In order to measure the mass of the eta meson with high accuracy using the d+p -> 3He+eta reaction, the momentum of the circulating deuteron beam in the Cooler Synchrotron COSY of the Forschungszentrum Juelich has to be determined with unprecedented precision. This has been achieved by studying the spin dynamics of the polarized deuteron beam. By depolarizing the beam through the use of an artificially induced spin resonance, it was possible to evaluate its momentum p with a precision of dp/p < 10-4 for a momentum of roughly 3 GeV/c. Different possible sources of error in the application of the spin resonance method are discussed in detail and its possible use during a standard experiment is considered.