The cold dark matter paradigm of structure formation is successful at recovering the basic skeletal structure of the universe -- the large-scale distribution of galaxies. However, agreement between theory and observation is less secure when this model is applied to galactic (and sub-galactic) scales. The "missing satellites problem" and discrepancies between the observed structure of dwarf galaxies and simulations have prompted us to develop an inverse method of characterizing galactic satellites. The extended atomic hydrogen disks of galaxies are ideal tracers of tidal interactions with satellites and the galactic gravitational potential well. Our "Tidal Analysis" method allows us to infer the mass, and relative position (in radius and azimuth) of satellites from analysis of observed disturbances in outer gas disks, without requiring knowledge of their optical light. I will present the proof of principle of this method by applying it to galaxies with known optical companions. I will also present our earlier prediction for a dim and yet undiscovered companion of the Milky Way. I will end by presenting preliminary work on the application of this method to characterize the density profile of the dark matter halo in spiral galaxies.