neglect the atmospheric effects.(Luminosity of the Sun L =3.96 x 1026 J s-1). a) 23 pc b) 125 pc c) 310 pc d) 453 pc

7. p#h#qQlQ ahs shQw qQnkqW obt q#kQy h#kQ qWp~wW@yn~ adEm wr#@v| vQX`lw~vy m = 6 sh qWp~wW@yn~ v#dQm wr#@v| vQX`lw~vy m = -1.5 @v|. qWp~wW@yn~ adEm wr#@v| sh qWp~wW@yn~ v#dQm wr#@v| Xk~wQ @]~wY awr anEp`wy kSmk~q? The magnitude of the faintest star you can see with your naked eyes in a very clear night sky is m = 6 and that of the brightest star is m = - 1.5. What is the energy flux ratio of the faintest to that of the brightest? a) 4

b) 0.4

c) 10-3

d) 10-4 .

8. p^}QvQ-cn~qY pq~{wQ@yhQ p^}QvQ@y~ sQt 384000 k.m. qErQn cn~qYy` phQt` a#wQ awr cn~qY m`syk~ (n]wY) qQn 27.3 k~ @v|. p^}QvQ@y~ s~kn~{y @s`yn~n. In the Earth-Moon system, it is found that moon is 384000 km away from the earth and the length of the lunar month (sidereal) is 27.3 days. Find the mass of the Earth. a) 1.5 x 106 kg b) 3 x 1019 kg c) 6 x 1024 kg d) 9 x 1031 kg

9. w`rk` vQw&ZykS vQsQn~ vs~wSvk vr~N`vlQy C`y`r$pgw klvQt 499 nm hQ a#wQ vr~N`vlW wWr#vk~ qk~n`lqW. vQq&g`r@y~qW @mm vr~N`vlW wWr#v a#w~@w~ 500 nm hQqW y. @d`p~lr~ a`crNyt an#v @mm vs~qSv clny vnE@y~ An astronomer photographs the spectrum of an object and finds a spectral line at 499 nm wavelength. In the laboratory, this spectral line occurs at 500 nm. According to the Doppler effect, this object is moving a) (p^}QvQ@yn~ ivwt) away from the Earth at 499/500 the speed of light. b) (p^}QvQ@yn~ ivwt) away from the Earth at 1/500 the speed of light. c) (p^}QvQy @vwt) toward the Earth at 499/500 the speed of light. d) (p^}QvQy @vwt) toward the Earth at 1/500 the speed of light.

10. sRr~yy`@g~ qWp~wQy L = 3.96 x 1026 J s-1 h` sRr~yy`@g~ ary R =7x108 m nm| hQr# @g~ sPl u;~Nw~v@yhQ (Te) agy vQy h#k~@k~ . -1 The luminosity of the Sun is L =3.96x1026 J s . If the radius of the sun is R =7x108 m what could be the effective temperature of the Sun Te? a) 6000 K

b) 5600 K

c) 6100 K

d) 5800 K

11. M87 @y`~{ mn~q`kQNQy, M51 sr~pQl`k`r mn~q`kQNQy @mn~ wSn~ gSNyk~ a$wQn~ pQhQt` a#wQ bv nQrW]ny k@L~ nm|, ]Wrp}yt s`@p~]v M87 @y`~{ mn~q`kQNQ@y~ pY@v|gy M51 sr~pQl`k`r mn~q`kQNQ@y~ pY@v|gy @mn~ @k`pmN @v| q? The giant galaxy M87 is observed to be 3 times farther away than the spiral galaxy M51. With respect to the Milky Way, what would be the velocity of the M87 galaxy as that of the M51 galaxy. a) 3 times smaller, b) 3 times bigger, c) 9 times smaller d) 9 times bigger 12.

p^}QvQy mwSpQtqW 60 kg brk~ a#wQ mQnQskS aMhr#t gQ@y~ nm|, aMhr# mwSpQtqW ohE@g~ br vQy h#k~@k~ The weight of a man on Earth’s surface is 60 kg. If he goes to the Mars, his weight at the Martian surface would be a) 10 kg b) 20 kg c) 60 kg d) 120 kg 2/5

13. mn~q`kQNQ@y~ pYx` mN~dl@y~ pQhQtQ wr#, sRr~yy`t s`@p~]v phw @vns~km| qk~vyQ. In comparison with the Sun, stars located in the galactic halo are expected to have a) low metal abundances. (adE @l`~h bhElw~vy) b) metal abundances similar to those in the Sun. (hQr#t sm`n @l`~h bhElw~vy) c) metal abundances higher than those in the Sun. (hQr#t vd` v#dQ @l`~h bhElw~vy) d) none of the above. (ihw ekk~vw~ @n`@v|).

