Modelling the reflective thermal contribution to the acceleration of the   Pioneer spacecraft
  We present an improved method to compute the radiative momentum transfer in the Pioneer 10 & 11 spacecraft that takes into account both diffusive and specular reflection. The method allows for more reliable results regarding the thermal acceleration of the deep-space probes, confirming previous findings. A parametric analysis is performed in order to set an upper and lower-bound for the thermal acceleration and its evolution with time. 
F. Francisco, O. Bertolami, P. J. S. Gil and J. P\'aramos
physics.space-ph astro-ph.IM gr-qc