[Fozzie (OP)]

If both the Pioneer Spacecraft are now dead and not communicating with us any more, and they are too far away to see with telescopes, how do we know that they are veering off course?

[damocles]

The best possibility that I can think of is that before we lost communication scientists had noticed minor departures from course, and that calculations from the gravitational fields of known astronomical objects might have indicated that these departures would amplify over the future trajectories of the spacecraft.

[imatfaal]

Hi Fozzie

To start with the Pioneer Anomaly isn't so much a veering off course as a slowing down in its progress from the sun more than expected (accelerating towards the sun at 10^-11 ms^-2 more than calculated- a tiny amount and will not reverse progress).  The error is most likely systematic and is also described by theories both mad and more mainstream.

To answer your question - we don't know - since 2003 pioneer 10 and 11 could have been doing loop the loops and skywriting rude messages about NASA; we have no idea what they are doing.  The anomaly (which is well documented - it is the explanation that is unknown) is based on the messages received from the 70's launch to the 2003 end of communication.  it is based on the analysis of this recorded data - of which there is a huge amount, lots of which is in strange formats and not easily readable.