   # What is the density of a 1.4 -M ⊙ neutron star? A 3.0- M ⊙ neutron star? Necessary data are provided in Problem 2. ( Notes: Density is mass divided by volume; the volume of a sphere is 4 3 π r 3 ; the mass of the Sun can be found in Celestial Profile: The Sun, Chapter 8.) ### Foundations of Astronomy (MindTap ...

14th Edition
Michael A. Seeds + 1 other
Publisher: Cengage Learning
ISBN: 9781337399920

#### Solutions

Chapter
Section ### Foundations of Astronomy (MindTap ...

14th Edition
Michael A. Seeds + 1 other
Publisher: Cengage Learning
ISBN: 9781337399920
Chapter 14, Problem 4P
Textbook Problem
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## What is the density of a 1.4-M⊙ neutron star? A 3.0-M⊙ neutron star? Necessary data are provided in Problem 2. (Notes: Density is mass divided by volume; the volume of a sphere is 4 3 π r 3 ; the mass of the Sun can be found in Celestial Profile: The Sun, Chapter 8.)

To determine

The density of Neutron stars of masses 1.4M0 and 3.0M0.

### Explanation of Solution

Necessary data is obtained from problem 2. It is found that from problem 2, radius of Neutron star having mass 3.0M0 is 7.8km.

Write the relation between mass and density.

ρ=mV

Here, ρ is the density, m is the mass, and V is the volume of H1 cloud.

Write the equation to find V.

V=43πR3

Rewrite the equation for ρ by substituting the above relation for V.

ρ=m43πR3=3m4πR3        (I)

Rewrite the above equation by substituting 1.4M0 for m.

ρ=3(1.4M0)4πR3        (II)

Here, M0 is the solar mass.

Rewrite equation (I) by substituting 3.0M0 for m.

ρ=3(3M0)4πR3        (III)

Conclusion:

Case 1: Neutron star of mass 1.4M0

Substitute 1.99×1030kg for M0 and 10km for R in equation (I) to find ρ.

ρ=3(1.4(1.99×1030kg))4π(10km(103m1km))3=8

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