The orbital properties of infalling satellite haloes set the initial conditions which control the subsequent evolution of subhaloes and the galaxies that they host, with implications for mass stripping, star formation quenching and merging. Using a high-resolution cosmological N-body simulation, we examine the orbital parameters of satellite haloes as they merge with larger host haloes, focusing primarily on orbital circularity and pericentre. We explore in detail how these orbital parameters depend on mass and redshift. Satellite orbits become more radial and plunge deeper into their host halo at higher host halo mass, but they do not significantly depend on satellite halo mass. Additionally, satellite orbits become more radial and plunge deeper into their host haloes at higher redshift. We also examine satellite velocities, finding that most satellites infall with less specific angular momentum than the host halo virial value, but that satellites are 'hotter' than the host virial velocity. We discuss the implications of these results to the processes of galaxy formation and evolution, and we provide fitting formulae to the mass and redshift dependence of satellite orbital circularity and pericentre. © 2010 The Author Monthly Notices of the Royal Astronomical Society © 2010 RAS.