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ASTR1001 Astrophysics Exam
Creation date：2024-06-11 16:31:57
Belonging category：物理Physical
Astrophysics Exam

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ASTR1001 Astrophysics Exam
Examination Duration: 3 hours
Instructions to Students:
Complete all six questions. Please show your working and explain what you are doing, so we can
give you partial marks if necessary.
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 3-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). Copying text from the internet or books, unless you
acknowledge it, constitutes academic misconduct. You may NOT post any part of the exam
online, or ask for help with it, including websites such as Chegg. We check for people using these
sites.
You may use sites like ChatGPT to suggest ideas, but you should not just copy their output as
your answer. Any verbatim use of its output will constitute academic misconduct. And we’ve
chosen questions that ChatGPT does not answer well…
Page 2 of 9
Question 1 (10 marks)
Imagine that you are reading a scientific paper, which is discussing how common
exoplanets are around Sun-like stars. The authors have been studying 100 Sun-like stars
for the last ten years. They took repeated radial velocity measurements, and brightness
measurements to look for transits. All observations were made with ground-based
telescopes.
They only detected 14 planets in the radial velocity measurements:
(Radial velocity results)
Only two transiting planets were discovered, both of which were also detected by the
radial velocity method:
(Transit results)
Based on their data, they come to the following five conclusions:
1) The radial velocity method is a better way to discover planets than the transit
method. Future projects should only use the radial velocity method.
2) Only 14% of Sun-like stars have planets.
3) Fewer than 1% of Sun-like stars have planets more than 5 AU from the star.
4) Fewer than 1% of Sun-like stars have Earth-like planets
5) Planets that are further from their star are more massive, on average.
Summer 2023/4 ASTR1001 Astrophysics
Page 3 of 9
For each of their conclusions, discuss whether it is true, based purely on their own
observations. Carefully explain what is and is not correct about each of their conclusions,
explaining your reasoning.
Question 2 (10 marks)

Imagine that you have discovered a new galaxy. You do not know the distance to this
galaxy, but you measure a flux from it of 7.9 × 10−13W −2. Its apparent radius is 4.2
arcmin.
You take a spectrum of the centre of the galaxy:
Summer 2023/4 ASTR1001 Astrophysics
Page 4 of 9
You also take a spectrum of the edge of the galaxy:
You may assume that H0=72 km/s/Mpc.
A) How far away is this galaxy (in Mpc)?
B) What is the radius of this galaxy (in kpc)?
C) How fast is the galaxy rotating (in km/s)?
D) What is the approximate stellar mass of the galaxy (in solar masses)?
E) What is the total gravitational mass of the galaxy (in solar masses)? Does it
contain dark matter?
Summer 2023/4 ASTR1001 Astrophysics
Page 5 of 9
Question 3
Imagine that the TESS satellite has been monitoring a Sun-like star (i.e. a star
with the same mass and radius as the Sun).
This star shows transits due to a planet orbiting it. These transits occur every
119.8 hours.
Here is the TESS graph of optical brightness as a function of time:
You decide to get infra-red data on this star, using the James Webb Space
Telescope (JWST). Here is a close-up of the optical (TESS) and infrared (JWST)
light curves of this star.
Summer 2023/4 ASTR1001 Astrophysics
Page 6 of 9
For all the following questions, clearly explain your reasoning, with diagrams
where appropriate.
A) What is the radius of this planet (in units of Jupiter radii)? (1 mark)
B) What is the distance of this planet from its star (in Astronomical Units)? (1
mark)
C) Sketch the optical light curve and indicate on the sketch the primary transit
(where the planet goes in front of the star) and the secondary transit (where the
star goes in front of the planet). (1 mark)
D) On your sketch, indicate the brightness of the star without the planet, and the
brightness of the day and night-sides of the planet. (1 mark)
E) At optical wavelengths, does the planet reflect light from its star? (1 mark)
F) At optical wavelengths, does the planet emit any light from its night side? (1
mark)
G) Is there any evidence that the planet is more reflective in some areas than
others, at optical wavelengths? (1 mark)
H) Does the planet emit its own light at infrared wavelengths? (1 mark)
I) Does the planet emit its own infrared light from its night side? (1 mark)
J) Is the day side of the planet hotter than the night side? (1 mark)

Question 4
A red giant star and a black hole both of equal mass M are in circular orbits of radius r
around their common centre of mass.
A) Derive an equation for the orbital velocity of the red giant. Show your working and
explain your reasoning. (8 marks)
B) If the star and black hole have masses of 4x1030 kg and their orbital radius is 2.5
AU, what is the orbital velocity of the red giant? (2 marks)

Question 5
Imagine that a white dwarf star has just been discovered. It has a radius of 8000 km, a
temperature of 10,000 K, and lies at a distance of 400 pc from the Earth.
If you assume that it radiates as a perfect Black Body:
A) Sketch the spectrum of the white dwarf, indicating the peak wavelength on your
sketch. (3 marks)
B) Calculate the luminosity of the white dwarf. (4 marks)
C) Calculate the flux you would measure from the white dwarf on Earth. (3 marks)
Summer 2023/4 ASTR1001 Astrophysics
Page 7 of 9

Question 6
Imagine that a foreign country is sending satellites over Australia, at an
altitude of 600 km. The Australian government wants to see what these
satellites are doing and work out what they might be capable of.
You propose to use the AAT telescope at the ANU’s Siding Spring
Observatory to take detailed pictures of these spacecraft as they pass over.
This telescope works at visible light wavelengths and has a primary mirror
diameter of 3.9m. Typical atmospheric seeing at Siding Spring on a good night
is 1.2 arcseconds.
A) What is the size of the smallest details you will be able to resolve on
these satellites? Will this be useful? (3 marks)
B) What is the size of the smallest details you will be able to resolve on
these satellites if you use adaptive optics? Will this be useful?
(3 marks)
C) You sometimes detect radar signals from the satellite, with a flux of
7.1x10-9 W m-2. From your optical image, you think that the satellite is
sending radar beams in your direction, using a dish to emit them in a
cone of angle =7 degrees centred on you (see diagram below).
Perhaps they are trying to make a radar map of your observatory.
Estimate the total radar power emitted by the satellite. 
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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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