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The very massive star system η Carinae exhibits regular 5.54 yr (2024 d) period disruptive events in wavebands ranging from the radio to X-ray. There is a growing consensus that these events likely stem from periastron passage of an (as yet) unseen companion in a highly eccentric orbit. This Letter presents 3D smoothed particle hydrodynamics (SPH) simulations of the orbital variation of the binary wind–wind collision, and applies these to modelling the X-ray light curve observed by the Rossi X-ray Timing Explorer ( RXTE). By providing a global 3D model of the phase variation of the density of the interacting winds, the simulations allow computation of the associated variation in X-ray absorption, presumed here to originate from near the apex of the wind–wind interaction cone. We find that the observed RXTE light curve can be readily fitted if the observer's line of sight is within this cone along the general direction of apastron. Specifically, the data are well fitted by an assumed inclination for the orbit's polar axis, which is thus consistent with orbital angular momentum being along the inferred polar axis of the Homunculus nebula. The fits also constrain the position angle φ that an orbital-plane projection makes with the apastron side of the semimajor axis, strongly excluding positions along or to the retrograde side of the axis, with the best-fitting position given by . Overall the results demonstrate the utility of a fully 3D dynamical model for constraining the geometric and physical properties of this complex colliding wind binary system. [ABSTRACT FROM AUTHOR]