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PSR J1012+5307, a millisecond pulsar in orbit with a helium white dwarf (WD),has been timed with high precision for about 25 years. One of the mainobjectives of this long-term timing is to use the large asymmetry ingravitational binding energy between the neutron star and the WD to testgravitational theories. Such tests, however, will be eventually limited by theaccuracy of the distance to the pulsar. Here, we present VLBI (very longbaseline interferometry) astrometry results spanning approximately 2.5 yearsfor PSR J1012+5307, obtained with the Very Long Baseline Array as part of theMSPSRPI project. These provide the first proper motion and absolute positionfor PSR J1012+5307 measured in a quasi-inertial reference frame. From the VLBIresults, we measure a distance of $0.83^{+0.06}_{-0.02}$kpc (all the estimatespresented in the abstract are at 68% confidence) for PSR J1012+5307, which isthe most precise obtained to date. Using the new distance, we improve theuncertainty of measurements of the unmodeled contributions to orbital perioddecay, which, combined with three other pulsars, places new constraints on thecoupling constant for dipole gravitational radiation$\kappa_D=(-1.7\pm1.7)\times 10^{-4}$ and the fractional time derivative ofNewton's gravitational constant $\dot{G}/G = -1.8^{\,+5.6}_{\,-4.7}\times10^{-13}\,{\rm yr^{-1}}$ in the local universe. As the uncertainties of theobserved decays of orbital period for the four leading pulsar-WD systems becomenegligible in $\approx10$ years, the uncertainties for $\dot{G}/G$ and$\kappa_D$ will be improved to $\leq1.5\times10^{-13}\,{\rm yr^{-1}}$ and$\leq1.0\times10^{-4}$, respectively, predominantly limited by the distanceuncertainties.

Very long baseline astrometry of PSR J1012+5307 and its implications on alternative theories of gravity