Exploring the weak limit of gravity at Solar System scales

Precision tracking of multiple spacecraft in the outer Solar System has shown an unmodelled perturbation, consisting of a small, constant, radial acceleration directed towards the Sun. Since its detection, a great deal of work has been devoted to explaining this Pioneer effect, both in terms of spacecraft-generated systematics and external physical causes. Its continuing importance is found in the fact that it has been impossible to explain away the effect through conventional means. This leaves open the possibility, however unlikely, that new physics is represented in the effect. This new physics, in turn, would be connected intimately to gravity with huge implications across astrophysics and beyond.;With this as motivation, this dissertation investigates two areas related to the Pioneer effect. The first goal is to investigate the use of planets, comets, and asteroids to determine the reality of the Pioneer effect through precision astrometry.;Here, we showed that asteroids can be used to evaluate the gravitational field in the outer Solar System. The observations can be conducted with modest allocations of telescope time, and would provide a definitive answer to the question within the next 20 years.;In assessing current knowledge of Pluto's orbit, we determined that it is not known well enough at present to preclude the existence of the Pioneer effect. We also showed that comets are not ideal candidates for measuring gravity in the outer Solar System, although some present intriguing observational targets for related reasons. Finally, we showed that Pan-STARRS and LSST are likely to lead to a capability to test gravity in the outer Solar System in the near future.;The second goal of the dissertation involved exploring two general mechanisms for explaining the Pioneer effect. The first approach involved investigating the effective mass density that would be produced in the Solar System as a result of the capture of elementary particle dark matter by means of a hypothetical weak interaction between the dark matter particles and the matter of the Sun. The second approach involved three body capture of dark matter from the Galactic halo into Solar orbit. The three bodies interacting are the Galactic barycenter, the Sun, and the dark matter particle.;In this phase of the dissertation, we showed that capture of Galactic dark matter into Solar orbit by a weak interaction with Solar matter does not accumulate dark matter in the region where the Pioneer effect manifests itself. It is possible that it does accumulate at smaller distances, however. Similarly, we showed that three body gravitational capture is not feasible as a cause of the Pioneer effect either. Dark matter captured by this mechanism would occur generally at distances far greater than that needed to cause the Pioneer anomaly. Thus, neither mechanism for capture of dark matter into Solar orbit sufficed to explain the Pioneer effect.;Finally, we discuss a number of future research areas that became apparent during the course of the research.