Foundations of Astronomy (MindTap Course List)
Foundations of Astronomy (MindTap Course List)
14th Edition
ISBN: 9781337399920
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 14, Problem 5P
To determine

The escape velocity at the surface of white dwarfs of masses 1.0M0 and 1.4M0.

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Answer to Problem 5P

The escape velocity at the surface of white dwarfs of masses 1.0M0 and 1.4M0 are 6.5×106m/s and 8.1×106m/s.

Explanation of Solution

Necessary data is obtained from problem 1. Radius of 1.0M0 mass white dwarf is 6363km and the radius of 1.4M0 mass white dwarf is 5691km.

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 1.0M0 for M

    ves=2G(1.0M0)R        (II)

Here, M0 is the mass of sun.

Rewrite equation by substituting 1.4M0 for M

    ves=2G(1.4M0)R        (III)

Conclusion:

Substitute 6.67×1011m3/kgs2 for G, 1.99×1030kg for M0, and 6363km for R in equation (I) to find vc.

    ves=2(6.67×1011m3/kgs2)(1.0(1.99×1030kg))6363km(103m1km)=0.0041×1016m/s=6.5×106m/s

Substitute 6.67×1011m3/kgs2 for G, 1.99×1030kg for M0, and 7000km for R in equation (I) to find vc.

    ves=2(6.67×1011m3/kgs2)(1.4(1.99×1030kg))5691km(103m1km)=0.0065×1016m/s=8.1×106m/s

Therefore, the escape velocity at the surface of white dwarfs of masses 1.0M0 and 1.4M0 are 6.5×106m/s and 8.1×106m/s.

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