We present the open source Python code BinaryStarSolver that solves for the orbital elements of a spectroscopic binary system. Given a time-series of radial velocity measurements, six orbital parameters are determined: the long-term mean, or systemic, radial velocity, the velocity amplitude, the argument of periastron, the eccentricity, the epoch of periastron, and the orbital period referred to by ${{gamma, K, omega, e, T_0, P}}$ respectively. Also returned to the user is the projected length of the semi-major axis, $a_{1}sin(i)$, and the mass function, $f(M)$. The determination of spectroscopic orbits and masses is an example of another important area of astrophysics, once the domain of professional astronomers, to which amateurs can now make significant contributions. This code, available from GitHub, is provided in support of that work, and should be of general use to the amateur and professional astronomical community.
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