14. hQr# vt` gmn~ gn~n` a`vr~wW {Rm@k~wSvk hQr#t a$wQn~m pQhQtn vQt qEr n]wY e~kk 31.5 vn awr hQr#t lgQn~m pQhQtn vQt qEr n]wY e~kk 0.5 @v|. {Rm@k~wS@v| k]@y~ a`vr~w k`ly p^}QvQ vr~; vlQn~ A Sun-orbiting periodic comet is the farthest at 31.5 A.U. and the closest at 0.5 A.U. The orbital period of this comet (in earth years) is a) 8 b) 16 c) 64 d) 76

15. qErs~} k~v`sryk rk~w vQs~}`pny z =2 @v|. @mm k~v`sry a@l`~ky mEk~w krWm arBn vQtqWt vd` kSmn s`{kykQn~ @m| vnvQt vQX~v@y~ Gnw~vy @vns~ vW aw~q ? Red shift Z, of a distant Quasar is equal to 2. By what factor the density of the Universe changed compared to the time when Quasar emits light? a.) 8 times smaller, b) 8 times larger, c) 27 times smaller, d) 64 times smaller

16. “”X nm| vR ek~wr` wr#vk Kn~d`Ak (+45dec:8RA) @v|. @mm wr#v s#p~w#m|br~ 22(Xrw~ vQ;Evy) qQn uq`vQy h#k~@k~~ kSmn @v|l`vtq? kSmn qQX`@vn~ q? A certain star “X” has the coordinates (+45dec:8RA). On Sept 22 (Autumnal equinox) at what time does this star rise and in what direction? a.) at 12:00pm local time in North East b) at 8.00pm local time in North West. c) at 2:00pm local time in North East d) at 2:00am local time in North East

17. @s.mQ. 21 wrAg a`y`my @y`q` mn~q`kQN`y pQLb[ krnE lbn g@v|;N iw` v#qgw~ h` pYbl vnE@y~ Radio observations at a wavelength of 21 cm are useful probes of the galaxy because a) they locate molecular hydrogen. ( ev` mgQn~ aNEk hyQdYjn~ @s`yn nQs`) b) they find hot, ionized hydrogen clouds in the spiral arms. ( ev` mgQn~ sr~pQl`k`r b`hE vl a#wQ uNEsm|, aynWk^w hyQdYjn~ vL` @s`yn nQs`) c) they map neutral hydrogen in the spiral arms. ( ev` mgQn~ sr~pQl`k`r b`hE vl a#wQ s~vx`vQk hyQdYjn~ @s`yn nQs`) d) they can detect dark matter. ( ev` mgQn~ a[Er# p{`r~} @s`y`gw h#kQ nQs`)

18. @qvn Ghnw~v@y~ wr# v#dQpErvw~, v` sh {RlQ al~pvw~ qk~nt a#w~@w~ kSmn vr~g@y~ mn~q`kQNQ vlq? Which type of galaxy is dominated by Population II stars and contains little or no gas or dust? a) elliptical, b) spiral, c) barred spiral, d) irregular

19. sQyU wrAga`y`myn~ hrh` mnQn lq q^X& vQX`lw~vy hqEn~vnE lbnE@y~ The apparent magnitude measured over all wavelengths is called 1. Absolute magnitude (nQr@p~] vQX`lw~vy) 2. Bolometric apparent magnitude (b@l`~mw Q Qk q^X& vQX`lw~vy) 3.Colour magnitude (vr~N vQX`lw~vy) 4. Bolometric absolute magnitude (b@l`~mQwQk nQr@p~] vQX`lw~vy)

20. T-@t`~rQ wr# ayw~vnE@y~ H-R sth@nhQ kSmn @k`tstq ? Which part of the H-R diagram that the T- Tauri stars are located 1. Red giant branch 2. Supergiant branch 3. Pre-main sequence branch

4. AGB branch

3/5

B @k`ts / PART B

amEN` a#wQ awQ@r~k hQs~ @k`l @yq`gnQmQn~ phw pYX~nvlt pQLQwSr# spyn~n. s$m awQ@r~k pQLQwSr# pwYykm ihlQn~ ob@g~ nm sh vQx`g aAky s[hn~ krn~n. (Please provide your answers to this part using attached additional blank sheets. Write your name and index number on top of each and every additional sheet)

