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: Stars And Galaxies
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