We present a revision to the visual orbit of the young , directly-imaged exoplanet 51 Eridani b using four years of observations with the Gemini Planet Imager . The relative astrometry is consistent with an eccentric ( e = 0.53 _ { -0.13 } ^ { +0.09 } ) orbit at an intermediate inclination ( i = 136 _ { -11 } ^ { +10 } deg ) , although circular orbits can not be excluded due to the complex shape of the multidimensional posterior distribution . We find a semi-major axis of 11.1 _ { -1.3 } ^ { +4.2 } au and a period of 28.1 _ { -4.9 } ^ { +17.2 } yr , assuming a mass of 1.75 M _ { \odot } for the host star . We find consistent values with a recent analysis of VLT/SPHERE data covering a similar baseline . We investigated the potential of using absolute astrometry of the host star to obtain a dynamical mass constraint for the planet . The astrometric acceleration of 51 Eri derived from a comparison of the Hipparcos and Gaia catalogues was found to be inconsistent at the 2–3 \sigma level with the predicted reflex motion induced by the orbiting planet . Potential sources of this inconsistency include a combination of random and systematic errors between the two astrometric catalogs or the signature of an additional companion within the system interior to current detection limits . We also explored the potential of using Gaia astrometry alone for a dynamical mass measurement of the planet by simulating Gaia measurements of the motion of the photocenter of the system over the course of the extended eight-year mission . We find that such a measurement is only possible ( > 98 % probability ) given the most optimistic predictions for the Gaia scan astrometric uncertainties for bright stars , and a high mass for the planet ( \gtrsim 3.6 M _ { Jup } ) .