21. 1998 a@g`~s~wS 22 qQn uwSr# sEm`wYvt qQs~vR vly`k`r sRr~ygYhNy, s}l vQ;~km|xy 10 cm h` f-anEp`wy 15 qE@r~]yk~ @y`q` 35 mm ptlyk~ mwt gw~ C`y`r$pyk pQtpwk~ phw q#k~@v|~. Ptly mw sthn~ vR mEl~m C`y`r$p@y~ sthn~ v wQ@bn a`k`ryt sRr~y w#tQ@y~ vQ;~km|xy 13.817 mm h` cn~qY w#tQ@y~ vQ;~km|xy 13.235 mm @v|. cn~qYy`t sh sRr~yy`t a#wQ qEr (kQ.mW. vlQn~) sh vly`k`r sRr~ygYhNy wQ@bn avs~}`@v|qW sRr~y w#tQy @k`pmN pYm`NykQn~ (pYwX W wyk~ @ls) cn~qy`@gn~ v#sW wQbR@y~q yn~n gNny krn~n. ( sRr~yy`@g~ vQ;~km|xy = 1392000 km, cn~qYy`@g~ vQ;~km|xy = 3476 km.) Below is a picture on a 35 mm film of annular eclipse in North Sumatra on August 22, 1998, taken with a telescope having effective diameter 10 cm and f-ratio 15. The diameter of the Sun’s disk in original picture on the film is 13.817 mm and the diameter of the Moon’s disk is 13.235 mm. Estimate the distances of the Sun and the Moon (expressed in km) from the Earth and the percentage of the solar disk covered by the Moon during the annular eclipse.(Diameter of the Sun = 1 392 000 km, Daimeter of the Moon= 3476 km.)

22. qQk~ sQqEr# vr~N`vlWm`nyk qL sthnk~ a#q @k`ts~ nm| krn~n. @mhQ adEp`dE pQLQb[ @ktQ vQs~wryk~ spyn~n. Sketch the optical parts of a slit spectrograph and label them. Discuss briefly its main drawbacks.

4/5

23. ap@g~ mn~q`kQNQ@y~ m{&@y~ a#wQ a[Er# a`g`{yk~ vt` sELg Q wv a#wQ v`yE vL` ptlykQn~ nQkSw~vn @r\dQ@y`~ wrAg nQrW]NvlqW hyQdYjn~ xYmN m`r# sAkY`n~wQ@y~ (nQX~cl vQt sAK&wy-rest frequency = 1420.41 MHz)) sAK`wy 1421.23 MHz bv nQrW]ny krn lqW. @mm v`yE vL`ptly a[Er# a`g`{@y~ sQt 0.2 pc qErQn~ pQhQtQ@y~ nm| h` ey v^w`k`r mgk k] gwv wQ@b|nm|, em vL`ptl@y~ @v|gy nQX~cy kr, ey ap @vwt @h`~ a@pn~ ivwt gmn~ krnv`q#yQ qk~vn~n. a[Er# a`g`{@y~ s~kn~{y gNny krn~n. Radio wavelength observations of gas cloud swirling around a black hole in the center of our galaxy show that radiation from the hydrogen spin-flip transition (rest frequency = 1420.41 MHz) is detected at a frequency of 1421.23 MHz. If this gas cloud is located at a distance of 0.2 pc from the black hole and is orbiting in a circle, determine the speed of this cloud and whether it's moving toward or away from us and calculate the mass of the black hole.

24. H-R sthnk~ a#[ ehQ pY{`n anEkYmQk wr#, rwS @y`~{ wr#, nWl~ @y`~{ wr#, sEqE v`mn wr#, rwS v`mn wr# phQtn

kl`p lkNE krn~n. sRr~yy` v#nQ wr#vk~ an~wrW] vl`vkQn~ a`rm|x vW wr#@v| avs`ny qk~v` vQk`Xy vn m`r~gy em sth@nhQm a#[ qk~vn~n. Draw the Hertzsprung-Russel (H-R) diagram and indicate the regions where you could find main sequence stars, red giants, blue giants, white dwarfs and red dwarfs. Indicate the track of a sun like star on the same diagram during its evolutionary history, i.e. birth from an interstellar cloud of gas and dust to its final demise.

