The two step least squares process of extracting the Sun's mean motion from the position data can be reduced to the multiplication of the positions by a single matrix, P.
The linear and non-linear functions can be represented by two matrices, f and g.
Repeated multiplication of the modified positions by P moves us closer to the approximate mean motion and the resulting period can be calculated.
The four decimal place accuracy of the previous result for the period may have been a coincidence but the uncertainty appears to be in the 3rd decimal place. The nonlinear portion of the positions no longer appears to be tilted.
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