Choose the Gauss triplet by time span rather than first/middle/last - #533
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Gauss truncates the Lagrange f and g series, so the interval has to be short against the orbital period. The triplet was the first, middle and last observation of seq[0], and seq[0] is by construction the longest-span chunk, so on a long arc it was as wide as it could be. The objects that fail to converge cold span a median 53 degrees of mean anomaly against 29 for those that fit. Pick the triplet whose outer span is nearest a target instead. The target is in mean anomaly, which needs a period, which needs the orbit being sought -- so it is converted to days with an ASSUMED a = 2.5 au rather than the object's own, about 60 days. That keeps it a prior and not an oracle; using each object's published a is slightly worse. A balance guard requires each sub-interval to be at least 10% of the outer span. Without it a repeated epoch can put the middle observation on an endpoint, which gives a zero-length interval and no usable root. Where no triplet qualifies the old first/middle/last choice is used, so behaviour is never worse than before. Measured cold on objects from the MPC catalog: regression, objects the old selection already fit 398/400 (99.50%) residue, objects it did not 39/46 (84.8%) Net 39 gained against 2 lost. The orbits are the same ones -- median |da/a| against the old selection is 1.7e-4 -- so this is a convergence improvement rather than a different answer. Closes #509.
The span selection exists to shorten over-wide triplets on long arcs. When the whole segment already fits inside the ~60 day target there is nothing to shorten -- the widest triplet is the best available, which is what first/middle/last takes anyway -- so the only thing the selection could change is the middle observation, which is not what it is for. On a short arc that is pure downside. The 3I/ATLAS fixture spans 19 days against the 60 day target, so both selections take the same outer pair; moving the middle point alone shifted the fit epoch by 8 days and cost 1% in position and 1.5% in velocity against JPL Horizons, on a weakly-constrained hyperbolic orbit. Caught by tests/layup/test_3i_atlas_validation.py, which now passes. The long-arc behaviour is unchanged, so the measured results stand: the regression sample is objects the old selection already fit, and the residue objects are long-arc by construction.
The fit epoch is the middle observation of the selected triplet, so choosing the triplet by time span moves it. Two of the three real-data objects shift: 119839 by 87 days and 742428 by 11 days. 609631 and 3I/ATLAS are unchanged once the short-arc guard is in. Both references were re-queried from JPL Horizons at the new epochs, at the full precision the epoch assertion needs, using the recipe recorded in the file's own _comment_. The fits were checked against the new states BEFORE they were stored: 119839 agrees to 3.8e-7 and 742428 to 3.9e-7 in relative position. So this is an epoch change, not a loosened comparison -- which matters, because regenerating a reference is exactly how a real regression gets hidden. That is not hypothetical here: before the short-arc guard, 3I/ATLAS was off by 1% in position, and regenerating its reference would have made that pass silently.
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Gauss truncates the Lagrange f and g series, so the interval between the outer two observations has to be short against the orbital period -- classically well under 60 degrees of mean anomaly. We were taking the first, middle and last observation of
seq[0], andseq[0]is by construction the longest-span chunk, so on a long arc the triplet was as wide as it could possibly be. Objects that fail to converge cold span a median 53 degrees of mean anomaly against 29 for those that fit.This picks the triplet whose outer span is nearest a target instead.
The target is in mean anomaly, which needs a period, which needs the orbit we are trying to find. It is converted to days using an assumed a = 2.5 au rather than the object's own -- about 60 days -- which keeps it a prior rather than an oracle. Using each object's published a is slightly worse, so there is no chicken-and-egg problem here.
A balance guard requires each sub-interval to be at least 10% of the outer span. Without it a repeated epoch can leave the middle observation sitting on an endpoint, giving a zero-length interval and no usable root. Where no triplet qualifies, the old first/middle/last choice is used, so behaviour is never worse than before.
Measured cold on objects from the MPC catalog:
Net 39 gained against 2 lost. The orbits are the same ones -- median |da/a| against the old selection is 1.7e-4 -- so this is a convergence improvement, not a different answer. Median runtime 2.8 s on the regression sample.
Worth noting for the issue: #509 proposed pooling several spans and trying each. We measured that at -13.9 points, nearly 5x the cost. Choosing the interval beats trying every interval.
Tests: 87 pass (36 IOD/Gauss, 51 wider fit suite).
Closes #509.