25. a`sn~n vX@yn~ @q~X`AX 180 k prwryk~ a#wQv p^}WvQ@y~ nQr]y mw sQtQn pEq~glyQn~ @q@q@nkS ekm @v|l`@v|qW psEbQ@m| a#wQ wr# @]~wYyt s@p~]v cn~~qYy`@g~ pQhQtWm nQrW]ny kryQ. cn~qYy`@g~ kYn~wQy (declination) XSn& @v|nm| em avs~}`v s[h` qL r$p sthnk~ aqQn~n. em pEq~glyQn~ @q@qn`t qk~nt l#@bn q^X& vQ;EvqAX@y~(right ascension) @vns gNny krn~n. Two persons, on the equator of the Earth separated by 180 in longitude, observe the Moon’s position with respect to the background star field at the same time. If the declination of the Moon is zero, sketch the situation and calculate the difference in apparent right ascension seen by those two persons.

vvvvvv

5/5

Please furnish the following information before the commencement of the examination Full Name of the Candidate(sm|pRrÑN nm): Examination Centre(m{&s~}`ny): Colombo/Batticaloa/Jaffna/Kelaniya/Peradeniya/Ruhuna/Vaunia Campus (underline)

IColombo/Peradeniya/Kelaniya/Ruhuna/Batticaloa?Jaffna Date of Birth (Yupn~ qQny):

Index Number (vQx`g aAky):

School & Grade(p`s#l sh @XY~NQy):

Telephone Number(qE.k.): Signature of the Candidate (aw~sn) :

XYW lAk` @x_wQk vQq&` a`ywny – INSTITUTE OF PHYSICS, SRI LANKA pLmEvn XYW lAk` kNQ;~T w`rk` vQq&` olQmp | Qy`d| wrMy-2011 THE 1ST SRI LANKAN JUNIOR ASTRONOMY OLYMPIAD COMPETITION-2011 (k`ly p#y 1 vQn`dQ 30)(Duration : 1 hour and 30 minutes) @mm pYX~n pwYy pYX~n A h` B @k`ts~ @qkkQn~ yEwS pYX~n 32 kQn~ smn~vQwy This paper consists of 32 questions in two parts (A & B). gNny kQrWm| s[h` sh B @k`tst pQLQwSr# s#pyWm s[h` amEN` a#wQ hQs~ kdq`sQ x`vQw` krn~n. Use the attached blank sheets for your calculations and also to answer the questions in Part-B. sQyUm pYX~n vlt @mm pYX~n pwY@y~m pQLQwSr# spy` sQyU kdq`sQ vQx`gy avs`n@y~qW vQx`g X`l`{QpwQ wSm` @vw x`r @qn~n Answer all the questions in this paper and submit all sheets to the supervisor at the end of the examination. gNk yn~wY x`vQw kl h#k/Electronic calculators are allowed. (pY@y`~jnvw~ qw~w / Useful information : a`@l`~k@y~ @v|gy / Speed of light c = 3 x 105 km/s, sr~vwY gSr#w~v`kr~Xn nQywy / Universal gravitational constant G = 6.67 x 10-11 m3 kg-1 s-2). sQAhl prQ~vr~wn@yhQ g#tU mwSvEv@h`w~ iAgWYsQ bsQn~ a#wQ pYXn ~ y bl` pQLQwSr# spyn~n.

A @k`ts / PART A A @k`tst aq`l pYX~n vlt @h`[m pQLQwSr @w`~r` rvEmk~ a#qWm @h`~ ytQn~ irk~ a#[Wm sQqEkrn~n (Answers to Part A should be made by circling or underlining the correct answer on the question paper)

1.

2.

s[ n#wQ p#h#qQLQ r`wYQykqW a[Er# @p@qsk sQt ob pQyvQ a#sQn~ ahs nQrW]Ny kL@h`w~ @k`pmN wr# pYm`Nyk~ q#kQy h#kQq? How many stars can you see with your naked eye on a clear, moonless night from a dark location? a) 6000-10000 b) less than a thousand(qhst adE) c) 15000-100000 d) more than you could count in your lifetime (jWvWw k`ly wSSl gnn~kr nQmkL @n`h#kQ wrm| ) xS@kñ~n~qYWy v`qW sAkl~p udEytQkSr# krmQn~ vQX~vy pQLQb[ nv aqhs~ iqQrQpw~kl vQq&ZyQn~ sh em k`l vkv`nE @m`nv`q? Which scientists played a major role in overturning the ancient idea of an Earth-centered universe, and about when? a) Aristotle and Copernicus; about 400 years ago (a#rQs~@t`~tl~ sh @k`pnQks~~-vsr 400 kt @pr) b) Copernicus, Kepler, and Galileo; about 400 years ago(@k`pnQks~, @kp~lr~ sh g#lQl@Q y`~~-vsr 400 kt pmN @pr) c) Aristotle and Plato; about 2,000 years ago (a#rQs~@t`~tl~ sh p~@l~@t`~ - vsr 2000 kt @pr) d) Newton and Einstein; about 100 years ago(nQv|tn~ sh ayQn~s~tyQn~-vsr 100 kt @pr) 1/6

