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ASTR1001 Astrophysics Exam

创建日期：2024-06-11 16:31:57

所属分类：物理Physical

标签： ASTR1001

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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