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Calculate mass from acceleration and radius

  1. Feb 27, 2015 #1
    1. The problem statement, all variables and given/known data
    How do you calculate the mass of an object just from the acceleration from gravity and the radius?

    2. Relevant equations
    My thoughts were F=GM/r2, then once you find F, you can calculate mass by M=F/A
    G= 6.67 x 10^11
    r = 12
    Acceleration = 2 m/s^2
    3. The attempt at a solution
    (6.67 x 10 ^-11) / 12^2 = 4.63 * 10 ^-13
    M = (4.63 * 10 ^-13)/(2 m/s^2) = 2.31 ^-13 kg
  2. jcsd
  3. Feb 27, 2015 #2


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    Hello 10 m/s, and welcome to PF :smile:

    Acceleration from gravity due to another object happens to be independent of mass. You are missing an m in your ##F = {G Mm\over r^2}## that, with ## F= ma## goes over in ##a = {G M\over r^2}##.

    [edit] compare gravitational acceleration at the surface of the earth:
    G = 6.67E-11 N/(m/kg)2
    M = 5.97E+24 kg
    r = 6.37E+06 m
    g = GM/r2 = 9.82E+00 m/s2
    Last edited: Feb 27, 2015
  4. Feb 27, 2015 #3
    I'm sorry, I still don't understand! What is 10 m/s?
    I didn't think my equations were right, but I really don't know what to try next. I don't know the mass which is really hanging me up.
  5. Feb 27, 2015 #4


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    10 m/s is 36 km/h, just a corny attempt at humor.

    You don't know the mass in what kind of situation ? Could you be a bit more elaborate in the problem statement ?

    Apparently you have two "things", 12 m apart, and "something" accelerates with 2 m/s2 ?
  6. Feb 27, 2015 #5
    Ha, that is funny!

    I'm trying to calculate the mass of an imaginary planet. All I have given to me is the radius (12m) and the acceleration due to gravity on that surface (which is 2 m/s2)
  7. Feb 27, 2015 #6


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    Well, then you're in business! So the problem statement is:

    What is the mass of a planet with radius 12 m (!?), given that the acceleration due to gravity on the surface of that planet is 2 m/s2.

    And you have the equation. Is it clear that GM/r2 is not a force but an acceleration ?

    It's a very dense planet. Just for the fun of it, calculate the density in kg/m2 assuming its a sphere...

    tip: work in symbols (a, G, M, r) as long as you can, until you have a final expression (a = ...) . Then check dimensions and then fill in numbers.
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