3.

aAXk ekkt vQkl` @k`pmN @v|q? How many arcseconds are in 1°? a) 360 b) 60 c) 3,600 d) 10,000

4.

p}QvQy mw pQhQtQ vQX`lwm qE@r~] vQq&Ew~ cEm|xk vrÑÑN`vlQ@y~ kvr pr`syk kQYy`w~mk @v|q? In what part of the electromagnetic spectrum do the biggest telescopes on Earth operate? a) infrared (a@{`~rk~w) b) visible(q^X&) c) radio (@r~dQ@y`~) d) X-ray(X-kQrN)

5.

hQr#@g~ s~kn~{yt s`@p~]v a@nkSw~ gYh@l~`k vl s~kn~{ s$s@qn~~@n~ @k@s~q? How does the Sun's mass compare with that of the planets? a) 1000 times more massive than Earth. (p^}QvQy @mn~1000 gSNyk~). b) 100 times more massive than all the planets combined. (gYh@l~`k sQyl~@l~ s~kn~{y @mn~ sQy gSNyk~ wrm| vQX`l@v|). c) It is about as massive as all the planets combined.(gYh@l~`k sQyl~@l~ s~kn~{yt sm`n wrm| vQX`l@v|). d) 1000 times more massive than all the planets combined. (gYh@l~`k sQyl~@l~ s~kn~{y @mn~ qhs~ gSNyk~ wrm| vQX`l@v|).

6.

hQr# sQt a$wQn~m pQhQtn~@n~ phw e~v`yQn~ kvrk~q? -Which of the following is furthest from the Sun? a) Pluto (plRR@t`~) b) a comet in the Kuiper belt (kSyQpr~ptQ@y~ a#wQ {Rm@k~wSvk~) c) a comet in the Oort cloud (u_t|vl`ptl@y~ a#wQ {Rm@k~wSvk~) d) an asteroid in the asteroid belt (gY`hk vLl~@l~ a#wQ gY`hkyk~)

7.

p^}QvQyt amwrv jly ayQs~@ls nQrW]Ny kl h#kQ gYh@l`~ky kSmk~q? Which planet, other than Earth, has visible water ice on it? a) Jupiter(bYhs~pwW) b) Mars (aghr#) c) Venus(sQkSr#)

8.

9.

d) Mercury(bE{)

@s_rgYh mN~dl@y~ pvwQn v#dQm Gnw~vyk~ a#wQ gYh@l`~~ky kSmk~q? Which is the densest planet in the solar system? a) Earth(p^}QvQy) b) Venus (sQkSr#) c) Jupiter(bYhs~pwW)

d) Mercury(bE{)

p^}QvQy h` a`sn~nñ vQX`lw~vykQn~ yEwS gYh@l`~ky kSmk~q? The planet closest in size to Earth is a) Venus(sQkSr#) b) Pluto(p~lR@t`~) c) Mars (aghr#)

d) Neptune(@np~cRn~)

10. phw s[hn~ a``k`X vs~wSn~ ph(Mercury- bE{, Venus- sQkSr#, Moon-cn~qYy`, Earth- p^}QvQy, Mars-aghr#) kSd` pYm`N@y~ sQt vQX`l ek qk~v` pQLQ@vl vnE@y~. Rank the five celestial worlds in order of size from smallest to largest: a) Mercury, Moon, Venus, Earth, Mars. b) Moon, Mercury, Venus, Earth, Mars. c) Mercury, Moon, Mars, Earth, Venus. d) Moon, Mercury, Mars, Venus, Earth. 11. pYm`Nvw~ wrmk v`yE@g~`lyk~ shQw cn~qYykS vn~@n~ kSmk~q? Which moon has the most substantial atmosphere? a) Titan b) Europa c) Mimas e) Io 12. p^}QvQy mw hmEvn axx&`vk`X@y~~ sQt a` @s_rgYh mN~dl@y~ @X~; vs~wSn~hqEn~vn nm. What do we call a small piece of solar system debris (came from space) found on Earth? a) asteroid (gY`hky) b) solar system debris(@s_rgYh mN~dl@y~ @X~; vs~wS) d) meteorite(ul~k`X~my) e) meteor(ul~k`v)

