The question: The stars in a binary system are observed to have an orbital perio

Question

The question:

The stars in a binary system are observed to have an orbital period of 16 yr and a separation of 8 AU.

(a) What is the sum of the masses of the two stars, in M?

(b) If the stars have identical apparent magnitudes and spectral types, what are their individual masses? Explain.

My thoughts:

The formula we use is 42 / PA2 = G(MA + MB) / a3

So I have plugged in 42 / 162 = (6.67 x 10-11 m3/(kg s2))(MA + MB) / 83

However, I am confused about units when you solve for the sum of the masses. And then I don't have anything yet for (b).

Explanation / Answer

To determine the total mass of the stars we use Kepler's third law ie

(mass 1 + mass 2) = (separation distance)3/(orbital period)2   

thus MA + MB = 83/ 162  = 2 solar masses or 2 M

2. if the stars have same apparent magniturde and same spectral type then they are of similar brightness and the center of mass is at the center. Thus the individual mass are equal ie each of them will have 1 Mo mass.

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