Support for the Thermal Origin of the Pioneer Anomaly

We investigate the possibility that the anomalous acceleration of the Pioneer 10 and 11 spacecraft is due to the recoil force associated with an anisotropic emission of thermal radiation off the vehicles. To this end, relying on the project and spacecraft design documentation, we constructed a comprehensive finite-element thermal model of the two spacecraft. Then, we numerically solve thermal conduction and radiation equations using the actual flight telemetry as boundary conditions. We use the results of this model to evaluate the effect of the thermal recoil force on the Pioneer 10 spacecraft at various heliocentric distances. We found that the magnitude, temporal behavior, and direction of the resulting thermal acceleration are all similar to the properties of the observed anomaly. As a novel element of our investigation, we develop a parametrized model for the thermal recoil force and estimate the coefficients of this model independently from navigational Doppler data. We find no statistically significant difference between the two estimates and conclude that, once the thermal recoil force is properly accounted for, no anomalous acceleration remains.

Figure 1

Illustrative representation of the thermal model of the Pioneer 10 spacecraft evaluated at 40 A.U. Top left: spacecraft body interior (temperature range: blue $-16°\mathrm{C}$, red $+10°\mathrm{C}$); bottom left: spacecraft exterior (blue $-155°\mathrm{C}$, red $-108°\mathrm{C}$); right: entire spacecraft (blue $-213°\mathrm{C}$, red $+136°\mathrm{C}$). Unmodeled struts that connect the RTGs to the spacecraft body are indicated with yellow-and-black dashed lines.

Figure 2

Pioneer 10 thermal power contributing to sunward acceleration, including solar heating and reflected solar radiation (hollow circles), solar heating only with reflected solar radiation removed (hollow squares), and all solar effects removed (filled circles). Positive values indicate radiation directed away from the Sun, resulting in a sunward acceleration of the spacecraft.

Figure 3

Comparison of the thermally induced and anomalous accelerations for Pioneer 10. The estimated thermal acceleration is shown with error bars. The stochastic acceleration estimate from 8 appears as a step function. For reference, the Doppler residuals of the stochastic acceleration are also shown in the bottom panel. Inner and outer error bars correspond to the subtotal and total shown in Table .

Figure 4

Comparison of the RTG (${\eta }_{\mathrm{RTG}}$) and electrical (${\eta }_{\mathrm{elec}}$) efficiency factors estimated independently from the Doppler and thermal analysis using Eq. (1). The $1\sigma$ error ellipse for the thermal analysis corresponds to the values in Table . For the Doppler analysis, the error ellipse corresponds to values of ${\eta }_{\mathrm{RTG}}$ and ${\eta }_{\mathrm{elec}}$ in Table  for which the excess in the Doppler residual exceeds the best-fit residual.