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24 September, 17:06

Calculate the average density in kilograms [kg] per cubic meter [m3] for a White Dwarf with a mass of

1 solar mass and the size of planet Earth. Be sure to use the correct units. (b) Calculate your own weight on the surface of the white dwarf star.

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  1. 24 September, 17:16
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    (a) 2 * 10^9 kg/m^3; (b) roughly the mass of the Statue of Liberty.

    Step-by-step explanation:

    (a) Density of white dwarf:

    D = m/V

    dа ta:

    1 solar mass = 2 * 10^30 kg

    1 Earth radius = 6.371 * 10^6 m

    Calculations:

    V = (4/3) πr^3 = (4/3) π * (6.371 * 10^6 m) ^3 = 1.083 * 10^21 m^3

    D = 2 * 10^30 kg/1.083 * 10^21 m^3 = 2 * 10^9 kg/m^3

    2. Weight on a white dwarf

    The formula for weight is

    w = kMm/r^2

    where

    k = a proportionality constant

    M = mass of planet

    m = your mass

    w (on dwarf) / w (on Earth) = [kM (dwarf) m/r^2] / [kM (Earth) m/r^2

    k, m, and r are the same on both planets, so

    w (on dwarf) / w (on Earth) = M (dwarf) / M (Earth)

    w (on dwarf) = w (on Earth) * [M (dwarf) / M (Earth) ]

    dа ta:

    M (Earth) = 6.0 * 10^24 kg

    Calculation:

    w (on dwarf) = w (on Earth) * (2 * 10^30 kg / 6.0 * 10^24 kg)

    = 3.3 * 10^5 * w (on Earth)

    Thus, if your weight on Earth is 60 kg, your weight on the white dwarf will be

    3.3 * 10^5 * 60 kg = 2 * 10^7 kg

    That's roughly as heavy as the Statue of Liberty is on Earth.
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