White Dwarfs and Neutron Stars. Recall that density is mass divided by volume, a
ID: 584984 • Letter: W
Question
White Dwarfs and Neutron Stars. Recall that density is mass divided by volume, and consult Appendix B as needed, (a) Calculate the average density of the earth in g/cirr. assuming our planet is a perfect sphere, (b) In about 5 billion years, at the end of its lifetime, our sun will end up as a white dwarf that has about the same mass as it does now but is reduced to about 15,000 km in diameter. What will be its density at that stage? (c) A neutron star is the remnant of certain supernovae (explosions of giant stars). Typically, neutron stars are about 20 km in diameter and have about the same mass as our sun. What is a typical neutron star density in g/cm3?Explanation / Answer
a) Radius of the earth = 6371 km = 6371*10^5 cm
mass of the earth = 5.972*10^24 kg = 5.972*10^27 g
volume of earth = 4/3 pi * r^3
V = 4/3 pi*(6371*10^5)^3 = 1.08*10^27 cm3
density = mass/ volume
density = 5.972*10^27 g / 1.08*10^27 cm3
density = 5.51 g/cm3
b) mass of the sun = 1.989*10^33 g
radius = 15000/2 = 7500 km = 7500*10^5 m
V = 4/3 * pi *r^3 = 4/3 * pi*(7500*10^5)^3
V = 1.767*10^27 cm3
density = M/V = 1.989*10^33 / 1.767*10^27 = 1.12*10^6 g/cm3
c) mass of the nuetron star = 1.989*10^33 g
radius = 20*10^5 cm
Volume = 4/3*pi*(20*10^5)^3
V = 3.35*10^19 cm3
density = mass/volume = 1.989*10^33/ (3.35*10^19) = 5.93*10^13 g/cm3
nuetron star density = 5.93*10^13 g/cm3
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