The authors have determined the masses and orbital parameters for the galaxies in the strongly interacting binary NGC 4782/4783 by finding a numerical simulation of the collision that accurately represents all of the observed properties of the system. With this simulation, the authors have completely determined the three-dimensional orientation and the dynamical state of the binary. The large relative velocity observed for the pair is the consequence of a high-speed encounter and is not an indicator of large galaxian masses. Large stellar velocity dispersions provide evidence for a tidal shock and are likewise not indicative of a large amount of mass. Some of the physical parameters that define the solution for the pair are (for H0 = 60 km s-1Mpc-1): log Mtot/M_sun; = 12.14, true relative velocity in plane of orbit 690 km s-1, true separation in plane of orbit 20.0 kpc, time since pericenter passage ≈25 million years, and time until merger (i.e., pair coalescence) ≈800 million years. Large velocity dispersions (from the shock) and strong distortions in the luminous matter distribution provide evidence for tidal stripping and tidal transfer of orbital energy and angular momentum into individual stars.