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Binary Star Analysis

  1. Oct 5, 2009 #1
    1. The problem statement, all variables and given/known data

    We observe a binary system in which the two stars are 1 and 2 arc sec, respectively, from the center of mass. The system is 10pc from us. The period is 33 yr. What are the masses of the two stars, assuming that i=90 degrees?

    2. Relevant equations



    3. The attempt at a solution

    I want to derive an equation for the masses based on what we know, so here goes.

    Based on a simple sketch of the system, we know mara = mbrb.

    We can label the distance between the two stars r = ra + rb

    re-arranging and substituting yields mara = mb(r-ra)

    Then ra = mbr/ma + mb = mbr/M where M = ma + mb

    Now, force of Gravity must equal centripetal force in this binary system, so Gmamb/r2 = mava2/ra

    since v = d/t, va = 2[tex]\pi[/tex]ra/T where T is the period.

    re-arranging once again yields ra = GmbT2/4r2[tex]\pi[/tex]2

    subbing in from our equation for ra yields M = 4r3[tex]\pi[/tex]2/GT2

    Now we have an equation for the total mass of the system, but I need individual masses.

    Can anyone confirm my equation? Am I on the right track? Where does the inclination of the system come in? Is it just for an assumption? Likewise, where does the system distance d away from us come into play? Am I missing something here? Any help would be appreciated thanks.
     
  2. jcsd
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