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Find mass of black hole in center of galaxy given eccentricity+

  1. Nov 14, 2013 #1
    1. The problem statement, all variables and given/known data
    Astronomers believe that there is a massive black hole at the center of the Milky Way galaxy. What evidence is there for that?
    A group of astronomers have observed a star "S2" in a 15.2-year orbit around the center of the galaxy. They measured the period of revolution T = 15.2 years, the eccentricity of the elliptical orbit ε = 0.87, and the semimajor axis of the orbit a = 4.62 mpc. [The unit: mpc = milli-parsec = 0.001 parsec.]

    (A) Calculate the mass of the compact object about which S2 is revolving.


    2. Relevant equations

    sm=semi-minor axis
    sM=semi-major axis

    Eccentricity=[itex]\sqrt{1-(sm/sM)^2}[/itex]

    Mass=[itex]\frac{4π^2r^3}{GT^2}[/itex]

    3. The attempt at a solution

    If I plug in my values to the eccentricity equation and solve for the semi-minor axis I get 7.031*1010 km. With that I can find r which is the average of the semi-major and semi-minor axis:

    r=1.06455*1011 km

    Plugging in my knows to the mass equation I get 3.11*10^36 kilograms which is incorrect. What am I doing wrong?

    Thank you!
     
  2. jcsd
  3. Nov 14, 2013 #2
    Apparently the way I figured out r was incorrect. It should be 1.426 *10^11 km. My answer is now correct!
     
  4. Nov 15, 2013 #3
    Why does the correct mass imply its a black hole? Density from known size?
     
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