The M51 system (NGC 5194/5195) provides an excellent problem both in spiral structure and in galaxy interactions. We present an analytic study of a computer experiment on the excitation mechanisms for M51’s spiral arms and whether or not a halo is important for these mechanisms. This work extends previous numerical studies of the M51 system by including self-gravitation in a two component disk: ’gas’ and ’stars’, and a dark halo. The analytic study provides two new observational constraints: the time (≈ 70 — 84 million years ago) and position angle of perigalacticon (300°). By using these constraints and a simple conic approximation, the search for the companion’s possible orbit is greatly simplified. This requires fewer N-body simulations than a fully self-gravitating orbit search. Fig. 1 shows the dust lane spiral pattern of M51 overlaid on an optical photograph. The analytically determined direction of perigalacticon is indicated with a line.