  Planet detection through microlensing is usually limited by a well-known
degeneracy in the Einstein timescale $t_E$, which prevents mass and distance of
the lens to be univocally determined. It has been shown that a satellite in
geosynchronous orbit could provide masses and distances for most standard
planetary events ($t_E \approx 20$ days) via a microlens parallax measurement.
This paper extends the analysis to shorter Einstein timescales, $t_E \approx 1$
day, when dealing with the case of Jupiter-mass lenses. We then study the
capabilities of a low Earth orbit satellite on even shorter timescales, $t_E
\approx 0.1$ days. A Fisher matrix analysis is employed to predict how the
1-$\sigma$ error on parallax depends on $t_E$ and the peak magnification of the
microlensing event. It is shown that a geosynchronous satellite could detect
parallaxes for Jupiter-mass free floaters and discover planetary systems around
very low-mass brown dwarfs. Moreover, a low Earth orbit satellite could lead to
the discovery of Earth-mass free-floating planets. Limitations to these results
can be the strong requirements on the photometry, the effects of blending, and
in the case of the low orbit, the Earth's umbra.