2/6

13. {Rm@k~wSvk vlQgy The tail of a comet a) always points toward the Sun (s$mvQtm hQr# @qst el~l vW wQ@b|) b) always points perpendicular to the Sun (s$mvQtm hQr#t lm|xkv pQhQt` wQ@b|) c) always points away from the Sun(s$mvQtm hQr#@gn~ ivwt el~l vW wQ@b|) d) they do not have tails near the Sun(hQr# asnñ~n@yqW e~v`t vl~g`` @n`pQhQtyQ) 14. p^}QvQy mwSpQtqW 60 kg brk~ a#wQ mQnQskS h[t gQ@y~ nm|, h[ mwSpQtqW ohE@g~ br vnE@y~ The weight of a man on Earth’s surface is 60 kg. If he goes to the moon, his weight at the lunar surface would be a) 10 kg

b) 20 kg

c) 60 kg

d) 120 kg

15. qE@r~]yk av@n@whQ n`xQ qERr 1 m sh ehQ up@n@w hQ n`xQ qEr 20 mm nm|, qE@r~]@y~ vQX`lny vnE@y~ If the focal length of the objective of a telescope is 1 m and the focal length of its eye piece is 20 mm, the magnification of the telescope is a) 10

b) 50

c) 100

d) 200.

16. p”’”^}QvQ@y~ sQtQn nQrW]kykSt s$m vQtm cn~qYy`@g~ ek~ p#w~wk~ pmNk~ @p@nn~@n~ The reason that we see the same side of the moon always is a) 5 degrees angle between the planes of the moon and earth. (cn~qYy`@g~ wlyw~ p”’”^}QvQ@y~ wlyw~ awr aAXk 5 k a`nwQy nQs`) b) Moon does not rotate at all . (cn~qYy` xYmNy @n`vn nQs`) c) Moon’s rotational speed is equal to the moon’s speed of revolution. (cn~qYy`@g~ xYmN k`ly sh prQxYmN k`ly sm`n nQs`) d) Tidal effect of the moon on the earth. (cn~qYy`@gn~ p^}QvQy mw a#wQvn uqm| nQs`) 17. hQr# vt` gmn~ gn~n` a`vr~wW {Rm@k~wSvk hQr#t a$wQn~m pQhQtn vQt qEr n]wY e~kk 31.5 vn awr hQr#t lgQn~m pQhQtn vQt qEr n]wY e~kk 0.5 @v|. {Rm@k~wS@v| k]@y~ a`vr~w k`ly p^}QvQ vr~; vlQn~ A Sun-orbiting periodic comet is the farthest at 31.5 A.U. and the closest at 0.5 A.U. The orbital period of this comet (in earth years) is a) 8

b) 16

c) 64

d) 76

18. sEr~y v`yE@g`~ly u;~Nw~vy anEv @k`ts~ wSnkt @bqQy h#k. e~v` pYk`X @g`~ly, vr~N @g`~ly sh @k@r`~n`v nmQ. pYk`X @g`~l@y~ s`mn& u”’;~nw~vy vnE@y~. Solar atmosphere can be divided into three major parts based on temperature. They are photosphere, chromosphere and corona. The average temperature of the photosphere is a) 4500 K

(b) 6000 K c) 10000 K d) 100000 K.

19. v`mn gYhykS@g~ k]Wy k`l`vr~wy vsr 560 bv @s~y`gn~n` lqW. hQr# vt`` yn ehQ pr`vlWy k]@y~ ar~{-mh`a]@y~ qQg vnE@y~. The orbital period of a dwarf planet is found to be 560 years. The length of the semi-major axis of its elliptical orbit around the sun is. a) 3.8

b) 22.8

c) 67.9

d) 131.2

3/6

20. r`wWY ah@s~ qWpQwQmw~m wr#v vnE@y~ The brightest star in the night sky is a) Sirius (sWrQys~) b) the North Star(uwSr# wr#v) c) Betelgeuse(@btl~~jRs~) d) Venus(sQkSr#) 21. sQAh r`XQ@y~ qWp~wQmw~m wr#k`v vnE@y~ The brightest star of the Leo constellation is a) Sirius b) Regulus

c) Antares

d) Algieba

22. phw r$py mgQn~ qk~v` a#wQ wr# rt`@v| nm vnE@y~ The name for the pattern of stars below is a) Ursa major(mh vls`), b) Scorpius(v^X~ck Q ), c) Orion (oryn~~), d) Taurus(v^;x)

