  The Apollo 11 Eagle Lunar Module ascent stage was abandoned in lunar orbit
after the historic landing in 1969. Its fate is unknown. Numerical analysis
described here provides evidence that this object might have remained in lunar
orbit to the present day. The simulations show a periodic variation in
eccentricity of the orbit, correlated to the selenographic longitude of the
apsidal line. The rate of apsidal precession is correlated to eccentricity.
These two factors appear to interact to stabilize the orbit over the long term.
