  We consider a traversable wormhole solution of Einstein's gravity conformally
coupled to a massless scalar field, a solution derived by Barcelo and Visser
based on the JNWW spacetime. We study the geodesic motion of time-, light- and
space-like particles in this spacetime. We solve the equations of motion
analytically in terms of the Weierstra\ss \ functions and discuss all possible
orbit types and their parameter dependence. Interestingly, bound orbits occur
for time-like geodesics only in one of the two worlds. Moreover, under no
conditions there exist time-like two world bound orbits.
