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 21, Problem 62Q
To determine

The density to which the matter of a dead 8M star must be compressed for the star to disappear inside its event horizon and comparison of this value with the density at the center of a neutron star about 3×1018 kgm3.

Expert Solution & Answer
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Answer to Problem 62Q

Density to which the matter of a dead 8M star must be compressed = 2.7×1017 kgm3

Density of the compressed star density at the center of the neutron star

Explanation of Solution

Given:

Mass of the dead star in solar mass = 8M

Density at the center of a neutron star = 3×1018 kgm3

Formula Used:

rs=2GMc2

Volume of a sphere=43πr3Density=MassVolume

Calculation:

8 solar mass = 8×2×1030 kg

G=6.7×1011 m3kg1s2

c=3×108 ms1

If the dead star is to be compressed for it to disappear inside the event sphere, it’s radius must be equal to the Schwarzschild radius. Hence, it’s radius can be found as follows.

rs=2GMc2rs=2×6.7×1011×8×2×1030(3×108)2rs=23.8×103 mRounding off to the first decimal placers=2.4×104 m

Assuming when the dead star is a perfect sphere when it is compressed.

Volume of the compressed star

43πr3=43×227×(2.4×104)3 m3=8821×15.625×1012m3=5.8×1013m3

Density =MassVolume=8×2×1030 kg5.8×1013m3=2.7×1017 kgm3

Conclusion:

Density to which the matter of a dead 8M star must be compressed = 2.7×1017 kgm3.

Density at the center of a neutron star = 3×1018 kgm3.

As 2.7×1017 kgm33×1018 kgm3

Density of the compressed star density at the center of the neutron star

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