LMC P3 is the most luminous gamma-ray binary discovered to date and the first detected outside of the Galaxy , with an orbital period of 10.301 d. We report on optical spectroscopic observations undertaken with the Southern African Large Telescope ( SALT ) using the High Resolution spectrograph ( HRS ) . We find the binary is slightly eccentric , e = 0.40 \pm 0.07 , and place the time of periastron at HJD 2457412.13 \pm 0.29 . Stellar model fitting finds an effective temperature of T _ { n } { eff } = 36351 \pm 53 K. The mass function , f = 0.0010 \pm 0.0004 M _ { \sun } , favours a neutron star compact object . The phases of superior and inferior conjunctions are 0.98 and 0.24 , respectively ( where phase 0 is at the Fermi -LAT maximum ) , close to the reported maxima in the GeV and TeV light curves .