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Gravitational Field Strength

  1. Nov 17, 2014 #1
    1. The problem statement, all variables and given/known data
    70d030c2091bcb8514dcab3cf06abd76.png
    2. Relevant equations
    g = GM / r^2, where g is the gravitational field strength, G is the gravitational constant, M is the mass of the attracting body, r is the radius of the attracting body.
    p = M / v, where p is density and v is the volume.
    Vs = 4/3 * pi * r^3, where Vs is the volume of a sphere, r is the radius of the sphere.
    3. The attempt at a solution
    g = M / r^2 (as G is constant)
    rearraging p = M / v, M = pv
    pv / r^2 = g
    (p * 4/3 * pi * r^3) / r^2 = g (assuming the planet is perfectly spherical)
    p * 4/3 * pi * r = g
    density of Q is 1/2 that of P, radius is 2x that of P.
    1/2 * 4/3 * pi * 2 = 4/3 * pi
    therefore, 4/3 * pi * 13.4 = 56.13Nkg^-1, however the answer is 13.4Nkg^-1? Can someone see where I've gone wrong?
     
  2. jcsd
  3. Nov 17, 2014 #2

    Simon Bridge

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    4/3 is a constant, and so is pi... just like G.
     
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