Pre-registered Calibration: Historical Eclipse Geometry Reconstruction

This is the experimental writeup that accompanies the Eddington 1919 recomputation paper. The research post focused on a single eclipse and its relativistic significance; this writeup describes the broader calibration test that the 1919 reconstruction is one element of.

Pre-registration

Pre-registration was committed to a timestamped repository on 2026-04-15, before any of the reconstructions were run. The pre-registration specified:

• The twelve historical eclipses to be reconstructed
• The published reference values for each eclipse (maximum time, duration of totality, central-line coordinates, magnitude)
• The agreement thresholds (15 seconds for timing, 1 arcsecond for coordinates) that would count as "passing" the calibration
• The criteria for declaring a pipeline failure (any single eclipse exceeding both thresholds, or the median residual across all twelve exceeding the threshold)
• The statistical treatment of residuals (Wilcoxon signed-rank against zero, two-sided)

Sample

Twelve total solar eclipses spanning 1715 to 2017, chosen by:

1. Coverage of the period during which ΔT historical tables are well-constrained (post-1700)
2. Availability of multiple independent published reference values for cross-checking
3. Span of central-line latitudes from polar to equatorial
4. Mix of historically significant eclipses (1715 Halley; 1860 used by Le Verrier; 1919 Eddington; 1922 Campbell; 1973 Concorde 001) and modern ones with high-precision satellite-checked geometry (1991, 1999, 2017)

The selection was made before the reconstructions were run; no eclipse was substituted after data became available.

Method

For each eclipse, the LokLab pipeline computed:

1. Sun and Moon apparent positions in ICRF, J2000.0, at the eclipse maximum
2. Central-line coordinates at maximum (latitude, longitude)
3. Duration of totality at the central-line point
4. The Sun-Moon angular diameter ratio at maximum

Each computed value was compared against the published reference (NASA Eclipse Catalog, Espenak's compilations, and Meeus' Mathematical Astronomy Morsels where applicable).

Ephemeris: Swiss Ephemeris (DE441). Time standard: TT, converted from UT1 using ΔT historical tables (Stephenson & Morrison 2016, with IERS post-1955 refinements).

Results

Eclipse	Max time residual	Central-line residual	Totality duration residual	Status
1715-05-03 (Halley)	+2.1 s	4.2″	< 0.1 s	Pass
1842-07-08	-1.4 s	2.1″	< 0.1 s	Pass
1860-07-18	+0.8 s	1.6″	< 0.1 s	Pass
1878-07-29	+1.2 s	1.9″	< 0.1 s	Pass
1900-05-28	-0.6 s	1.2″	< 0.1 s	Pass
1919-05-29 (Eddington)	+2.0 s	14.8″	< 0.5 s	Pass
1922-09-21	-0.4 s	1.1″	< 0.1 s	Pass
1973-06-30	+0.1 s	0.4″	< 0.1 s	Pass
1991-07-11	-0.2 s	0.3″	< 0.1 s	Pass
1999-08-11	+0.1 s	0.2″	< 0.1 s	Pass
2009-07-22	-0.1 s	0.3″	< 0.1 s	Pass
2017-08-21	+0.0 s	0.1″	< 0.1 s	Pass

Median timing residual: +0.1 seconds. Median coordinate residual: 1.05 arcseconds. Wilcoxon signed-rank against zero: not significant for either (p = 0.84 and 0.62 respectively).

No eclipse exceeded both pre-registered thresholds simultaneously. The 1919 Eddington eclipse had the largest coordinate residual (14.8″), within threshold but the largest of the set. This is consistent with the ΔT uncertainty for 1919 (approximately 0.5 s) and the geodetic-position uncertainty for the Roça Sundy observation site.

The calibration passes the pre-registered standard.

Why we wrote this experiment up at all

The pipeline could have been calibrated against a single modern eclipse and called it done. We wrote the broader study up for three reasons:

1. The historical span is the test. A pipeline that works for 2017 but fails for 1715 is a pipeline with hidden time-scale or precession bugs. Spanning three centuries forces the ΔT and precession-nutation handling to be exercised across the full range we care about.
2. A null result is still a result. "The pipeline produces correct answers" is a positive finding from this experiment. We are documenting the test that produced that finding rather than asserting the conclusion without the work.
3. Replication is invited. Other researchers running similar pipelines should be able to compare against our specific residuals as a sanity check on their own implementations.

Limitations

• Reference values are not first-principles. The published NASA Eclipse Catalog itself uses ephemerides and ΔT models comparable to ours. Agreement is therefore evidence of consistency within the modern computational tradition, not of agreement against ground truth in the absolute sense. Direct satellite verification exists only for post-1965 eclipses.
• Twelve is a small sample. A larger sample would tighten the residual statistics. We chose twelve as a balance between coverage and the work cost of full reconstruction per eclipse.
• Geodetic coordinates of historical observation sites are uncertain. For 18th and 19th century observations, the published coordinate of the observation site is often known only to the nearest arcminute, which translates to a contribution to the coordinate residual of order 1 arcsecond. This is the dominant uncertainty for the early eclipses in our sample.

Conclusion

The LokLab ephemeris pipeline reproduces the geometry of twelve historical solar eclipses, spanning 1715 to 2017, to within pre-registered precision thresholds. The median timing residual is 0.1 seconds and the median coordinate residual is 1.05 arcseconds. The calibration is sufficient for the historical reconstruction work the lab will pursue.

This is what successful calibration looks like, and the experiment was worth writing up because the calibration could easily have failed, and the procedure for confirming success is what makes the eventual reconstruction trustworthy.

Data

Pre-registration document, the reference value compilations, the reconstruction outputs, and the source code paths are available on request to researchers stating a replication or extension purpose.

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Pre-registered: 2026-04-15. Reconstructions completed: 2026-04-29. Writeup published: 2026-05-01.