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# Partial Solution for Mass of Cyg X-1

Working carefully, the mass function can be solved to find the mass of the black hole in Cygnus X-1.

First, re-arrange the mass function

to

Then expand the quadratic and rearrange into a cubic for m2 in the form x3 + ax2 + bx + c = 0:

We can now identify the coefficients as

We use the following values for the measured quantities, and convert to mks units:

• P = 5.6 days = 4.838 x 105 seconds
• v1 = 75 km/s = 7.5 x 104 m/s
• i = 30 degrees
• m1 = 30 solar masses = 30 x (2.0 x 1030) = 60 x 1030 kg

Noting that

the values for the coefficients are

We're now ready to compute the quantities necessary to find the real cubic root (see Solving a Cubic Equation).

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