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Introduction to Astrophysics Exam Paper
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- The University Of Sheffield (TUOS)
Introduction to Astrophysics Exam Paper
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PHY104PHY472
Data Provided:
Formula sheet and physical constants
Data Provided:
A formula sheet and table of physical constants is attached to this paper.
DEPARTMENT OF PHYSICS & Autumn Semester 2009-2010
ASTRONOMY
DEPARTMENT OF PHYSICS AND ASTRONOMY
ADVANCED QUANTUM MECHANICS 2 hours
Spring 2020
AnswerIntroduction to Astrophysics
question ONE (Compulsory) and TWO other questions, one each from3 hours
section A and section B.
Instructions:
All questions are
Answer all marked
FOUR out offrom
questions ten.Section
The breakdown
A and ONE on the right-hand
question side
from Section B. of the
paper is meant as a guide to the marks that can be obtained from each part.
Answering the exam questions should take no more than NINETY minutes, but you will have
THREE hours in a 24-hour window to complete the exam and upload your answers to Black-
board.
Section A is worth 20 marks in total and all questions in section B are worth 15 marks each.
The breakdown on the right-hand side of the paper is meant as a guide to the marks that can
be obtained from each part.
Cross through any work that you do not wish to be examined.
PHY104 TURN OVER
1
PHY472 TURN OVER
, PHY104
SECTION A
1. A star has an absolute visual magnitude of 4.0. What is the apparent visual magnitude
of an unresolved star cluster, if it consists of 500 of these stars, is located at a distance
of 2.0 kpc, and has a colour excess of E(B-V) = 0.30 mag? [5]
Note: You may assume that the ratio of visual extinction to colour excess is 3.0
2. For a galaxy cluster in spherical equilibrium, the virial theorem can be used to derive
a statistical estimate of the total mass of the cluster:
5Rc hvr2 i
Mc = ,
G
where Mc is the mass of the cluster, Rc is the radius of the cluster, and hvr i is the
mean radial velocity of galaxies within the cluster. Estimate the total mass of a rich
cluster, which sits at an average distance of 19 Mpc, has an angular diameter of 2.6◦ ,
and whose galaxies have a mean radial velocity relative to each other of 375 km s−1 . If
the cluster is host to 200 major galaxies, with 90% of the cluster mass attributed to
intra-cluster medium, what is the average mass of each galaxy in Solar masses? [5]
3. A binary system has an apparent V-band magnitude of 6.7 mag. If the system has
a parallax of 2.4 milli-arcsec, and the primary is 0.8 magnitudes brighter than the
secondary in the V-band, what are the absolute V-band magnitudes of the two compo-
nents? Estimate the spectral types of the components if B−V = –0.15 for both stars.
[5]
4. Runaway stars are usually defined as having peculiar space velocities in excess of
30 km s−1 . A bright star in the Small Magellanic Cloud (distance 60 kpc) has an
anomalous proper motion of 0.10 ± 0.05 milli-arcsec per year as measured by the
GAIA satellite. In addition, it has an observed radial velocity of 150 ± 5 km s−1 ,
versus an average of 135 km s−1 for neighbouring stars. Is the star a runaway? Show
your working to justify your answer. How would its radial velocity be measured in
practice? [5]
PHY104 CONTINUED
2
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