Concept explainers
(a)
The separation between the two clusters at the time when the light was emitted from
Answer to Problem 42Q
The separation between the two clusters at the time when the light was emitted from
Explanation of Solution
Given:
The redshift is,
The separation between the two clusters at present is
Formula Used:
The expression for the separation between the two clusters at the time when the light was emitted from the quasar is given by,
Calculation:
The expression for the separation between the two clusters at the time when the light was emitted from the quasar is calculated as,
Conclusion:
The separation between the two clusters at the time when the light was emitted from
(b)
The average density of matter at the time when the light was emitted from
Answer to Problem 42Q
The average density of matter at the time when the light was emitted from
Explanation of Solution
Given:
The redshift is,
The average density of matter in today’s universe is,
Formula Used:
The expression for average density of matter is given by,
Calculation:
The average density of matter is calculated as,
Conclusion:
The average density of matter at the time when the light was emitted from
(c)
The temperature of the cosmic background
Answer to Problem 42Q
The temperature of the cosmic background radiation at the time when the light was emitted from
Explanation of Solution
Given:
The redshift is,
Formula Used:
The expression for the radiation temperature is given by,
Here,
The expression for the mass density of radiation is given by,
Here,
Calculation:
The cosmic microwave background has a temperature of
The radiation temperature is calculated as
The mass density of radiation is calculated as
Conclusion:
The temperature of the cosmic background radiation at the time when the light was emitted from
(d)
Whether the universe was matter-dominated, radiation-dominated or dark-energy-dominated at the time when the light was emitted from
Explanation of Solution
Introduction:
Consider part (b). The average density of matter at the time when the light was emitted from
Consider part (c). The mass density of radiation at the time when the light was emitted from
The mass density of radiation is less than the average density of matter at the time when the light was emitted from
Conclusion:
The universe was matter-dominated at the time when the light was emitted from
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Chapter 25 Solutions
UNIVERSE (LOOSELEAF):STARS+GALAXIES
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- I asked the following question and was given the attached solution: Suppose that the universe were full of spherical objects, each of mass m and radius r . If the objects were distributed uniformly throughout the universe, what number density (#/m3) of spherical objects would be required to make the density equal to the critical density of our Universe? Values: m = 4 kg r = 0.0407 m Answer must be in scientific notation and include zero decimal places (1 sig fig --- e.g., 1234 should be written as 1*10^3) I don't follow the work and I got the wrong answer, so please help and show your work as I do not follow along easily thanksarrow_forwardIn vacuum, the H-alpha line has a rest-frame wavelength of 656.461 nm. You took a spectrum of the center of a galaxy at an observatory on the ground and measured a wavelength of 656.65 nm for the H-alpha line. What is the radial velocity of the galaxy relative to the observer [km/s]? Note that the index of refraction of air is 1.0003 at that wavelength. As a result, the rest-frame wavelength of the H-alpha line in air differs from the rest-frame wavelength in vacuum.arrow_forwardThe most distant quasar is "J0313-1806". Its redshift is z = 7.64. [ z = (femitted - fobserved)/ fobserved] Assume that the redshift is due to relative motion. Then how fast is the quasar moving away from Earth? (speed as the fraction of c = ) | .704 According to Hubble's Law, the distance (r) depends on the speed of recession (v) according to v = Hor where Ho~ 20km/s Mly How many years are required for light to travel from the quasar to Earth? (years = )arrow_forward
- The geometry of spacetime in the Universe on large scales is determined by the mean energy density of the matter in the Universe, ρ. The critical density of the Universe is denoted by ρ0 and can be used to define the parameter Ω0 = ρ/ρ0. Describe the geometry of space when: (i) Ω0 < 1; (ii) Ω0 = 1; (iii) Ω0 > 1. Explain how measurements of the angular sizes of the hot- and cold-spots in the CMB projected on the sky can inform us about the geometry of spacetime in our Universe. What do measurements of these angular sizes by the WMAP and PLANCK satellites tell us about the value of Ω0?arrow_forwardThe Friedmann equation in a matter-dominated universe with curvature is given by 87G -pR² – k , 3 where R is the scale factor, p is the matter densi, and k is a positive constant. Demonstrate that the parametric solution 4G po 4тG Po R(0) (1 – cos 0) 3 k and t( (e – sin 0) 3 k3/2 solves this equation, where 0 is a variable that runs from 0 to 27 and the present-day scale factor is set to Ro = 1. %3Darrow_forwardConsider the following FLRW spacetime: ds^2 = −dt^2 + t ^2/ t ^2 ∗ (dx^2 + dy^2 + dz^2 ), where t∗ is a constant. a) State whether this universe is spatially open, closed or flat. a) State whether this universe is spatially open, closed or flat. b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function of time t, starting at t = 0. c) Taking galaxy A to be located at (x, y, z) = (0, 0, 0), determine the proper distance to galaxy B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect to galaxy A.arrow_forward
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