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Calculating Binary Star Masses

  1. Mar 15, 2014 #1
    Hello,

    I wasn't sure whether I should post this is the homework section since it's technically a textbook problem, but I figured I'd get better responses here. The problem is as follows:

    Sirius is a visual binary with a period of 49.94 years. Its measured parallax is .37931"## \pm ##.00158", and the angular extent of the semimajor axis of the reduced mass is 7.61". The ratio of the distances of Sirius A and B to the center of mass is ## a_A / a_B = .466 ##. Find the masses of the two stars, assuming that the motion is in the plane of the sky.

    First, you can use the ratio to get ## m_A / m_B = 1/.466 = 2.146##. I'm pretty sure I next have to use the 7.61", but I don't know how. After that, I would have all the unknowns in Kepler's third except the masses, so I could solve the system. So how do I get the semimajor axis of the smaller star?
     
  2. jcsd
  3. Mar 15, 2014 #2

    mfb

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    Textbook questions belong to the homework section. I moved it with a redirect in the original forum.

    Okay.
    This is related to the true semi-major axis of the system, if you know the distance. There is another parameter given that allows to calculate the distance.

    Find the semi-major axis of the reduced mass first.
     
  4. Mar 15, 2014 #3
    Using the parallactic angle yields ## d [pc] = 1/p" = 1/.37921 = 2.6363 pc##. Now what?

    By the way, the "reduced mass" just refers to the star with lower mass, right?
     
    Last edited: Mar 15, 2014
  5. Mar 15, 2014 #4

    mfb

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    You got an angle (as seen from earth) and a distance...

    No.
     
  6. Mar 15, 2014 #5
    Yeah, my bad... 7.61" = a / 2.636 pc ---> a = 3.00 E12 after converting 7.61" to rad and 2.636 to m. So is this the same a that goes in kepler's third equation? Or do I have to go back and use the semimajor axis ratio that I was given
     
  7. Mar 15, 2014 #6

    mfb

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    Should be. Check the link to the reduced mass.
    There was no given semi-major axis, you had to calculate it.
     
  8. Mar 16, 2014 #7
    Got it. Thank you very much.
     
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