  We outline a general procedure to derive first-order differential equations
obeyed by geodesic orbits over two-dimensional (2D) surfaces of revolution
immersed or embedded in ordinary three-dimensional (3D) Euclidean space. We
illustrate that procedure with an application to a wormhole model introduced by
Morris and Thorne (MT), which provides a prototypical case of a `splittable
space-time' geometry. We obtain analytic solutions for geodesic orbits
expressed in terms of elliptic integrals and functions, which are qualitatively
similar to, but even more fundamental than, those that we previously reported
for Flamm's paraboloid of Schwarzschild geometry. Two kinds of geodesics
correspondingly emerge. Regular geodesics have turning points larger than the
`throat' radius. Thus, they remain confined to one half of the MT wormhole.
Singular geodesics funnel through the throat and connect both halves of the MT
wormhole, perhaps providing a possibility of `rapid inter-stellar travel.' We
provide numerical illustrations of both kinds of geodesic orbits on the MT
wormhole.
