We assume that the helium-I lines emitted by the massive binary system \eta Carinae are formed in the acceleration zone of the less-massive secondary star .
We calculate the Doppler shift of the lines as a function of orbital phase and of several parameters of the binary system .
We find that a good fit is obtained if the helium lines are formed in the region where the secondary wind speed is v _ { zone } = 430 ~ { } km~ { } s ^ { -1 } .
The acceptable binary eccentricity is in the range 0.90 \lesssim e \lesssim 0.95 , and the inclination angle ( the angle between a line perpendicular to the orbital plane and the line of sight ) is in the range 40 ^ { \circ } \lesssim i \lesssim 55 ^ { \circ } .
Lower values of e require higher values of i , and vice versa .
The binary system is oriented such that the secondary star is in our direction ( closer to us ) during periastron passage .
The orbital motion can account in part to the Doppler shift of the peak in X-ray emission .