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Thread: Poissons equation, gravitational field.

  1. #1
    Junior Member
    Jan 2010

    Poissons equation, gravitational field.

    A spherical planet of radius (3/2)R is composed of two solid regions of different, but constant, mass distributions. The core is located at r<=R and has a uniform density p0 and total mass M. The outer region has mass distribution p1 and total mass (19/2)/M

    Obtain a general expression for the gravitational field g(r), using poissons equation, at a general point r from the planets centre.

    Also determine the gravitational field experienced by a satelite orbiting the planet at a general distance r>(3/2)R, express the answer in terms of the known mass of the planet core.

    Any help greatly appreciated.
    Last edited by featherbox; November 21st 2010 at 11:39 AM. Reason: Title.
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  2. #2
    Super Member Rebesques's Avatar
    Jul 2005
    My house.
    The potential g satisfies \Delta g=0, and so g=g(r)=c(r)/r^2, \ 0<r\leq (3/2)R for a radial function c(r). Easily, c=GM(r), G being the constant of universal attraction and M(r) being the total mass up to the radius r. Now, graph g for r, considering the cases r\leq R and r>R.

    And for the last part, use the fact that M=(4/3)\pi p_0R^3.
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