  A comprehensive description is given of a space--time model of an
accelerating massive particle. The particle radiates gravitational waves with
optical shear. The wave fronts are smoothly deformed spheres and the particle
experiences radiation reaction, similar to an accelerating charged particle,
and a loss of mass described by a Bondi mass--loss formula. The space--time is
one of the Bondi--Sachs forms but presented in a form here which is
particularly suited to the construction of the model particle. All details of
the calculations are given. A detailed examination of the gravitational field
of the particle is provided which illustrates the presence of gravitational
radiation and also exhibits, in the form of a type of singularity found in some
Robinson--Trautman space--times, the absence of an external field to supply
energy to the particle.
