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Astronomy: Speed at the edge of the galaxy

  1. Apr 7, 2015 #1
    1. The problem statement, all variables and given/known data
    The number of stars in the galaxy is N=10^12 and the radius of the galaxy is Rgalaxy = 20 kPc
    Let m be the average mass of a star in the galaxy.
    what is the velocity of a star at the edge of the galaxy (relative to the center of the galaxy)

    2. Relevant equations

    3. The attempt at a solution
    I had to make 2 assumptions here:
    1) uniform distribution of stars, ## σ=\frac{Nm}{\pi R^2}## .
    2) the star in question is at a distance of R+##\epsilon## from the center, and then take the limit of ##\epsilon ## goes to 1 light year (or any other distance that is way smaller then R).

    In order to solve the question I need to find the force, F, on the star and solve ##F=\frac{mv^2}{R}## for v.

    In order to find the force, one has to solve the integral ##F=Gmσ \int\limits_0^R\int_0^{2\pi}\frac{rdrd\theta}{(R+\epsilon)^2+r^2-2rRCos(\Theta)}##.
    And that is where i'm stuck.
    Ideas?

    Thanks,
    Raz.
     
  2. jcsd
  3. Apr 7, 2015 #2

    phyzguy

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  4. Apr 7, 2015 #3
    Hmm... Haven't thought of that. But what if the distribution is exponential (##e##)? will the shell theorem still hold?
    My intuition says that different distributions will result in different speeds.
     
  5. Apr 7, 2015 #4

    phyzguy

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    The shell theorem always holds as long as the distribution is spherically symmetric.
     
  6. Apr 7, 2015 #5
    Thanks. that simplifies things...
    any ideas as to why Mathematica won't solve that integral, though?
     
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