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Homework Help: Two body orbital system question

  1. Jan 25, 2007 #1
    1. The problem statement, all variables and given/known data
    The observed period of the binary system Cygnus X-1, presumed to be a bright star and a black hole, is equal to 5.6 days. If the mass of the visable (the star) is 20*Mass of the Sun, and the black hole has a mass 16*Mass of the Sun, show taht the semimajor axis of the orbit of the black hole relative to the visable star is roughly 1/5 the distance from the Earth to the sun.


    2. Relevant equations
    Period (using AU) relationship to semimajor axis of a system

    T = [m,sub 1 + m, sub 2]^(-1/2)*a^3/2, where 'a' is the semi-major axis and both values of 'm' are given in units of mass of the sun.

    Reduced mass: (m,sub 1)*(m,sub 2)/((m, sub 1)+(m, sub 2))

    Postion vector of particle 1 relative to particle 2

    R= (r(from center of mass), sub 1)*(1+ ratio of masses)

    3. The attempt at a solution

    I am not entirly sure where to go with this, however, I did calculate some values so far:

    u= 8.888*Mass of Sun
    a= .020384 AU, note that the value of this semi-major axis is for the binary system as a whole, not relative to either one of the points.

    Any ideas where to go with all of this?

    (I am still working at it, but a hint would be nice)
     
  2. jcsd
  3. Jan 26, 2007 #2

    Kurdt

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    Binary stars obey Kepler's laws.
     
  4. Jan 27, 2007 #3
    I will be retracting my question....

    After stareing at the question for a good 3 hours, my brain kicked in and noticed that I had done a simple math mistake (seriously, I moved the decimal place over 1 too many). I guess thats what I get when I do homework late at night.

    sorry of the stupid question.
     
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