Name _
Solutions to Final Exam
March 30, 2010
This test consists of three parts. For the first part, you may write your answers directly on the
exam, if you wish. For the other parts, use separate sheets of paper. Useful equations can be
found at the star
Name _
Final Exam
March 30, 2010
This test consists of three parts. For the first part, you may write your answers directly on the
exam, if you wish. For the other parts, use separate sheets of paper. Useful equations can be
found at the start of part 3.
Physics 310 Cosmology
Solution Set L
1. [10] In class, we demonstrated that for flat rotation curves, V 2 R V02 , the
rotational and epicycle angular velocity are related by 2 . Consider
instead the following two cases:
(a) [5] What is the formula for the
Physics 310 Cosmology
Solution Set M
1. [20] A set of Type Ia supernovae has their
peak apparent magnitude m and their red
shift z measured. The results are collected
in the table at right. Assume, for
purposes of this problem, that Type Ia
supernovae hav
Physics 310 Cosmology
Solution Set N
1. For this problem, we will assume that non-relativistic formulas work for orbits
near a black hole. We wish to estimate the maximum amount of power that can
be extracted from a mass m that is working its way in towar
Physics 310 Cosmology
Solution Set O
1. [15] The critical density c is the density required to have a universe with 1 .
The contribution of any component to i is i i c
(a) [4] Find a formula for c in terms of Hubbles constant today H0. Evaluate
the critic
Physics 310 Cosmology
Solution Set P
1. [20+5] In class we found a formula for the age of the Universe assuming there is
only matter with a density parameter . The formula was:
t0 H
1
0
1
dx
x 1
0
The assumptions was that matter has a density proportion
Physics 310 Cosmology
Solution Set Q
z
Event
T (K)
kBT (eV)
1. [15] Estimate the
31.3
0.00270
Reionization
10.5
age of the
109
0.0259
Room Temp
300.
universe (in
1089
2970
Recombination
0.256
convenient
multiples of the year), the red shift z, the tempera
Physics 310 Cosmology
Solution Set R
1. [7] For each of the following, estimate the thermal energy kBT of the universe.
Use g eff 3.36 .
(a) When primordial tritium decays (t = 17.8 y).
Since this is early in the universe (well before the matter dominated
Physics 310 Cosmology
Solution Set S
1. [30] How flat is/was the universe? For this problem, our goal will be to
determine the approximate value of in the distant past. The current value is
0 1.0023 0.0016
(a) [3] Assuming the actual value is no larger th
Physics 310 Cosmology
Solution Set T
1. [15] There is an additional problem with neutrinos as dark matter: It turns out
the Pauli exclusion principle makes it hard to fit them in a galaxy. The
computation is a bit complex, but we can approximate it pretty
Physics 310 Cosmology
Solution Set U
1. [10] Suppose the universe is filled with matter in some regions, and anti-matter
in others. Lets imagine the segregation occurred at the time of quark
confinement, so somehow the quarks congregated together, and so
Physics 310 Cosmology
Solution Set V
1. [12] This question concerns the relative strength of electric and gravitational
forces.
(a) [3] Write a formula for the gravitational force between two electrons. Find
the ratio of the gravitational force to the Cou
Name _
Midterm Exam
March 4, 2010
This test consists of three parts. For the first part, you may write your answers directly on the
exam, if you wish. For the other parts, use separate sheets of paper. Useful equations can be
found on the last page of thi
Name _
Midterm Exam
March 4, 2010
This test consists of three parts. For the first part, you may write your answers directly on the
exam, if you wish. For the other parts, use separate sheets of paper. Useful equations can be
found at the start of part 3.