  The flattened, possibly co-rotating plane of satellite galaxies around
Centaurus A, if more than a fortuitous alignment, adds to the pre-existing
tension between the well-studied Milky Way and M31 planes and the $\Lambda$CDM
model of structure formation. It was recently reported that the Centaurus A
satellite plane (CASP) may be rotationally supported, but a further
understanding of the system's kinematics is elusive in the absence of full
three-dimensional velocities. We constrain the transverse velocities of 27
satellites that would rotationally stabilise the Centaurus A plane, and
classify the satellites by whether their possible orbits are consistent with
the CASP. Five satellites are identified to be unlikely to participate in the
plane, two of which are clearly non-members. Despite their previously reported
line-of-sight velocity trend suggestive of a common co-rotating motion, 17 out
of 22 potential CASP members are consistent with either orbital direction
within both the full range of possible kinematics as well as when limiting
orbits to those within the plane. On the other hand, disregarding the 5
off-plane satellites found to be inconsistent with CASP membership enhances the
significance of the CASP's line-of-sight velocity trend fivefold. Our results
are robust with different mass estimates of the Centaurus A halo, and the
adoption of either spherical or triaxial NFW potentials.
