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Homework Help: Planet density

  1. May 5, 2006 #1
    2 part question

    The density of a certain planet varies with radial distance as: D(r) = Do*[1-(a*r/Ro)], where Ro= 3.1623×106 m is the radius of the planet, Do = 3160 kg/m3 is its central density, and a = 0.160. Calculate the total mass of this planet.

    Calculate the weight of a one kilogram mass located on the surface of the planet.

    i tried integrating D(r) with and plugin in the radius of the planet but it doesn't work

    i know this question has somethin to do with integrating through shell method but i'm not sure how to do it

    can any1 help me?
     
  2. jcsd
  3. May 5, 2006 #2

    Hootenanny

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    Why doesn't it work?

    ~H
     
  4. May 5, 2006 #3

    nrqed

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    I am not sure what you integrated exactly but here are some thoughts:

    First, you must determined the total massof the planet, right? This is given by the integral of [itex] D(r) dV = D(r) r^2 sin(\theta) dr d\theta d\phi [/itex]. The angular integrals are trivial and give [itex] 4 \pi [/itex]. The radial integral is straightforward.

    Then, you must use this in the universal law of gravitation to determine the *weight* of 1 kg at the surface of the planet, [itex] F= {G m M \over r^2} [/itex].

    Patrick
     
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