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White dwarf gravity homework

  1. May 9, 2010 #1
    1. The problem statement, all variables and given/known data

    After a star like the Sun has exhausted most of the hydrogen in its core it expands and cools to form a red giant. Eventually, when it has exhausted all its nuclear fuel, it sheds its outer layers and contracts and becomes a white dwarf of similar size to the Earth as shown below. Note that the mass of the sun is 2 × 1030 kg, the radius of the Earth is 6,380 km and Newton's gravitational constant G is 6.67 × 10–11 N m2 kg–2.

    Consider a white dwarf of 0.650 solar mass and 0.500 earth radii.

    (a) Calculate the average density of the white dwarf

    (b) Calculate the free-fall acceleration on the surface of the white dwarf

    3. The attempt at a solution

    (a) I beleive the average density is given by mass/volume

    mass is [tex]0.650 \times (2 \times 10^{30})=1.3 \times 10^{30}[/tex]

    volume is [tex]\frac{4}{3}\pi (0.5 \times 6380)^3 = 1.35 \times 10^{11}[/tex]

    m/v=9.6 × 1018

    But the correct answer is 9560000000 kg/m³. I appreciate it if anyone could show me what's wrong with my working :confused:
  2. jcsd
  3. May 9, 2010 #2


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    Science Advisor

    Re: Gravity

    You used the Earth radius in km, so you calculated the density in kg/km^3, not kg/m^3.
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