The Pioneer Anomaly - Simple Calculation Errors?

The Pioneer Anomaly:

It seems reasonable that when the range to prime focus is dynamic, the accuracy of the algorithm is going to have inherent limits; that is, the accuracy of the calculation is going to be inversely proportional to the size of the time increment used in the arithmetic iteration of the r vector force. Restated; in calculating the position of a hyperbolic trajectory it seems reasonable that there will be error introduced; with the sum error increasing as a function of time increment value and number of iteration steps. This results from the inverse square relationship of gravity to distance. This type of iteration error is introduced because the net gravitational force is calculated as remaining constant through each time iteration step even though that force is changing, ever so slightly, as the range changes during that same time increment. It seems reasonable that when attempting to extrapolate the position of any object many years into the future, error will result from both this inherent iteration error as well as the limit of processor precision.

Also, what if the early algorithms used to predict the position of the Pioneer and other heliocentric hyperbolic missions calculated the R vector relative to Sun Center of Mass instead of Solar System Bary-center?

Since Solar System Bary-Center is a dynamic position relative to sun center of mass, and is the true focus of any heliocentric trajectory; any algorithm using sun center of mass as the prime focus would introduce error to both the calculated flight path angle and gravitational force at range.

On a different but related note: It seems probable that any heliocentric hyperbolic trajectory on or near Earth Orbital Plane is cutting the Solar Magnetic Field Lines at nearly the optimum angle for induction. However so slight, the dynamic braking (Lentz Braking) inherent in any induction process would not be negligible over a period of decades.

Perhaps we would be wise to consider this in extrapolating the position of Apophis in the 2029 close approach.

Gavilan