  When a space-craft reaches a large radial velocity, we expand the time
dependent radial distance to linear order in time. In the Schwarzschild metric
this linear term in time leads to a significant un-modelled clock acceleration.
For Pioneer 10, this acceleration is found to be about $40\%$ of the observed
anomalous acceleration. As measured distances are geocentric distances instead
of the heliocentric distances in the model, this un-modelled acceleration has
an annual oscillation with amplitude close to observations. For Pioneer 11, we
find that the un-modelled acceleration "On-Set" is caused by the flyby energy
Increase to the space-craft's orbit.
