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Concept explainers
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 6.5×106 m/s and 8.1×106 m/s.
Explanation of Solution
Necessary data is obtained from problem 1. Radius of 1.0M0 mass white dwarf is 6363 km and the radius of 1.4M0 mass white dwarf is 5691 km.
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 6.67×10−11 m3/kg⋅s2 for G, 1.99×1030kg for M0, and 6363 km for R in equation (I) to find vc.
ves=√2(6.67×10−11 m3/kg⋅s2)(1.0(1.99×1030kg))6363 km(103m1 km)=√0.0041×1016 m/s=6.5×106 m/s
Substitute 6.67×10−11 m3/kg⋅s2 for G, 1.99×1030kg for M0, and 7000 km for R in equation (I) to find vc.
ves=√2(6.67×10−11 m3/kg⋅s2)(1.4(1.99×1030kg))5691 km(103m1 km)=√0.0065×1016 m/s=8.1×106 m/s
Therefore, the escape velocity at the surface of white dwarfs of masses 1.0M0 and 1.4M0 are 6.5×106 m/s and 8.1×106 m/s.
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Chapter 14 Solutions
EP WEBASSIGN FOR SEEDS/BACKMAN'S FOUNDA
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