  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
parameterized 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.
