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Gravitational Fields and Density.

  1. Jan 29, 2012 #1
    1. The problem statement, all variables and given/known data
    If a planet has a diameter of 6*103km and, one of it's satellites is in a circular orbit of radius 9.0*103km with a time period of 8.0 hours.
    What is the density of the planet?


    2. Relevant equations
    ρ=m/v - density v=4/3 *∏*r2
    GMm/r2 = mw2r


    3. The attempt at a solution
    Firstly convert the Km into M,
    Diameter of planet = 6*106 → 3*103
    Radius of Satellite = 9.3*106
    Time period = 28800s

    Where G = 6.7*10-11




    Therefore I used

    GMm/r2 = mw2r


    And subbing in the values;


    (6.7*10-11)Mm/(9.3*106+3*106)=m.288002(9.3*106+3*106)


    So I cancelled out the little m and rearranged the equation for M,


    Giving M an answer as 1.87*1033

    I then subbed it into the equation for Density,


    1.87*1033/4/3*∏(3*106) which gives me an answer of 4.96*1019,

    However the given answer is 4.6*103, Any guidance would be appreciated ;D.
     
  2. jcsd
  3. Jan 29, 2012 #2

    Doc Al

    User Avatar

    Staff: Mentor

    OK.
    (1) Why did you add the radii?
    (2) ω is the angular frequency, not the period.
    (3) On the left side, that radius must be squared.
     
  4. Jan 29, 2012 #3
    volume is (4/3)πr^3 you have written (4/3)πr^2 and you have not cubed the value in your calculation
    Also ω = 2π/T and you have used T as pointed out by Doc Al
     
    Last edited: Jan 29, 2012
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