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abstract: 'We study the usage of the X-ray light curve, column density toward the hard X-ray source, and emission measure (density square times volume), of the massive binary system $\eta$ Carinae to determine the orientation of its semi-major axis. The source of the hard X-ray emission is the shocked secondary wind. We argue that, by itself, the observed X-ray flux cannot teach us much about the orientation of the semi-major axis. Minor adjustment of some unknown parameters of the binary system allows to fit the X-ray light curve with almost any inclination angle and orientation. The column density and X-ray emission measure, on the other hand, impose strong constrains on the orientation. We improve our previous calculations and show that the column density is more compatible with an orientation where for most of the time the secondary$-$the hotter, less massive star$-$is behind the primary star. The secondary comes closer to the observer only for a short time near periastron passage. The ten-week X-ray deep minimum, which results from a large decrease in the emission measure, implies that the regular secondary wind is substantially suppressed during that period. This suppression is most likely resulted by accretion of mass from the 