Ay 21 - Lecture 2
An Overview:
A refresher of the special and general theories of relativity Homogeneity and isotropy Metric, Robertson-Walker Cosmological redshift Comoving and proper coordinates The Friedmann Equation Cosmological parameter

Ay 21 - Lecture 3
An Overview:
Cosmological Equations of State Computing cosmological models
Various examples
Global Geometry and Dynamics of the Universe, Part II
Distances in cosmology Basics of cosmological tests Horizons
Recall the defi

Problem Set 6 - Solution
E. S. Phinney, and J. Sebastian Pineda
March 4, 2012
1. C& O equation 29.101 expresses the Saha Equation for our universe with only hydrogen.
f
mH a3
=
1f
f b,0
2me kT
h2
3/2
eI /kT ,
(1)
where a is the scale factor and T = T0 /a

Problem Set 5 - Solution
E.S. Phinney, and J. Sebastian Pineda
March 4, 2012
1.
a) We consider a source at rest in comoving coordinates at redshift z = a(t0 )/a(te ) 1. We
want to nd out how this redshift changes over the present time, so we dierentiate z

Problem Set 4 - Solution
E.S. Phinney, Kunal Mooley and J. Sebastian Pineda
February 6, 2012
1. Age of the Universes
As done in class, the present-day age of a Universe with density parameters ( , k , M , r )
is,
t0 =
1
H0
0
1
dz
E (z ) 1 + z
(1)
where E

Problem Set 3 - Solution
E.S. Phinney, and J. Sebastian Pineda
January 30, 2012
1. Olbers Paradox revisited
We consider a t = 10 Gyr old non-expanding universe. With this nite age only light that as
come from stars within ct has had enough time to reach t

Problem Set 2 - Solution
E.S. Phinney, Kunal Mooley and J. Sebastian Pineda
January 24, 2012
1. The Virial Theorem:
a) Consider a collection of N particles interacting via attractive harmonic oscillator gravity. The total force on mass, mi is
Gmi mj (ri r

Problem Set 1 - Solution
E.S. Phinney, Kunal Mooley and J. Sebastian Pineda
February 2, 2012
1. Finding and interpreting data on a galaxy:
a) Perusing the database you can nd several images of NGC2639. The most useful is the
HST image reproduced below. Fr

Astronomy 21 Midterm Exam, 2012 Winter
Galaxies and Cosmology
3 Feb, 2012
Due in class 2:30pm Weds 8 Feb, 2012
E. S. Phinney
Do not download or open the exam until you are ready to take it.
Please write the exam in a Blue Book (available in the bookstore)