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ASTR1001 Astrophysics
Creation date：2024-05-24 18:00:07
Belonging category：物理Physical
Astrophysics

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ASTR1001 

Astrophysics
Examination Duration: 4 hours
Instructions to Students:
Complete all six questions. They are all worth equal marks.
A formula sheet and a list of useful constants and definitions is at the end of the exam paper.
You may write or word-process your exam. You should save it as a single pdf file and upload that
to Wattle before the 4-hour deadline is over. Please leave enough time to complete the upload
before the deadline.
You must not communicate with other people during the exam: what you write must be entirely
your own work.
You are allowed to access any notes and the internet during the exam, and use any software you
wish (except communication software).
The exam is randomised – other students in the class are doing different questions.

Question 1
Imagine that you have discovered a pair of stars, 79.3 parsecs away from the
earth, and only 2.1 astronomical units apart from each other.
A) What would be the apparent separation of the stars, as viewed from the
Earth, in arcseconds? (2 marks)
B) Imagine that you want to use an optical telescope to get an image of
the pair, clearly resolving the two stars. What sort of telescope would
you need, and how large must it be? (4 marks)
C) Using your telescope, you discover that the two stars look very similar
to each other, both having fluxes of around 1.3x10-15 W m-2, and having
spectra that peak at around 340 nm. Deduce as much as you can about
these stars. (4 marks)
Question 2
A) For the pair of stars in the previous question, derive an equation for
their orbital period, assuming that they have equal masses and move in
circular orbits. Clearly show the steps in your derivation. (5 marks)
B) If they are white-dwarf stars, roughly how long would you have to
observe them to see one complete orbit? (2 marks)
C) Do you think that current or future gravitational wave detectors will be
able to detect gravitational waves from this pair of stars? Carefully
explain your reasoning. (3 marks)
Question 3
Imagine that you have just discovered a strange object out in space:
It consists of a fuzzy reddish object in the centre, surrounded by a blue ring of radius 3.5
arcseconds. The flux from the reddish object is 5.5 x 10-15 W m-2.
Summer 2020/1 ASTR1001 Summer
Astrophysics
Page 3 of 7
You take a spectrum of the fuzzy reddish object in the centre: it looks like the spectrum
of a fairly old and massive galaxy, with the Hydrogen H-alpha absorption line (lab
wavelength 656.3 nm) shifted to 717.5 nm. You also take a spectrum of the blue ring: it
looks like the spectrum of a young galaxy which is actively forming stars. It has an H-
alpha emission line at 778.8 nm.
You conclude that this is an Einstein Ring, where the fuzzy red object is a galaxy
gravitationally lensing a blue background galaxy.
Deduce as much as you can about the red galaxy.
Question 4
Imagine that you have been studying a Sun-like star that is roughly 25 light-years form
the Earth.
You have made repeated radial-velocity measurements, using an iodine cell to get high
precision:
You also monitored the visible light flux from this star, using the TESS satellite:
Summer 2020/1 ASTR1001 Summer
Astrophysics
Page 4 of 7
and here is a close-up of the top of the TESS graph:
Summer 2020/1 ASTR1001 Summer
Astrophysics
Page 5 of 7
You believe that there is a planet orbiting this star.
Deduce as much as you can about this planet and its orbit. Clearly explain your
reasoning.
Question 5
A) What is the cosmic microwave background radiation? What does it look like?
Where does it come from and how was it produced? (3 marks)
B) What are the acoustic peaks of the cosmic microwave background? How are they
measured? Sketch their spectrum and carefully explain its features and how they
are created. (4 marks)
C) How can measurements of the acoustic peaks be used to measure the curvature
of space-time and the average density of matter in the universe? (3 marks)
Question 6
List three different situations in astronomy where you get accretion disks.
For each of the three situations, draw a labelled sketch showing where the disks are
found and marking their key features. Explain carefully the observational evidence for
the existence of all three types of disks. (10 marks)
Case category
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CMP7000A CMP-7038B Math 263 LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 ​COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 ​BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 ​LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ​ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 ​FINC5090 ​MATH1052 ​SciComp Elec4622 ​FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 ​MAT 237 BISM2201 EEE8099 Physics 11 ECE2238B Biostat 234 ​ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 ​MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum
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