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    susus's Avatar
    susus Posts: 138, Reputation: 2
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    #1

    Dec 16, 2010, 03:09 PM
    Density of Planet
    Density of Planet
    A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is 1.65 hours. What is density of the planet? Assume that the planet has a uniform density.
    (in kg/m^3)
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #2

    Dec 17, 2010, 06:58 AM

    Susus:

    Here's a hint to get you started: use good old F=ma, where F is the force of gravity between the planet and the satellite, and a is the acceleration of a mass in circular motion:



    Recall that density = mass/volume, and the volume of a sphere is



    Can you take it from here?
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    susus Posts: 138, Reputation: 2
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    #3

    Dec 17, 2010, 08:10 AM
    Comment on ebaines's post
    Thanks I appreciate what you are doing.. I just too much fool for understanding what I have to do now :)
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #4

    Dec 17, 2010, 08:17 AM

    Susus - please do not mark posts as unhelpful, unless it is actually in error.

    The little m's cancel out- so it does not matter what the satellite's mass is.

    You don't really care out big M, you only care about big M divided by R^3, because you are trying to determine the density of the planet, not its mass. If you manipulate the equations I gave you previously you can find a formula for M/R^3.
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    susus Posts: 138, Reputation: 2
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    #5

    Dec 17, 2010, 11:41 AM
    Comment on ebaines's post
    4*pi^2*r/P^2 = G*m/r^2
    4*pi^2*r^3/(G*P^2) = m

    Now use the definition of density as mass divided by volume.
    density = d = m/v = m/[(4/3)*pi*r^3]
    d = 3*pi/(G*P^2)
    d= 4000 ;) thanks..

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