  Many astronomers have speculated that the solar system contains undiscovered
massive planets or a distant stellar companion. The acceleration of the solar
system barycenter can constrain the mass and position of the putative
companion. In this paper we use the most recent timing data on accurate
astronomical clocks (millisecond pulsars, pulsars in binary systems and
pulsating white dwarfs) to constrain this acceleration. No evidence for
non-zero acceleration has been found; the typical sensitivity achieved by our
method is a/c=a few times 10^{-19} s^{-1}, comparable to the acceleration due
to a Jupiter-mass planet at 200 AU. The acceleration method is limited by the
uncertainties in the distances and by the timing precision for pulsars in
binary systems, and by the intrinsic distribution of the period derivatives for
millisecond pulsars. Timing data provide stronger constraints than residuals in
the motions of comets or planets if the distance to the companion exceeds a few
hundred AU. The acceleration method is also more sensitive to the presence of a
distant companion (> 300-400 AU) than existing optical and infrared surveys. We
outline the differences between the effects of the peculiar acceleration of the
solar system and the background of gravitational waves on high-precision
timing.
