Foundations of Astronomy
Foundations of Astronomy
13th Edition
ISBN: 9781305079151
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 14, Problem 6P
To determine

The escape velocity at the surface of Neutron stars of masses 1.4M0 and 3.0M0.

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Answer to Problem 6P

The escape velocity at the surface of Neutron stars of masses 1.4M0 and 3.0M0 are 1.9×108m/s and 3.2×108m/s respectively.

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 equation to find the escape velocity.

    ves=2GMR        (I)

Here, ves is the escape velocity, G is the gravitational constant, M is the mass of star, and R is the radius of star.

Rewrite equation by substituting 1.4M0 for M

    ves=2G(1.4M0)R        (II)

Here, M0 is the mass of sun.

Rewrite equation by substituting 3.0M0 for M

    ves=2G(3.0M0)R        (III)

Conclusion:

Case 1:Escape velocity star with mass 1.4M0.

Substitute 6.67×1011m3/kgs2 for G, 1.99×1030kg for M0, and 10km for R in equation (II) to find vc.

    ves=2(6.67×1011m3/kgs2)(1.4(1.99×1030kg))10km(103m1km)=3.71×1016m/s=1.9×108m/s

Case 1: Escape velocity star with mass 3.0M0.

Substitute 6.67×1011m3/kgs2 for G, 1.99×1030kg for M0, and 7.8km for R in equation (III) to find ves.

    ves=2(6.67×1011m3/kgs2)(3.0(1.99×1030kg))7.8km(103m1km)=10.2×1016m/s=3.2×108m/s

Therefore, the escape velocity at the surface of Neutron stars of masses 1.4M0 and 3.0M0 are 1.9×108m/s and 3.2×108m/s respectively.

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