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Homework Help: Gravitational Acceleration given mass and radius

  1. Apr 9, 2014 #1
    1. The problem statement, all variables and given/known data
    If you lived on a planet with five times the mass of Earth and twice the radius, what would be the gravitational acceleration at the surface of your planet?

    2. Relevant equations
    Mass of Earth = 6.00*10^24 kg
    Radius of Earth = 6.38*10^3 km

    3. The attempt at a solution
    So, when I started out doing this, I quickly plugged in earth's radius (in m), mass (in kg) and the gravitational constant just to make sure it came out at 9.8 because I know that's what Earth's gravitational acceleration from the surface is, but none of the answer I get are even close. I can't even get this right and I still have to do the actual problem (using 5x the mass and 2x the radius).
  2. jcsd
  3. Apr 9, 2014 #2


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    Instead of making us guess where you went wrong, how about posting your work?
  4. Apr 9, 2014 #3


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    it does work. we did it the other day sitting around.
    Mass of Earth ≈ 5.97*10^24 kg
    Radius of Earth ≈ 6.38*10^3 KM = 6.38*10^6 m
    G≈ 6.67 × 10^-11

    [itex]\frac{M_{earth}}{r_{earth}^2}G ≈ \frac{5.97*10^{24}}{6.38*10^{12}}*6.67*10^{-11}[/itex]
    [itex]=\frac{5.97*6.67*10}{6.38} ≈9.805[/itex]
  5. Apr 9, 2014 #4


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    It's worth persevering to get that right, but you don't need it for this question.
    You can solve it just by taking g = 9.8m/s2 for Earth and adjusting it. What effect will 5 times the mass have on that? What effect will twice the radius have?
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