  Binary pulsars provide an excellent system for testing general relativity
because of their intrinsic rotational stability and the precision with which
radio observations can be used to determine their orbital dynamics.
Measurements of the rate of orbital decay of two pulsars have been shown to be
consistent with the emission of gravitational waves as predicted by general
relativity, providing the most convincing evidence for the self-consistency of
the theory to date. However, independent verification of the orbital geometry
in these systems was not possible. Such verification may be obtained by
determining the orientation of a binary pulsar system using only classical
geometric constraints, permitting an independent prediction of general
relativistic effects. Here we report high-precision timing of the nearby binary
millisecond pulsar PSR J0437-4715, which establish the three-dimensional
structure of its orbit. We see the expected retardation of the pulse signal
arising from the curvature of space-time in the vicinity of the companion
object (the `Shapiro delay'), and we determine the mass of the pulsar and its
white dwarf companion. Such mass determinations contribute to our understanding
of the origin and evolution of neutron stars.
