Binary Stars On-Line Worksheet Solutions

  1. Two stars of a binary system are found to be 6 AU apart and have an orbital period of 3 years. If Star A is twice as massive as Star B, then what are the masses of Star A and B?

    2. Ma = 2Mb
    Ma + Mb = (6^3)/(3^2) = 24
    2Mb + Mb = 24
    3Mb = 24
    Mb = 8 solar masses
    Ma = 2*8 = 16 solar masses
  2. The radial velocities of two stars of a binary system are 40 km/s and 120 km/s. If the two stars are 4 AU apart and have an orbital period of 2 years, what are the masses of the two stars?

    3. Ma = 3Mb
    Ma + Mb = (4^3)/(2^2) = 16
    3Mb + Mb = 16
    4Mb = 16
    Mb = 4 solar masses
    Ma = 3*4 = 12 solar masses
  3. Given the following radial velocity curve, find the masses of the two stars.

    4. P = 1.5 years
    a = (Vrel*P)/(10*pi)
    a = (6*1.5)/(10*pi) = 0.2865 AU
    5Ma = Mb
    Ma + Mb = (0.2865^3)/(1.5^2) = 0.01045
    Ma + 5Ma = 0.01045
    6Ma = 0.01045
    Ma = 0.00174 solar masses
    Mb = 0.00174*5 = 0.00871 solar masses

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