MACHO parallaxes from a single satellite

Massive Compact Objects (Machos) are currently being discovered at substantially higher rates than would be expected from standard models of known stellar populations. To determine whether they are due to non-standard distri- butions of known populations or to a heretofore unknown (`dark') population, one must acquire more information about the individual events. Space-based parallaxes are potentially the best tool for extracting additional information. To leading order, parallax measurements by a single satellite result in a four- fold degeneracy: two possible values of $ ilde v$ and two possible signs for the component of motion perpendicular to the projected satellite-Earth vector. It had been believed that a second satellite would be required to break this degeneracy. I show that the velocity difference between the satellite and the Earth allows one to partially or totally break the degeneracy using a single satellite. For most Macho events it is possible to measure $ ilde v$ and $ ilde r_e$. For some it is also possible to measure $Phi$. The proposed Space Infrared Telescope could measure $sim 100$ parallaxes per year by applying $sim 400,$hr of telescope time.Comment: 12 pages, request PostScript file to gould@payne.mps.ohio-state.edu, OSU-TA-15/9