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Universal gravitational problem

  1. Jan 8, 2012 #1
    1. The problem statement, all variables and given/known data

    Planet X has a mass 8 times that of Earth and the acceleration due to gravity at its surface is 19.6 m/s2. The radius of the planet x compared to earth is:

    The answer is 2times bigger

    2. Relevant equations

    Fg = gm1m2 / r^2

    3. The attempt at a solution

    Is earths gravity 9.8 and the gravity of planet x is 19.6.
    Where would I put these values in ?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 8, 2012 #2

    jedishrfu

    Staff: Mentor

    Check your relevant equation what do each of the variables and constants mean?

    In particular, f=Gmm/r^2 where G is what?
     
  4. Jan 8, 2012 #3
    Isn't g universal gravitational constant which is 6.67 x 10^-11?
    Or is this where the 19.6m/s^2 should go into?
     
  5. Jan 8, 2012 #4
    G*m_1 is the acceleration due to gravity for a body
     
  6. Jan 8, 2012 #5

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Denote the universal gravitational constant by G. People use the notation g for the gravitational acceleration on the surface of the Earth: g≈9.81 m/s2

    According to the law of universal gravitation, the force of gravity on an object of mass m is F=GmM/R2 at the surface of the Earth. M is the mass of Earth (5.97 x 10^24 kg) and R is the Radius of Earth (6.37 x 10^6 m).
    The gravitational acceleration is F/m=g=GM/R2. Plug in the data: it is 9.81 m/s2

    19.6 m/s2 is the gravitational acceleration at the surface on an other planet. How does it related to the radius and mass of the planet?

    ehild
     
  7. Jan 9, 2012 #6
    So f=mg=GmM/r^2
    Then say the mass of earth is 2. Planet x is 8 times of the earth, so then 16.
    Earth has gravity 9.8 and planet x has gravity 19.6.
    Then the equation is really this: g=m/r^2
    So earth is square root ( 2/9.8)=0.45
    planet x is square root (16/19.6) = 0.903
    Oh, okay yeah and it's twice larger.
    Okay I get it,
    Thank you so much.^_^
     
  8. Jan 10, 2012 #7

    ehild

    User Avatar
    Homework Helper
    Gold Member

    You are welcome :smile:

    ehild
     
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