Study of the anomalous acceleration of Pioneer 10 and 11

Our previous analyses of radio Doppler and ranging data from distant spacecraft in the solar system indicated that an apparent anomalous acceleration is acting on Pioneer 10 and 11, with a magnitude $a_P\sim 8\times {10}^{-8}\hspace{0.5em}{\mathrm{c}\mathrm{m}/\mathrm{s}}^2,$ directed towards the Sun. Much effort has been expended looking for possible systematic origins of the residuals, but none has been found. A detailed investigation of effects both external to and internal to the spacecraft, as well as those due to modeling and computational techniques, is provided. We also discuss the methods, theoretical models, and experimental techniques used to detect and study small forces acting on interplanetary spacecraft. These include the methods of radio Doppler data collection, data editing, and data reduction. There is now further data for the Pioneer 10 orbit determination. The extended Pioneer 10 data set spans 3 January 1987 to 22 July 1998. (For Pioneer 11 the shorter span goes from 5 January 1987 to the time of loss of coherent data on 1 October 1990.) With these data sets and more detailed studies of all the systematics, we now give a result of $a_P=(8.74\mathrm{}\pm 1.33)\times {10}^{-8}$ ${\mathrm{c}\mathrm{m}/\mathrm{s}}^2.$ (Annual-diurnal variations on top of $a_P,$ that leave $a_P$ unchanged, are also reported and discussed.)