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Homework Help: Find the radius of the star

  1. Mar 16, 2016 #1
    1. The problem statement, all variables and given/known data

    P=Kρ^2 is a solution to the equation of the combination of the Hydrostatic Support equation and the mass continuity equation. Find the radius of the star.

    2. Relevant equations
    ρ(r) = (A / r) sin (root( 2πG/K) r)

    3. The attempt at a solution
    The first part of this was to prove first it was a solution which I have done fairly easily, however the last part about the radius has left me confused.
    I figured the density at the surface (r=R) was equal to zero therefore:

    0=(A / r) sin (root( 2πG/K) r)

    And for the non trivial solution:

    sin (root( 2πG/K) r)=0

    so root(2πG/K) r)=nπ (for n integer)

    However this would give a range of radii for the star which doesn't seem right.
    Can you see what I've done wrong, thanks?
  2. jcsd
  3. Mar 16, 2016 #2


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    Staff: Mentor

    You get a position of zero density at root(2πG/K) r)=π. Do you expect matter outside this region? What would support it?
    Is ρ(r) = (A / r) sin (root( 2πG/K) r) even valid outside that region?
  4. Mar 16, 2016 #3
    What happens to the other solutions? Surely root(2πG/K) r)=2π etc is still valid? and the density should only hold for the star up to radius R, and no there wouldn't be matter outside the region.
  5. Mar 18, 2016 #4


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    Staff: Mentor

    It is a mathematical solution, but the density profile is not described by a sine in that area any more. The density is zero after the function hits its first zero.
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