The Near Earth Asteroid Rendezvous (NEAR) mission spacecraft will arri
ve at asteroid 433 Eros in February 1999. Following an initial period
of characterization, the science phase of the mission will commence, a
nd unprecedented information concerning an asteriod's shape, mass, den
sity, composition and rotational dynamics will be sent to Earth for an
alysis. It will also mark the start of orbital operations about the sm
allest mass and the most complex and irregular gravity field ever orbi
ted in the history of space exploration. The smallness of Eros' mass a
nd the severity of its distortion from the usual spheroid bodies encou
ntered in planetary exploration leads to fundamental differences in th
e orbital dynamics about it. This paper reviews the expected orbital d
ynamics of the NEAR spacecraft at Eros and discusses the problem of or
bit control of the NEAR spacecraft orbit. The dynamical environment ma
y be differentiated according to whether the spacecraft is close to or
far from Eros. When far from Eros, the spacecraft must contend with t
he solar tide and solar radiation pressure forces which are large pert
urbations to the Eros attractive force. When close to Eros, the spacec
raft must contend with the irregular gravity held of the body. Orbits
exist which are quite unstable and may crash onto the asteroid surface
in a matter of days. Obviously, it is important to understand when an
d where such orbits exist, and how they may be avoided. There are a nu
mber of mission specific constraints which the NEAR spacecraft must op
erate under. These include pointing, operational, and safety concerns
as well as science directives and goals. The application of these cons
traints in the NEAR spacecraft environment at Eros is discussed, inclu
ding some specific strategy implementations.