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Homework Help: Mass of invisible binary companion

  1. Dec 2, 2009 #1
    Hey guys, got this question that's been giving me some trouble.

    The spectral lines in a low-mass main sequence star are observed to show sinusoidal velocity variations with an amplitude of 500km/s and a period of ten hours. Calculate the lower mass limit of the unseen binary companion.

    Here's how far i've managed to get:

    I started with newton's adaptation of kepler's third law

    1. M1+M2=(4(PI)2a3)/(GP2)

    where 'a' is the seperation of the two masses

    2. a=r1+r2

    I don't know the radius of either orbit but i do know the velocity of one and the period.

    3. V1=(2(PI)r1)/P
    4. V2=(2(PI)r2)/P

    I then rearranged 3 and 4 to get r in terms of P and V and substituted into 2 to get

    5. a=(P/2(PI))*(V1+V2)

    Then substituting 5 into 1 gives

    6. M1+M2=(P/2(PI)G)*(V1+V2)3

    I now want to get rid of the V2.


    So i make V2= V1*(M1/M2)

    Substitute this into 6 and with a bit of fiddling i get

    7. M23/(M1+M2)2=(PV13)/(2(PI)G)

    I've been told the visible star is a 'low-mass main sequence star' so i can make a rough estimate of M1. Now my only unknown is M2...
    However! I've been playing with 7 for ages and simply cannot isolate M2 :uhh:

    So i've either messed up somewhere along the way to 7 or my algebra is failing me.

    Any suggestions or help would be great guys!

  2. jcsd
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