Universe: Stars And Galaxies
Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 25, Problem 21Q
To determine

(a)

The age of the universe.

Expert Solution
Check Mark

Answer to Problem 21Q

The age of the universe is 19.542billionyear.

Explanation of Solution

Given:

The value of the Hubble’s constant 1 is H1=50km/s/Mpc.

The value of the Hubble’s costant 2 is H2=75km/s/Mpc.

The value of the Hubble’s costant 3 is H3=100km/s/Mpc.

Formula used:

The life of the universe is given by,

T1=1H1

Calculation:

The life of the universe is calculated by,

T1=1H1=150 km/s/Mpc=150 km/s/( Mpc)( 10 6 pc Mpc )=150 km/s/( 10 6 pc)

Solve further,

T1=150 km/s/( 3.08568× 10 19 km)=( 3.08568× 10 19 km)50km/s=6.17136×1017s( 1year [ ( 3600 )( 24 )( 365.25 )]s)=1.9542×1010year

Solve further,

T1=1.9542×1010year( 1billionyear 10 9 year)=19.542billionyear

Conclusion:

The age of the universe is 19.542billionyear.

To determine

(b)

The age of the universe.

Expert Solution
Check Mark

Answer to Problem 21Q

The age of the universe is 13.004billionyear.

Explanation of Solution

Formula used:

The life of the universe is given by,

T2=1H2

Calculation:

The life of the universe is calculated by,

T2=1H2=175 km/s/Mpc=175 km/s/( Mpc)( 10 6 pc Mpc )=175 km/s/( 10 6 pc)

Solve further,

T2=175 km/s/( 10 6 pc)=175 km/s/( 10 6 pc( 206265AU 1pc ))=175 km/s/( 206265× 10 6 AU)=175 km/s/( 206265× 10 6 AU)( 149597871km 1AU )

Solve further,

T2=175 km/s/( 3.08568× 10 19 km)=( 3.08568× 10 19 km)75km/s=4.10666×1017s( 1year [ ( 3600 )( 24 )( 365.25 )]s)=1.30043×1010year

Solve further,

T2=1.30043×1010year( 1billionyear 10 9 year)=13.004billionyear

Conclusion:

The age of the universe is 13.004billionyear.

To determine

(c)

The age of the universe and how the age of globular cluster is used to place the limit on the maximum value of Hubble’s constant.

Expert Solution
Check Mark

Answer to Problem 21Q

The age of the universe is 9.7779billionyear.

Explanation of Solution

Formula used:

The life of the universe is given by,

T3=1H3

Calculation:

The life of the universe is calculated by,

T3=1H3=1100 km/s/Mpc=1100 km/s/( Mpc)( 10 6 pc Mpc )=1100 km/s/( 10 6 pc)

Solve further,

T2=1100 km/s/( 10 6 pc)=1100 km/s/( 10 6 pc( 206265AU 1pc ))=1100 km/s/( 206265× 10 6 AU)=1100 km/s/( 149597871km 1AU )( 206265× 10 6 AU)

Solve further,

T2=1100 km/s/( 3.08568× 10 19 km)=( 3.08568× 10 19 km)100km/s=3.08568×1017s( 1year [ ( 3600 )( 24 )( 365.25 )]s)=9.7779×109year

Solve further,

T2=9.7779×109year( 1billionyear 10 9 year)=9.7779billionyear

Conclusion:

The age of the universe is 9.7779billionyear.

The age of the universe is decreasing as the value of the Hubble’s constant is increasing. Since. the age of the globular cluster cannot be less than the universe, as it is not possible that consist of the universe is older than the universe. So the age of the universe is more than the globular cluster and it apply the maximum limit on the value of the Hubble’s constant.

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Students have asked these similar questions
Estimate the age of the universe for a Hubble constant of (a)50km/s/Mpc, (b) 75km/s/Mpc, and (c) 100 km/s/Mpc. On the basis of the answers, explain how the ages of globular clusters could be used to put a limit on the maximum value of the Hubble constant.
Explain how the Hubble constant, H0, can be used to make an estimate for the age of the Universe. Use the value of H0 = 0.07×103 kms-1/Mpc to estimate the Universe’s age. Comment on the significance of your answer.
How old is the wild the universe be, assuming space-time IS FLAT and the expansion of the universe has NOT been accelerating?
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