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 she
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.
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 f
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, fo
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 e
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
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
T
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
convenie
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
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
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
computa
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
confineme
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 electron
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
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