Ph 444
Solutions for Problem Set 5
1. (Ryden 5.4) The proper distance today to a galaxy with redshift z in a flat, singlecomponent universe with an equation of state defined by the parameter w is given by equation (5.54) from Ryden: dp (t0 ) = c H0 2 1 +
Ph 444
Problem Set 1
Due: Tuesday, September 14, 2010
1. Ryden problem 2.2 2. Ryden problem 2.4 3. Ryden problem 2.5 4. As discussed in lecture, the number of galaxies per unit area on the sky as a function of magnitude is one way to test for the the homo
Ph 444
Problem Set 7
Due: Friday, November 19, 2010
1. Ryden problem 9.3 (Imagine that at the time of recombination, the baryonic portion of the universe consisted entirely of 4 He. . . ) A slightly tricky point here is what to use for nbaryon when calcul
Ph 444
Problem Set 3
Due: Friday, October 1, 2010
1. Calculate the critical mass density and its uncertainty using the current best estimate of the Hubble constant, H0 = 70.6 1.8 km s-1 Mpc-1 . 2. The Millennium Galaxy Catalog yields a local luminosity de
Ph 444
Problem Set 6
Due: Friday, November 12, 2010
1. (Ryden problem 7.5) The surface brightness of an astronomical object is defined as its observed flux divided by its observed angular area; thus, f /()2 . For a class of objects that are both standard
Ph 444
Solutions for Problem Set 6
1. (Ryden 7.5) The flux, f , received from a standard candle of luminosity L is (Ryden equation 7.21) L f= , (1) 4d2 L where dL is the luminosity distance. The angular diameter, , of a standard yardstick of size is (Ryde
Ph 444
Problem Set 8
Due: Tuesday, November 30, 2010
1. Ryden problem 10.1 (Suppose the neutron decay time were n = 89 s instead of n = 890 s . . . ) 2. Ryden problem 10.2 (Suppose the difference in rest energy of the neutron and proton were Qn = (mn - mp
Ph 444
Problem Set 2
Due: Tuesday, September 21, 2010
1. A simple model for the lumpiness of the universe is that all of the matter is collected into clumps, each of mass mc , with a number density nc . These clumps could represent galaxies, clusters of g
Blk img
POSSII.F.DSS2.443
N
1'
12:59:48.72 +27:58:49.3 / 13.12' x 12.92'
E
Blink sequence by Aladin
Produced by Aladin (Centre de Donnees astronomiques de Strasbourg)
http:/aladin.u-strasbg.fr
Blk img
2MASS.K.000128N_KI1120173
N
1'
12:59:48.72 +27:58:49.3
Ph 444
Solutions for Problem Set 1
1. (Ryden 2.2) To decide how far one can see on average in a universe filled with spherical objects of radius R, it is simplest to think of a long cylinder along the line of sight. If an object is closer than R to the li
Ph 444
Solutions for Problem Set 3
2 1. The critical energy density is c = 3H0 /(8Gc2 ) and so the critical density is 2 c = 3H0 /(8G). The uncertainty in the critical density is
c = c c
c H0 = H0 H0 H0 = 2 H0
2 3H0 6H0 H0 = H0 8G 8G
(1) (2)
I find that f
Ph 444
Solutions for Problem Set 4
1. (Ryden 4.2) The acceleration of the universe is governed by equation (4.64) from Ryden: 4G a = - 2 ( + 3P ) + . (1) a 3c 3 Initially only a density of non-relativistic matter is present. Non-relativistic matter has P
Ph 444
Solutions for Problem Set 6
1. (Ryden 9.3) This problem examines the recombination of helium in the early universe. For simplicity, it considers a universe containing only He and assumes that the amount of doubly ionized helium is negligible. The l
Ph 444
Problem Set 4
Due: Friday, October 8, 2010
1. Ryden problem 4.2. Assume that the value of is held fixed as some nonrelativistic matter is turned into radiation. 2. Ryden problem 5.2. Note that in this problem, the source of light remains at a fixed
Ph 444
Problem Set 5
Due: Friday, October 15, 2010
1. Ryden problem 5.4. 2. Ryden problem 6.3. 3. In class this week, I presented an interesting derivation for a flat, dust-filled Universe of the proper distance of a photon as a function of time that orig
Ph 444
Numerical Assignment 1
Due: Friday, November 5, 2010
The fluctuations in the cosmic microwave background (CMB) radiation provide some of our most powerful constraints on the properties of the universe. We will see later in the course that an import
Ph 444
Solutions for Numerical Assignment 1
1. The particle horizon at the time t is calculated by taking each interval of proper distance, cdt , covered by a photon between t and t + dt , increasing it by the expansion of the universe between t and t, a(