  If a galaxy resides in a cluster, then its passage through the pervasive
intracluster medium will produce a detectable signature in the X-ray emission
from the cluster. The simplest kinematic information that can be extracted from
this signature is the galaxy's direction of motion on the plane of the sky.
This paper explores the constraints on cluster dynamics that could be derived
from such information. In particular, we show that it is possible to define a
projected anisotropy parameter, B(R), which is directly analogous to the usual
orbital anisotropy parameter. We describe an estimator for this quantity,
Bhat(R), which can be derived in a robust and straightforward manner. Using a
simple dynamical model, we demonstrate the ambiguity between the distribution
of mass and the distribution of galaxy orbits when interpreting the traditional
measures of cluster kinematics (the projected density of galaxies and their
line-of-sight velocity dispersion). As an example, we show how two very
different dynamical models can fit the kinematic properties of the Coma
cluster. We demonstrate that the measurement of Bhat using a relatively small
sample of wake directions (N_{wake} ~ 50) would provide an effective mechanism
for lifting this degeneracy. Thus, by combining X-ray measurements of wake
directions with number counts and line-of-sight velocities derived from optical
data, it will prove possible to measure both the orbit distribution and the
form of the gravitational potential in clusters of galaxies.
