This note begins this new subject area by developing UFT363 to evaluate the precessing orbit in an incompressible fluid spacetime. The numerical problem is the simultaneous solution of Eqs. (3), (4), (11) and (12) to give the differential orbital function (6). Finally this is integrated numerically to give the orbit. It is already known that this is a precessing orbit from numerical work by co author Horst Eckardt. The development in this note allows the spin connection to be determined uniquely. Other types of fluid spacetime can be used, for example a compressible spacetime. So the theory of precessing orbits can be merged with the well known equations of fluid dynamics.