Foundations of Astronomy, Enhanced
Foundations of Astronomy, Enhanced
13th Edition
ISBN: 9781305980686
Author: Michael A. Seeds; Dana Backman
Publisher: Cengage Learning US
bartleby

Concept explainers

Question
Book Icon
Chapter 14, Problem 3P
To determine

The density of white dwarfs of masses 1.0M0 and 1.4M0.

Expert Solution & Answer
Check Mark

Answer to Problem 3P

The density of white dwarfs of masses 1.0M0 and 1.4M0 are 1.39×109kg/m3 and 1.95×109kg/m3 respectively.

Explanation of Solution

Necessary data is obtained from problem 1.

Write the empirical relation between mass and radius of star.

    R1R2=(M2M1)13        (I)

Here, R1,R2 are the radii of stars and M2,M1 are the masses.

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

Here, R is the radius.

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

    ρ=m43πR3=3m4πR3        (II)

Rewrite the above equation by substituting 1.0M0 for m and replace R by R1.

    ρ=3(1.0M0)4πR13        (III)

Here, M0 is the solar mass.

Rewrite equation (I) by substituting 1.4M0 for m and replace R by R2.

    ρ=3(1.4M0)4πR23        (IV)

Conclusion:

Case 1: Radius corresponds to 1.0M0.

Substitute 7000km for R1, 0.75M0 for M1 and 1.0M0 for M2 to find R2.

    7000kmR2=(1.0M00.75M0)13=1.10

Rewrite the expression for R2.

    R2=7000km1.10=6363km

Substitute 2×1030kg for M0 and 6363km for R1 in equation (III) to find ρ.

    ρ=3(1.0(2×1030kg))4π(6363km(103m1km))3=6×1030kg3.23×1021m3=1.85×109kg/m3

Case 2: Radius corresponds to 1.4M0.

Substitute 7000km for R1, 0.75M0 for M1 and 1.4M0 for M2 to find R2.

    7000kmR2=(1.4M00.75M0)13=1.23

Rewrite the expression for R2.

    R2=7000km1.23=5691km

Substitute 2×1030kg for M0 and 5691km for R2 in equation (IV) to find ρ.

    ρ=3(1.4(2×1030kg))4π(5691km(103m1km))3=8.4×1030kg2.31×1021m3=3.6×109kg/m3

Therefore, the density of white dwarfs of masses 1.0M0 and 1.4M0 are 1.85×109kg/m3 and 3.6×109kg/m3 respectively.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
A typical white dwarf has a mass of about 1.0MSunMSun and the radius of Earth (about 6400 kilometers). Calculate the average density of a white dwarf, in kilograms per cubic centimeter.
A 1.8 M neutron and a 0.7 M white dwarf have been found orbiting each other with a period of 28 minutes. What is their average separation? Convert your answer to units of the Suns radius, which is 0.0047 AU. (hint: Use the version of Keller's third law for the binary stars Ma + Mb = a^3/p^2 ; make sure you express quantities in unites of AU, solar masses, and years. NOTE: a year is 3.2 x 10^7 s)  ___________ solar radii
A visual binary has a parallax of 0.4 arcseconds, a maximum separation a = 6.0 arcseconds, and an orbital period P = 80 years. What is the total mass of the binary system in units of Mo, assuming a circular orbit?
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Stars and Galaxies (MindTap Course List)
Physics
ISBN:9781337399944
Author:Michael A. Seeds
Publisher:Cengage Learning
Text book image
Foundations of Astronomy (MindTap Course List)
Physics
ISBN:9781337399920
Author:Michael A. Seeds, Dana Backman
Publisher:Cengage Learning
Text book image
Astronomy
Physics
ISBN:9781938168284
Author:Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher:OpenStax
Text book image
Stars and Galaxies
Physics
ISBN:9781305120785
Author:Michael A. Seeds, Dana Backman
Publisher:Cengage Learning