  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 ~ 8 x 10^{-8}
cm/s^2, directed towards the Sun (anderson,moriond). 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 +/- 1.33) x 10^{-8}
cm/s^2. (Annual/diurnal variations on top of a_P, that leave a_P unchanged, are
also reported and discussed.)
