Precision Timing Measurements of PSR J1012+5307

We present results and applications of high precision timing measurements of the millisecond pulsar J1012+5307. Combining our radio observations with results based on optical observations, we derive complete 3-D velocity information for this system. Correcting for Doppler effects, we derive the intrinsic spin parameters of this pulsar and a characteristic age of 8.6 +/- 1.9 Gyr. Our upper limit for the orbital eccentricity of only 8 * 10^-7 (68% C.L.) is the smallest ever measured for a binary system. We demonstrate that this makes the pulsar an ideal laboratory to test certain aspects of alternative theories of gravitation. Our precise measurements suggest deviations from a simple pulsar spin-down timing model, which are consistent with timing noise and the extrapolation of the known behaviour of slowly rotating pulsars.