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Homework Help: Compute the mass of a black hole

  1. Sep 26, 2010 #1
    1. The problem statement, all variables and given/known data
    New observations of the stars orbiting the black hole at the Galactic Center (Sgr
    A*) have improved the measurements. Here are the latest results from Gillessen et
    al. (2009) for star S0-2: period P = 15:8 yr, semimajor axis a = 1025 AU, and
    eccentricity e = 0:880; and for star S0-16: P = 47:3 yr, a = 2130 AU, and e = 0:963.
    (a) Compute the mass (in units of solar masses) of Sgr A* implied by the new results.
    Do the two stars give a consistent answer?


    2. Relevant equations
    M=(4pie^2 a^3)/Gp^2


    3. The attempt at a solution
    For s0-2 i first converted AU to cm and years to seconds then 4pie^2(1.53e16)^3 /(6.6743e-8)(498599430)^2
    and got 8.52e16 grams then 4284399 Mo is this correct the formula i used to find mass of the black hole?
     
  2. jcsd
  3. Sep 26, 2010 #2

    fzero

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    Science Advisor
    Homework Helper
    Gold Member

    I think you're missing a factor of pi, double check the formula

    M=(4 pi^2 e^2 a^3)/Gp^2

    Something's fishy because 4 * 106 [tex]M_\odot[/tex] is the right order of magnitude, but 8.52e16 grams is 17 orders of magnitude smaller than a solar mass.

    My computation is 3.34 106 [tex]M_\odot[/tex]. The WA expression is

    http://www.wolframalpha.com/input/?i=4+%28pi^2%29+%28.880%29^2+%281025+*+149597870.700+*10^3%29^3+%2F%28+%286.67428+*+10^%28-11%29%29+%2815.8+*31556952++%29^2+%281.988+*+10^30++%29

    if you want to compare.
     
  4. Sep 27, 2010 #3
    ok thanks ill check again later
     
  5. Sep 27, 2010 #4
    formula is correct what i have well that is to find the mass of the interior orbit of the star also its 8.52e39 idk why i always write down something wrong when i do physics lol
     
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