  Analysis of the radio-metric tracking data from the Pioneer 10/11 spacecraft
at distances between 20--70 astronomical units (AU) from the Sun has
consistently indicated the presence of an anomalous, small, constant Doppler
frequency drift. The drift is a blue-shift, uniformly changing with rate a_t =
(2.92 +/- 0.44) x 10^(-18) s/s^2. It can also be interpreted as a constant
acceleration of a_P = (8.74 +/- 1.33) x 10^(-8) cm/s^2 directed towards the
Sun. Although it is suspected that there is a systematic origin to the effect,
none has been found. As a result, the nature of this anomaly has become of
growing interest. Here we discuss the details of our recent investigation
focusing on the effects both external to and internal to the spacecraft, as
well as those due to modeling and computational techniques. We review some of
the mechanisms proposed to explain the anomaly and show their inability to
account for the observed behavior of the anomaly. We also present lessons
learned from this investigation for a potential deep-space experiment that will
reveal the origin of the discovered anomaly and also will characterize its
properties with an accuracy of at least two orders of magnitude below the
anomaly's size. A number of critical requirements and design considerations for
such a mission are outlined and addressed.
