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When a space-craft reaches a large radial velocity, we expand the timedependent radial distance to linear order in time. In the Schwarzschild metricthis 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 observedanomalous acceleration. As measured distances are geocentric distances insteadof the heliocentric distances in the model, this un-modelled acceleration hasan annual oscillation with amplitude close to observations. For Pioneer 11, wefind that the un-modelled acceleration "On-Set" is caused by the flyby energyIncrease to the space-craft's orbit.

Un-modelled Pioneer 10/11 clock acceleration from the Schwarzschild metric and Flyby energy Increase