We present 3D hydrodynamical simulations of ram pressure stripping of massive disc galaxies in clusters. Studies of galaxies that move face-on have predicted that in such a geometry the galaxy can lose a substantial amount of its interstellar medium. But only a small fraction of galaxies is moving face-on. Therefore, in this work we focus on a systematic study of the effect of the inclination angle between the direction of motion and the galaxy's rotation axis. In agreement with some previous works, we find that the inclination angle does not play a major role for the mass loss as long as the galaxy is not moving close to edge-on. We can predict this behaviour by extending Gunn & Gott's estimate of the stripping radius, which is valid for face-on geometries, to moderate inclinations. The inclination plays a role as long as the ram pressure is comparable to pressures in the galactic plane, which can span two orders of magnitude. For very strong ram pressures, the disc will be stripped completely, and for very weak ram pressures, mass loss is negligible independent of inclination. We show that in non-edge-on geometries the stripping proceeds remarkably similar. A major difference between different inclinations is the degree of asymmetry introduced in the remaining gas disc. We demonstrate that the tail of gas stripped from the galaxy does not necessarily point in a direction opposite to the galaxy's direction of motion. Therefore, the observation of a galaxy's gas tail may be misleading about the galaxy's direction of motion.
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