  We have found that Proxima Centauri, the star closest to our Sun, will pass
close to a pair of faint background stars in the next few years. Using Hubble
Space Telescope (HST) images obtained in 2012 October, we determine that the
passage close to a mag 20 star will occur in 2014 October (impact parameter
1.6"), and to a mag 19.5 star in 2016 February (impact parameter 0.5"). As
Proxima passes in front of these stars, the relativistic deflection of light
will cause shifts in the positions of the background stars by ~0.5 and 1.5 mas,
respectively, readily detectable by HST imaging, and possibly by Gaia and
ground-based facilities such as VLT. Measurement of these astrometric shifts
offers a unique and direct method to measure the mass of Proxima. Moreover, if
Proxima has a planetary system, the planets may be detectable through their
additional microlensing signals, although the probability of such detections is
small. With astrometric accuracies of 0.03 mas (achievable with HST spatial
scanning), centroid shifts caused by Jovian planets are detectable at
separations of up to 2.0" (corresponding to 2.6 AU at the distance of Proxima),
and centroid shifts by Earth-mass planets are detectable within a small band of
8 mas (corresponding to 0.01 AU) around the source trajectories. Jovian planets
within a band of about 28 mas (corresponding to 0.036 AU) around the source
trajectories would produce a brightening of the source by >0.01 mag and could
hence be detectable. Estimated timescales of the astrometric and photometric
microlensing events due to a planet range from a few hours to a few days, and
both methods would provide direct measurements of the planetary mass.
