(a)
To calculate: Compactness of Earth.
Compactness of Earth is
Given:
Mass of Earth:
Radius of Earth:
Compactness is the ratio of Schwarzschild radius to Actual radius.
Formula used:
Schwarzschild radius
Calculation:
Let compactness be denoted by
Substituting the given values we get-
Conclusion:
Compactness of Planet earth is
(b)
To calculate: Compactness of Sun.
Compactness of Sun is
Given:
Mass of Sun:
Radius of Sun:
Compactness is the ratio of Schwarzschild radius to Actual radius.
Formula used:
Schwarzschild radius
Calculation:
Let compactness be denoted by
Substituting the given values we get-
Conclusion:
Compactness of Sun is
(c)
To calculate: Compactness of Neutron Star.
Compactness of Neutron Star is
Given:
Density of Star:
Radius of Star:
Compactness is the ratio of Schwarzschild radius to Actual radius.
Formula used:
Schwarzschild radius
Calculation:
Let compactness be denoted by
Substituting the given values we get-
Since
Conclusion:
Compactness of Star is
(d)
To calculate: Compactness of Black hole.
Compactness of Black hole is1.
Given:
Compactness is the ratio of Schwarzschild radius to Actual radius.
Formula used:
Schwarzschild radius
Calculation:
Let compactness be denoted by
According to question the Schwarzschild radius of black hole is comparable to its actual radius therefore
Conclusion:
Compactness of Black hole is
(b)
To calculate: Compactness of Sun.
Compactness of Sun is
Given:
Mass of Sun:
Radius of Sun:
Compactness is the ratio of Schwarzschild radius to Actual radius.
Formula used:
Schwarzschild radius
Calculation:
Let compactness be denoted by
Substituting the given values we get-
Conclusion:
Compactness of Sun is
(c)
To calculate: Compactness of Neutron Star.
Compactness of Neutron Star is
Given:
Density of Star:
Radius of Star:
Compactness is the ratio of Schwarzschild radius to Actual radius.
Formula used:
Schwarzschild radius
Calculation:
Let compactness be denoted by
Substituting the given values we get-
Since
Conclusion:
Compactness of Star is
(d)
To calculate: Compactness of Black hole.
Compactness of Black hole is1.
Given:
Compactness is the ratio of Schwarzschild radius to Actual radius.
Formula used:
Schwarzschild radius
Calculation:
Let compactness be denoted by
According to question the Schwarzschild radius of black hole is comparable to its actual radius therefore
Conclusion:
Compactness of Black hole is
(c)
To calculate: Compactness of Neutron Star.
Compactness of Neutron Star is
Given:
Density of Star:
Radius of Star:
Compactness is the ratio of Schwarzschild radius to Actual radius.
Formula used:
Schwarzschild radius
Calculation:
Let compactness be denoted by
Substituting the given values we get-
Since
Conclusion:
Compactness of Star is
(d)
To calculate: Compactness of Black hole.
Compactness of Black hole is1.
Given:
Compactness is the ratio of Schwarzschild radius to Actual radius.
Formula used:
Schwarzschild radius
Calculation:
Let compactness be denoted by
According to question the Schwarzschild radius of black hole is comparable to its actual radius therefore
Conclusion:
Compactness of Black hole is
(d)
To calculate: Compactness of Black hole.
Compactness of Black hole is1.
Given:
Compactness is the ratio of Schwarzschild radius to Actual radius.
Formula used:
Schwarzschild radius
Calculation:
Let compactness be denoted by
According to question the Schwarzschild radius of black hole is comparable to its actual radius therefore
Conclusion:
Compactness of Black hole is

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Chapter 13 Solutions
Fundamentals of Physics, Extended
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