  We show that a space-based gravitational microlensing survey for terrestrial
extra-solar planets is feasible in the near future, and could provide a nearly
complete picture of the properties of planetary systems in our Galaxy. We
present simulations of such a survey using a 1-2m aperture space telescope with
a ~2 square degree field-of-view which is used to continuously monitor ~10^8
Galactic bulge main sequence stars. The microlensing techniques allows the
discovery of low mass planets with high signal-to-noise, and the space mission
that we have studied are sensitive to planets with masses as low as that of
Mars. By targeting main sequence source stars, which can only be resolved from
space, the space-based microlensing survey is able to detect enough light from
the lens stars to determine the spectral type of one third of the lens stars
with detected planets, including virtually all of the F, G, and K stars which
comprise one quarter of the event sample. This enables the determination of the
planetary masses and separations in physical units, as well as the abundance of
planets as a function of stellar type and distance from the Galactic center. We
show that a space-based microlensing planet search program has its highest
sensitivity to planets at orbital separations of 0.7-10 AU, but it will also
have significant sensitivity at larger separations and will be able to detect
free-floating planets in significant numbers. This complements the planned
terrestrial planet transit missions which are sensitive to terrestrial planets
at separations of =< 1 AU. Such a mission also detect ~50,000 giant planets via
transits, and it is, therefore, the only proposed planet detection method that
is sensitive to planets at all orbital radii.
