A scientific earth satellite that is guided in a drag-free orbit by a shielded, free-falling proof mass has been proposed by a number of investigators. This paper examines the feasibility and some of the applications of this scheme. The control and guidance system is analyzed with respect to system performance and gas usage requirements. The principal trajectory errors that are due to vehicle gravity, stray electric and magnetic fields, and sensor forces are investigated. It is found that drag and solar radiation pressure forces may be effectively reduced by three to five orders of magnitude for 100to 500-mile orbits and that the deviation from a purely-gravitational orbit may be made as small as 1 m/yr. Such a satellite could be used to make precise measurements in geodesy and aeronomy; and, if a spherical proof mass is spun as a gyroscope, its random drift rate would probably be less than 0.1 sec-arc/yr. Such a gyroscope could be used to measure the effects that would ultimately limit the performance of the best terrestrial or satellite-borne gyros, and it might also be good enough to perform the experiment proposed by G. E. Pugh and L. I. Schiff to test general relativity.