Orbital Parameters for the $250 M_\odot$ Eta Carinae Binary System

We show that recent observations of He I and N II lines of $\eta$ Carinae may provide support for an orbital orientation where the secondary star is closest to us at periastron passages. This conclusion is valid both for the commonly assumed masses of the two stars, and for the higher stellar masses model where the very massive evolved primary star mass is $M_1=170 M_\odot$ and its hot secondary star mass is $M_2 = 80 M_\odot$. The later model better explains the change in the orbital period assuming that the ninetieth century Great Eruption was powered by accretion onto the secondary star. Adopting the commonly used high eccentricity $e \simeq 0.9$ and inclination $i=41^\circ$, we obtain a good fit to newly released Doppler shift observations of He I emission and absorption lines assuming they are emitted and absorbed in the acceleration zone of the secondary stellar wind. Our model in which the secondary star is in the foreground at periastron is opposite to the view presented recently in the literature.