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Problem A.l : Journey to Proxima Centauri (a Points)
The diameter of the Sun is 1.39 million kilometres and the Earth is 8.3 light minutes fur away.
Proxima Centauri is the nearest star - it has a dista nce of 4.24 light years to our Sun.
(a) How long does it take to travelto Proxima Centauriwith
(i) an airplane (920 km/h)or(ii) with the Voyoger I space probe (17 km/s).
(b) Let the Sun have the size of a tennis batt (diameter: 6.7 cm): How far away is the Earth and
how far away is Proxima Centauri on this scale?
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Problem A.2 z Orbit of the Solar System (4 Points)
The Milky Way has a diameter of about 15O,O0O light years. Our solar system is locate d 27,OOO
light years from the center of the Milky Way and orbits the center with a speed of 220 km/s.
(a) How long does it take for the solar system to circte the center of the Milky Way?
(b) The earth has formed about 4.5 biltion years ago. How often has the earth circled the center?
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Problem A.3 : Distance to Arcturus (4 Points)
The stellar parallax of the starArcturus in the constellation Bocites was measures with 0.09'.
(a) Catcutate the distance (in parsec) between Arcturus and the Earth.
(b) How long does it take to send a light message from Earth to Arcturus?
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Problem A.4 : From Earth to Mars (a Points)
For a special mission to Mars you need to know the smallest distance between Earth and Mars.
However, you have lost your astronomy book and you could onty find these values:
Distance Earth to Sun: 149.6 mitlion km
Orbital period Earth: 1.00 years
Orbital period Mars: 1.88 years
By using these values and assuming that Mars and Earth move an circutar orbits, calculate the
smallest possible distance between Earth and Mars.
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Problem B.l : New Star (6 Points)
You have discovered a new star in the Mitky Way: Your new star is red and has 3/5 the temper:a-
ture of our Sun. The new star emits a total power that is 100,000 times greater than the power
emitted by our Sun.
(a) Determine the spectraltype (i.e. spectral ctassification) of the new star.
(b) How many times bigger is the radius of the new star compared to the radius of our Sun?
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Problem 8,2 z Moon Satellite (6 Points)
TheMoonhasamass olM :7.3-7022 kg,aradiusof .R : T.T.T06mandarotationperiodofT : 27.3 days. Scientists are ptanning to place a satellite around the Moon that always remains
above the same position (geostationary).
(a) Calculate the distance from the Moon's surface to this satetlite.
(b) Explain if such a Moon sateltite is possibte in reatity.
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Problem 8.3 : Binary Star System (6 Points)
You are the captain of a spaceship that is circling through a binary star system. Due to the gravi-
tational forces and the rocket engines, the orbit of your spaceship looks like that:
The position of your spaceship (in AU) at the time t (in days) is given by:
r:Ssin(t) a:sin(2t) z:0
(a) How long does it take your spaceship to circle the orbit once?
(b) Find an equation that calcutates the velocity u(t) of you.rpacethip at a given time t.(c) The two stars are positioned at the points (4, 0, 0) and (-4,0, 0): What is the distance of your
spaceship to the stars at the time t : t?
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Problem 8.4: Asteroid Collision (6 Points)
A warning system has calculated that two asteroids witl cotlide not far from Earth any time soon.
The smaller asteroid has the mass ?n and moves with the velocity u-. The bigger asteroid has the
mass M : 3rn and the vetocity of uy : iu*.They cottide at an angte of a : 60" and turn into a
single heavy asteroid (inelastic collision):
Ma
(a) Calculate the velocity of the single object after the collision.
(b) Determine the angle 0 after the collision.
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Answer fottowing questions related to this article:
(a) Why is it difficulty for LyC rodiation to escape galaxies with high star formation rates?
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(b) What is the difference between the density- bounded medium and the picket fence model?
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the spectratshape of the perforoted siell mode/ (se6 a#cle: figure 1, right box).' .€t*Pe'tn +his modej , LgoA.hnc shapa ilormv{c on'rts csntrql p*\( *nrf ,W*F.+{nt*9lur4caur,rsrl Sfrlhi\,n<s ) ,,..ffniol,r is suPenwposr) pnthB c,hanro|<rni{lr d'o*W'WWofrl-a {t^"+ "dnnrcr3ss fttd, aph calty *rrrat< gae'
(d) What is the SunburstArc and how was it discovered? ^ ,
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(e)When did the scientist observe-[he object and which instruments did they use?
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(f) What is the redshift of the SunburstArc and how was it determined from the data?
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Problem CJ l/.he Sunburst Arc (10 Points)
This problem requires you to read following recently pubtished scientific article:
The Sunburst Arc: Direct Lymon o escope obserued in the brightest known lensed golaxy,
T.E. Rivera-Thorsen, H. Dahle, M. Gronke, M. Bayliss, J.R. Rigby, R. Simcoe, R. Bordoloi, M. Turner, and G. Furesz,
Astronomy & Astrophysics 608, (20I7). 1-;nk: https://iaac.space/doc/Pre-Final-Article-20l7-sunburst-Arc.pdf
G) Exptain the difference between the right and the left diagram in figure 4 (see articte).
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Answer foltowing questions related to this article:
(a) What are the cunent methods to determine the dark matter density I radialvelocity and what
are the disadvantages of these methods? l+ is dVfennin*a f-..p 'lhv. Gglaalib folahoro 4flO,Mensursd*'lqlJ"egtr*.ff
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ne""thed s*eodY lsto#e "(b) Explain the new method. for measuring dark matter density that is proposed in the article.
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Problem C.2 z Dark Matter (10 Points)
This problem requires you to read following recently published scientific article:
Probing Dark Matter Using Precision Meosurements ofStellar Accelerations.A. Ravi, N. Langellier, D.F. Phillips, M. Buschmann, B.R. Safdi, R.L. Walsworth,
arXiv:1812.07578, (2018). Link: https://iaac.space/doc/Pre-Final-Article-2018-1812.07578.pdf
sity is given by pnm x
(d) How much does the vetocity of the stars change during the lifetime of a human (80 years)?
40 LnA
. (e) What is important for measuring stellar acceferations and which instrumentS tan be used?
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