The twin Pioneer spacecraft have been tracked for over thirty years as they headed out of the solar system. After passing 20 AU from the Sun, both exhibited a systematic error in their trajectories that can be interpreted as a constant acceleration towards the Sun. This Pioneer Effect is most likely explained by spacecraft systematics, but there have been no convincing arguments that that is the case. The alternative is that the Pioneer Effect represents a real phenomenon and perhaps new physics. What is lacking is a means of measuring the effect, its variation, its potential anisotropies, and its region of influence. We show that minor planets provide an observational vehicle for investigating the gravitational field in the outer solar system, and that a sustained observation campaign against properly chosen minor planets could confirm or refute the existence of the Pioneer Effect. Additionally, even if the Pioneer Effect does not represent a new physical phenomenon, minor planets can be used to probe the gravitational field in the outer Solar System and since there are very few intermediate range tests of gravity at the multiple AU distance scale, this is a worthwhile endeavor in its own right.

The inverse square law of gravity is poorly probed by experimental tests at distances of $10 AU. Recent analysis of the trajectory of the Pioneer 10 and 11 spacecraft have shown an unmodeled acceleration directed toward the Sun, which was not explained by any obvious spacecraft systematics, and occurred when at distances greater than 20 AU from the Sun. If this acceleration represents a departure from Newtonian gravity or is indicative of an additional mass distribution in the outer solar system, it should be detectable in the orbits of trans-Neptunian objects (TNOs). To place limits on deviations from Newtonian gravity, we have selected a well-observed sample of TNOs found orbiting between 20 and 100 AU from the Sun. By examining their orbits with modified orbital fitting software, we place tight limits on the perturbations of gravity that could exist in this region of the solar system.

This paper deals with the problem of astrometric determination of the orbital elements of the outer planets, in particular by assessing the ability of astrometric observations to detect perturbations of the sort expected from the Pioneer effect or other small perturbations to gravity. We also show that while using simplified models of the dynamics can lead to some insights, one must be careful to not over-simplify the issues involved lest one be misled by the analysis onto false paths. Specifically, we show that the current ephemeris of Pluto does not preclude the existence of the Pioneer effect. We show that the orbit of Pluto is simply not well enough characterized at present to make such an assertion. A number of misunderstandings related to these topics have now propagated through the literature and have been used as a basis for drawing conclusions about the dynamics of the solar system. Thus, the objective of this paper is to address these issues. Finally, we offer some comments dealing with the complex topic of model selection and comparison.