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A simple astrophysics rough estimate exercise

  1. May 24, 2015 #1
    1. The problem statement, all variables and given/known data
    1.png

    2. Relevant equations
    (mv2)/r=(GMm)/r2 --------(1)
    r≈8kpc≈2.47×1020m
    v≈220kms-1

    3. The attempt at a solution

    Using equation (1) and solving for M I got

    M=(v2r)/G=(4.84×10102.47×1020)/6.67×10-11

    M=1.79×1041 kg

    does this answer seem correct?

    P.S. This is not a homework assignment, it's an exercise from an introductory book I'm reading.
     
  2. jcsd
  3. May 24, 2015 #2

    gneill

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    Staff: Mentor

    Your result looks fine for the given estimation method.
     
  4. May 24, 2015 #3
    Thanks for the quick response

    Would the given estimation method be appropriate?
    Moreover, would you have any other Newtonian estimation methods to suggest?
     
  5. May 24, 2015 #4

    gneill

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    Staff: Mentor

    The method is a reasonable first approximation. It'll fall short by at least an order of magnitude though; Consider the actual shape of the galaxy as opposed to the assumed shape for the method. Also consider that the Sun does not orbit outside the entire galaxy, but rather within it: The galaxy is about 30 kpc across.

    Other methods of estimation would involve much more effort and more complicated math. For example, the actual shape is more disk-like than spherical, and does not have a uniform density, making estimating the mass of the outlying portions tricky.

    A better estimate might had by using the globular clusters which orbit outside the Milky Way as the "test particles", rather than the Sun.
     
  6. May 24, 2015 #5
    Thank you
     
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