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 nonzero acceleration has been found; the typical sensitivity achieved by our method is a⊙/c ~ a few × 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.
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