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We present relativistic analyses of 9257 measurements of times-of-arrival from the first binary pulsar, PSR B1913+16, acquired over the last thirty-five years. The determination of the "Keplerian" orbital elements plus two relativistic terms completely characterizes the binary system, aside from an unknown rotation about the line of sight; leading to a determination of the masses of the pulsar and its companion: 1.438 ± 0.001 M and 1.390 ± 0.001 M , respectively. In addition, the complete system characterization allows the creation of tests of relativistic gravitation by comparing measured and predicted sizes of various relativistic phenomena. We find that the ratio of observed orbital period decrease due to gravitational wave damping (corrected by a kinematic term) to the general relativistic prediction, is 0.9983 ± 0.0016; thereby confirming the existence and strength of gravitational radiation as predicted by general relativity. For the first time in this system, we have also successfully measured the two parameters characterizing the Shapiro gravitational propagation delay, and find that their values are consistent with general relativistic predictions. We have also measured for the first time in any system the relativistic shape correction to the elliptical orbit, δ θ , although its intrinsic value is obscured by currently unquantified pulsar emission beam aberration. We have also marginally measured the time derivative of the projected semimajor axis, which, when improved in combination with beam aberration modelling from geodetic precession observations, should ultimately constrain the pulsar's moment of inertia.

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We present strong observational evidence for a relationship between the direction of a pulsar's motion and its rotation axis. We show carefully calibrated polarization data for 25 pulsars, 20 of which display linearly polarized emission from the pulse longitude at closest approach to the magnetic pole. Such data allow determination of the position angle of the linear polarisation which in turn reflects the position angle of the rotation axis. Of these 20 pulsars, 10 show an offset between the velocity vector and the polarisation position angle which is either less than 10\degr or more than 80\degr, a fraction which is very unlikely by random chance. We believe that the bimodal nature of the distribution arises from the presence of orthogonal polarisation modes in the pulsar radio emission. In some cases this orthogonal ambiguity is resolved by observations at other wavelengths so that we conclude that the velocity vector and the rotation axis are aligned at birth. Strengthening the case is the fact that 4 of the 5 pulsars with ages less than 3 Myr show this relationship, including the Vela pulsar. We discuss the implications of these findings in the context of the Spruit & Phinney (1998)\nocite{sp98} model of pulsar birth-kicks. We point out that, contrary to claims in the literature, observations of double neutron star systems do not rule out aligned kick models and describe a possible observational test involving the double pulsar system.Comment: MNRAS, In Pres