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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