The results of a coordinated space-based photometric and ground-based spectroscopic observing campaign on the enigmatic γ-ray binary LS 5039 are reported. 16 d of observations from the MOST satellite have been combined with high-resolution optical echelle spectroscopy from the 2.3-m ANU Telescope in Siding Spring, Australia. These observat ions were used to measure the orbital parameters of the binary and to study the properties of stellar wind from the O primary. We found that any broad-band optical photometric variability at the orbital period is below the 2 mmag level, supporting the scenario that the orbital eccentricity of the system is near the 0.24 ± 0.08 value implied by our spectroscopy, which is lower than values previously obtained by other workers. The low amplitude optical variability also implies the component masses are at the higher end of estimates based on the primary's O6.5V((f)) spectral type with a primary mass of ∼26 M⊙ and a mass for the compact star of at least 1.8 M⊙. The mass-loss rate from the O primary was determined to be 3.7 to 4.8 × 10−7 M⊙ yr−1
