The orbital motion of a neutron star about its optical companion presents a window through which to study the orbital parameters of that binary system. This has been used extensively in the Milky Way to calculate these parameters for several high-mass X-ray binaries. Using several years of RXTE PCA data, we derive the orbital parameters of four Be/X-ray binary systems in the SMC, increasing the number of systems with orbital solutions by a factor of three. We find one new orbital period, confirm a second and discuss the parameters with comparison to the Galactic systems. Despite the low metallicity in the SMC, these binary systems sit amongst the Galactic distribution of orbital periods and eccentricities, suggesting that metallicity may not play an important role in the evolution of high-mass X-ray binary systems. A plot of orbital period against eccentricity shows that the supergiant, Be and low eccentricity OB transient systems occupy separate regions of the parameter space; akin to the separated regions on the Corbet diagram. Using a Spearmans rank correlation test, we also find a possible correlation between the two parameters. The mass functions, inclinations and orbital semimajor axes are derived for the SMC systems based on the binary parameters and the spectral classification of the optical counterpart. As a by-product of our work, we present a catalogue of the orbital parameters for every high-mass X-ray binary in the Galaxy and Magellanic Clouds for which they are known.
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