23. r$p@yhQ a#wQ kQrN sthn mgQn~ qk~vn qE@r~] vr~gy vnE@y~ The type of telescope shown by a ray diagram in this figure is (a) Newtonian (b) Cassegrain (c) Coude (d) Maksukov 24. sEr~yy`@g~ q^X&vn p^;~Ty hqEn~vn~@n~ kSmn nmkQn~q? What name is given to the Sun’s visible ‘surface’? a) corona (@k`@r~`ñ~n`v ) b) chromosphere (vrÑN@g`~ly) c) limb (q`ry) d) photosphere(pYk`X@g`~ly) 25. sRr~ygYhNyk~ sQqEvn vQt ey n#rBWmt h#kQ pQrQs~ v`sy krn~@n~ When a solar eclipse occurs, the people who are able to witness the event are a) at any place on the daylight side of the Earth (p^}QvQ@y~ qhvl~k`ly a#wQ @pq@shQ o|n$m w#nkt) b) in the eclipse path only(gYhN p}y @pq@shQ pmNQ.) c) on the night time side of the Earth (p^}QvQ@y~ r`wYW @pq@shQ) d) near Sunset(hQr# b#s y`mt a`snñ~n @pq@shQ) 26. aghr# “rwSgh Y y’`” yn nmQn~ h#qQnvWmt @h~wSv - Mars is nicknamed the ‘red planet’ because a) it is hot (ey a{Qk u;ñw~vykQn~yEk~w nQs`) b) it is covered with a rusty, red dust (ey mlkdvn~ rwS {RvQl~lkQn~ v#sW wQbWm) c) it has a red atmosphere( eyt rw~p#h# v`yE@g`~lyk~wQbWm) d) all of the above(ihw s[hn~ sQyl~l) 27. sRr~yy`@g~ bhElv pvwQn mRlqYv& kSmk~q? Which chemical element is the most abundant inside the Sun? a) carbon (k`bn~) b) oxygen (~ok~sQjn~) c) helium (hWlQym|) d) hydrogen(hyQdYjn~) 4/6

28. wm vr~;yt vd` wm qQny qQgS vn ek~ gYh@l`~kyk~ @s_rgYh mN~dl@y~pvwW. em gYh@l`~k@y~ nm Only one planet in the solar system has a day which lasts longer than its year. Name of this planet is a) Venus(sQkSr#) b) Mercury(bE{) c) Uranus (yE@rñns~) d) Jupiter(bYhs~pwW) 29. cn~qYy` b#s yn~@n~ @p.v. 6.00 t nm| cn~qYy` @g~ kl`v. If the Moon is setting at 6 A.M., the phase of the Moon must be a) full (pRr~ÑN) b) third quarter (av ads[) c) first quarter (pEr ads[) d) waning crescent. (av atvk) 30. qhvl~ k`l@y~qW obt wr# nQrW]Ny kl h#kQnm| uw~wr`r~{ @g~`l@y~ rtkqW @qn lq qQnkqW obt @p@nn @qy phw @v|. sRrR~ yy` @mhQ wQ@bnE@y~ mQ}En r`XQ@y~y. If you could see stars during the day, this is what the sky would look like at noon on a given day. The Sun is in the constellation Gemini.

E

W

S hQr# b#syn vQt ey wQ@bn r`XQy vnE@y~~ When the sun sets, you will find it in the constellation a) Leo (sQAh) b) Canis Major (mh bl~l`) c) Gemini(mQ}En)

d) Taurus(v^;x)

============================================================ B @k`ts / PART B

@mm @k`t@s~ pYX~nvlt pQLQwSr# phw @k`tEkr a#wQ avk`Xy wSl spyn~n. (Please provide your answers to this part in the space provided at the end)

________________________________________________________________ 31. @t`lmQ vQsQn~ p#h#qQlQ kl a`k`ryt vQX~vy pQLQb[ xS@kññ~n~qWEYy a`k^wQ@y~ sthnhk~a#q qk~vnñ~n. Sketch the geocentric model of the Universe as explained by Ptolemy. 32

tQtQys~-@b`~@d| nQymy vQs~wr kr emgQn~ hQr# sQt @snsEr# gYhy`t a#wQ qEr n]wY e~kk vlQn~ a#s~w@m|n~wS krnñ~n. Describe the Titius Bode law and estimate the distance to planet Saturn from the Sun in Astronomical Units (AU). ****

5/6

Name of the candidate(nm):

Index number(vQx`g aAky):

Please provide your Answer to Question No.31 in this space (31 vn pYXñ~nñy s[h` vn pQLQwSr @mm @k`tEv wSl spynñ~n).

Answer

Please provide your Answer to Question No.32 in this space (32 vn pYXñ~nñy s[h` vn pQLw Q Sr @mm @k`tEv wSl spynñ~n).

