Universe
Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 25, Problem 21Q

(a)

To determine

The age of the universe for a Hubble constant of 50km/s/Mpc.

(a)

Expert Solution
Check Mark

Answer to Problem 21Q

Solution:

20 billion years.

Explanation of Solution

Given data:

The Hubble constant is 50km/s/Mpc.

Formula used:

The relation between the age of the universe and the Hubble constant is given by the following expression,

T0=1H0

Here, T0 is the age of the universe and H0 is the Hubble constant.

Explanation:

Recall the relation between the age of the universe and the Hubble constant.

T0=1H0

Substitute 50km/s/Mpc for H0,

T0=150 km/s/Mpc=1 Mpc50 km/s(3.09×1019 km1 Mpc)=6.18×1017 s(1 ly3.156×107 s)=1.96×1010 yr

Upon further solving,

T020 billion years.

Conclusion:

Therefore, the age of the universe is 20 billion years.

(b)

To determine

The age of the universe for a Hubble constant of 75km/s/Mpc.

(b)

Expert Solution
Check Mark

Answer to Problem 21Q

Solution:

13 billion years.

Explanation of Solution

Given data:

The Hubble constant is 75km/s/Mpc.

Formula used:

The relation between the age of the universe and the Hubble constant is given by the following expression,

T0=1H0

Here, T0 is the age of the universe and H0 is the Hubble constant.

Explanation:

Recall the relation between the age of the universe and the Hubble constant.

T0=1H0

Substitute 75km/s/Mpc for H0,

T0=175 km/s/Mpc=1 Mpc75 km/s(3.09×1019 km1 Mpc)=6.18×1017 s(1 ly3.156×107 s)=13×109 year

Upon further solving,

T0=13 billion year.

Conclusion:

Therefore, the age of the universe is 13 billion years.

(c)

To determine

The age of the universe for a Hubble constant of 100km/s/Mpc. The explanation for the use of the ages of the globular clusters for the maximum value of the Hubble constant.

(c)

Expert Solution
Check Mark

Answer to Problem 21Q

Solution:

10 billion years.

Explanation of Solution

Given data:

The Hubble constant is 100km/s/Mpc.

Formula used:

The relation between the age of the universe and the Hubble constant is given by the following expression,

T0=1H0

Here, T0 is the age of the universe and H0 is the Hubble constant.

Explanation:

Recall the relation between the age of the universe and the Hubble constant.

T0=1H0

Substitute 100km/s/Mpc for H0,

T0=1100 km/s/Mpc=1 Mpc100 km/s(3.09×1019 km1 Mpc)=6.18×1017 s(1 ly3.156×107 s)=9.79×109 yr

Upon further solving,

T0=9.79 billion years.

From the calculation in all the three parts, the value of H0 gives a corresponding value of T0, which is less than the ages of oldest stars present in a globular cluster.

Conclusion:

Therefore, the universe must be older than the oldest stars of the globular cluster. So, the Hubble constant should be such that the age of the universe is older than that of the oldest star in the globular cluster.

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