The Advanced X-Ray Astrophysics Facility (AXAF) satellite is planned t
o be placed in a high-altitude, highly elliptical orbit in the fall of
1998. This orbit is subject to perturbations by the Sun and Moon that
will make it change in a manner that is sensitively dependent on the
initial conditions and start time and, hence, predictable over long in
tervals of time only through numerical integration of the equations of
motion. The characteristics of such integrated trajectories are discu
ssed here for the AXAF and for the solid motor upper stages used to pl
ace it in orbit.