It's better to include the sinusoidal terms with the linear terms when doing a least squares fit as the following example shows. Again, Gadbury's 1672 Sun positions were used. It's difficult to tell if the period has changed over the elapsed time. The value used for T appears to be stable, yielding the itself back for the estimate of the period. For comparison, the value given in the Explanatory Supplement to the Astronomical Almanac is 365.2421897 days.
The result varies with the number of sinusoidal terms used for the fit. I have some doubts about this fit even though it gave the minimum error.
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