If the microlensing events now being detected toward the Large Magellanic
Cloud (LMC) are due to lenses in the Milky Way halo, then the events should
typically have asymmetries of order 1% due to parallax from the reflex motion
of the Earth. By contrast, if the lenses are in the LMC, the parallax effects
should be negligible. A ground-based search for such parallax asymmetries would
therefore clarify the location of the lenses. A modest effort (2 hours per
night on a 1 m telescope) could measure 15 parallax asymmetries over 5 years
and so marginally discriminate between the halo and the LMC as the source of
the lenses. A dedicated 1 m telescope would approximately double the number of
measurements and would therefore clearly distinguish between the alternatives.
However, compared to satellite parallaxes, the information extracted from
ground-based parallaxes is substantially less useful for understanding the
nature of the halo lenses (if that is what they are). The backgrounds of
asymmetries due to binary-source and binary-lens events are estimated to be
approximately 7% and 12% respectively. These complicate the interpretation of
detected parallax asymmetries, but not critically.Comment: Submitted to ApJ, 17 pages, including 2 embedded figure