We present results and applications of high precision timing measurements of the binary millisecond pulsar J1012+5307 .
Combining our radio timing measurements 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 \pm 1.9 Gyr .
Our upper limit for the orbital eccentricity of only 8 \times 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 precision 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 .