Using the measured common distance from the observer, angular separation of a dwarf satellite from its mother galaxy and their relative radial velocities, plus three criticable assumptions: circularity of the orbit, spherical symmetry of the gravitational potential, and that the radius of the dwarf galaxy is limited by tidal interaction with the mother, the authors show how to derive the orbital elements of the satellite. A trial of the method with the satellites of M31, M32 and NGC 205, gave results consistent with all three assumptions. Here the authors apply it to two systems, NGC 128 and NGC 1023, and their satellites, concluding that it is a useful exploratory tool, but that at its best it requires better data than the literature offers.