  A value for the mass of the eta meson has been determined at the COSY-ANKE
facility through the measurement of a set of deuteron laboratory beam momenta
and associated 3He center-of-mass momenta in the d+p -> 3He+X reaction. The eta
was then identified by the missing-mass peak and the production threshold
determined. The individual beam momenta were fixed with a relative precision of
3 x 10^-5 for values around 3 GeV/c by using a polarized deuteron beam and
inducing an artificial depolarizing spin resonance, which occurs at a
well-defined frequency. The final-state momenta in the two-body d+p -> 3He+eta
reaction were investigated in detail by studying the size of the 3He momentum
ellipse with the forward detection system of the ANKE spectrometer. Final
alignment of the spectrometer for this high precision experiment was achieved
through a comprehensive study of the 3He final-state momenta as a function of
the center-of-mass angles, taking advantage of the full geometrical acceptance.
The value obtained for the mass, m(eta)=(547.873 +- 0.005(stat) +- 0.027(syst))
MeV/c^2, is consistent and competitive with other recent measurements, in which
the meson was detected through its decay products.
