  We evaluate the extent of the regions within the $\alpha$ Centauri AB star
system where small planets are able to orbit for billion-year timescales, and
we calculate the positions on the sky plane where planets on stable orbits
about either stellar component may appear. We confirm the qualitative results
of Wiegert and Holman (AJ 113, 1445, 1997) regarding the approximate size of
the regions of stable orbits, which are larger for retrograde orbits relative
to the binary than for prograde orbits. Additionally, we find that mean motion
resonances with the binary orbit leave an imprint on the limits of orbital
stability, and the effects of the Lidov-Kozai mechanism are also readily
apparent.