Answer

6/6

Please furnish the following information before the commencement of the examination Full Name of the Candidate: Examination Centre: Colombo/Batticaloa/Jaffna/Kelaniya/Peradeniya/Ruhuna (underline) IColombo/Peradeniya/Kelaniya/Ruhuna/Batticaloa?Jaffna Index Number: Date of Birth: Signature of the Candidate :

XYW lAk` @x_wQk vQq&` a`ywny – INSTITUTE OF PHYSICS, SRI LANKA w`rk` vQq&`v h` w`rk` @x_wQk vQq&`v pQLQb[ ps~vn XWY lAk` olQm|pQy`d| wrM`vlQy-2011 THE 5TH SRI LANKAN OLYMPIAD ON ASTRONOMY AND ASTROPHYSICS - 2011 (k`ly p#y 1 vQn`dQ 30)(Duration : 1 hour and 30 minutes) @mm pYX~n pwYy pYX~n A h` B @k`ts~ @qkkQn~ yEwS pYX~n 25 kQn~ smn~vQwy This paper consists of 25 questions in two parts (A & B). gNny kQrWm| s[h` sh B @k`tst pQLQwSr# s#pyWm s[h` amEN` a#wQ hQs~ kdq`sQ x`vQw` krn~n. Use the attached blank sheets for your calculations and also to answer the questions in Part-B. sQyUm pYX~n vlt @mm pYX~n pwY@y~m pQLQwSr# spy` sQyU kdq`sQ vQx`gy avs`n@y~qW vQx`g X`l`{QpwQ wSm` @vw x`r @qn~n Answer all the questions in this paper and submit all sheets to the supervisor at the end of the examination. gNk yn~wY x`vQw kl h#k/Electronic calculators are allowed. (pY@y`~jnvw~ qw~w / Useful information : a`@l`~k@y~ @v|gy / Speed of light c = 3 x 105 km/s, sr~vwY gSr#w~v`kr~Xn nQywy / Universal gravitational constant G = 6.67 x 10-11 m3 kg-1 s-2). sQAhl prQ~vr~wn@yhQ g#tU mwSvEv@h`w~ iAgWYsQ bsQn~ a#wQ pYXn ~ y bl` pQLQwSr# spyn~n.

A @k`ts / PART A A @k`tst aq`l pYX~n vlt @h`[m pQLQwSr @w`~r` rvEmk~ a#qWm @h`~ ytQn~ irk~ a#[Wm sQqEkrn~n (Answers to Part A should be made by circling or underlining the correct answer on the question paper)

1.

What is the approximate range of temperatures on the lunar surface? a) -150 0C to 0 0C b) 0 0C to 100 0C c) -150 0C to 120 0C d )0 0C to 120 0C

2. From Kepler's third law, an asteroid with an orbital period of 8 years lies at an average distance from the Sun equal to a) 4 astronomical units. b) 8 astronomical units. c) 16 astronomical units. d) 2 astronomical units.

3.

4.

The lunar cycle of phases and the Moon’s orbital period around the Earth differ slightly. Which line in the table is correct? orbital period / day lunar cycle / day a) 27.3 28.0 b) 27.3 29.5 c) 28.0 29.5 d) 29.5 27.3 The mean mass density for a super massive black hole with total mass of 1×108 Schwarzschild radius would be (here 8

mEU s~kn~{y 1×10

=1.99 x 10

30

inside the

kg).

vn sEpQrQ vQX`l kUkShryk sQq~{Q m`yQm a#wSlw s`m`n& Gnw~vy vnE@y(@mhQ

30

=1.99 x 10 kg).)~.

a) 1.85 x 103 kg

5.

b) 1.99 x 1030 kg

8

5

c) 3.00 x 10 kg

d)6.67 x 10 kg

A student sees a thin, crescent Moon. At what time of day, and whereabouts in the sky, would this be visible? a) due south at midnight b) in the east at dawn c) in the north near Polaris d) in the west at sunset

6. Which of the following statements does not use the term angular size or angular distance correctly? a) The angular distance between those two bright stars in the sky is about 2 meters. b) The angular size of the Moon is about 1/2 degree. c) The angular distance between those two houses in the distance is 30°. d) You can use your outstretched hand to estimate angular sizes and angular distances.

7.

The radial velocity curve for binary system is shown in the figure. The radial velocities are plotted with the corresponding phases of the bunary system. Which statement is true about the properties of radial velocities (VA, VB), orbital periods (TA, TB) and the masses (MA, MB) of the binary system. A B

(a) (b) (c) (d)

VA>VB, VATB, TA=TB, TAMB MA>MB MA