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Binary system calculations.

  1. Mar 1, 2013 #1
    1. The problem statement, all variables and given/known data

    See attachment.

    2. Relevant equations



    3. The attempt at a solution

    Ok, so for Qd) my attempt was:
    d = vt = 75x10^3 * (2*2.8*86400*365) = 1.32x10^13 m, (circumference of orbit)
    because the star periodically shifts from red to blue shifted frequencies every 2.8 years so I guess the full orbit to be 2*2.8 years.

    Then 2∏r = 1.32x10^13, -> r = 2.1x10^12m?

    Now for Qe) All I could figure is that the relevant eqn is (2∏/T)2 = G*(ma + mb)/(ra + rb)3

    But with the information I have, 1stly from the assumpt that ma >> mb I can say that:

    (2∏/T)2 = G*(ma)/(ra + rb)3 right?

    Considering X-major is ma. Now I can rearrange for the mass but I still have missing information, I just have radius of the orbit for x-minor, but not x-major. I even have the orbital period. Just not ra.

    Can someone give me a helping hand here, how do I find ra? Also have I done everything thus far correctly?
     

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  2. jcsd
  3. Mar 1, 2013 #2

    TSny

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    Your work looks correct to me.

    Under the assumption that ma >> mb, you have ra << rb. So, I think you can safely neglect ra relative to rb.
     
  4. Mar 1, 2013 #3
    Lol that does make sense, silly me, thanks. Hopefully that's correct. :)
     
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