Could the Pioneer anomaly have a gravitational origin?

If the Pioneer anomaly has a gravitational origin, it would, according to the equivalence principle, distort the motions of the planets in the Solar System. Since no anomalous motion of the planets has been detected, it is generally believed that the Pioneer anomaly can not originate from a gravitational source in the Solar System. However, this conclusion becomes less obvious when considering models that either imply modifications to gravity over long distances or gravitational sources localized to the outer Solar System, given the uncertainty in the orbital parameters of the outer planets. Following the general assumption that the Pioneer spacecraft move geodesically in a spherically symmetric space-time metric, we derive the metric disturbance that is needed in order to account for the Pioneer anomaly. We then analyze the residual effects on the astronomical observables of the three outer planets that would arise from this metric disturbance, given an arbitrary metric theory of gravity. Providing a method for comparing the computed residuals with actual residuals, our results imply that the presence of a perturbation to the gravitational field necessary to induce the Pioneer anomaly is in conflict with available data for the planets Uranus and Pluto, but not for Neptune. We therefore conclude that the motion of the Pioneer spacecraft must be nongeodesic. Since our results are model-independent within the class of metric theories of gravity, they can be applied to rule out any model of the Pioneer anomaly that implies that the Pioneer spacecraft move geodesically in a perturbed space-time metric, regardless of the origin of this metric disturbance.

Figure 1

Gross perturbation to orbital radius (${10}^3\mathrm{km}$) over a complete period for the three outer planets.

Figure 2

Gross perturbation to angular velocity in $\mathrm{arc}\sec /\mathrm{yr}$ over a complete period for the three outer planets.

Figure 3

Gross perturbation to the argument of latitude $\phi$ (in arc sec) over a complete period for the three outer planets.

Figure 4

The net perturbation to the argument of latitude after removal of the zero-order secular term.

Figure 5

Actual r.a. residuals (in arc sec) for the three outer planets, courtesy of E. M. Standish, JPL.

Figure 6

Simulated (solid lines) and predicted-real r.a. residuals (in arc sec) for the three outer planets. Dashed lines indicate the standard deviation of the real residuals.