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We describe a simple model that explains the qualitative and (approximate) quantitative features of the distribution of orbital velocities of merging pairs of dark matter haloes. Our model considers a primary dark matter halo as a perturber in a background of secondary haloes with velocities described by linear theory. By evaluating the ensemble of secondary haloes on orbits within the perturbing halo's 'loss cone' we derive the distribution of orbital parameters of these captured haloes. This model is able provide qualitative explanations for the features of this distribution as measured from N -body simulations, and is in approximate quantitative agreement with those measurements. As the velocity dispersion of the background haloes is larger on smaller scales our model predicts an overall increase in the characteristic velocities of merging haloes, relative to the virial velocities of those haloes, in lower mass systems. Our model also provides a simple explanation for the measured independence of the orbital velocity distribution function on redshift when considered at fixed peak height. By connecting the orbital parameter distribution to the underlying power spectrum our model also allows for estimates to be made of the effect of modifying that power spectrum, for example by including a truncation at large wavenumber. For plausible warm dark matter models, we find that this truncation has only a small effect on the predicted distributions. [ABSTRACT FROM AUTHOR]