Computing Solar Eclipses — Research

Catalogues and types

workingupdated 2026-09-15cataloguescanonsaroseclipse-typesenumeration
  • Meeus's series finds all of them. Chapter 52 of the 1991 Astronomical Algorithms needs no ephemeris, finds all 221 eclipses of 1951 to 2050 and types every one correctly, with a worst error of 1.11 min in the time of greatest eclipse 1 2.
  • The NASA files are the fixture. One ASCII catalogue of 11,898 rows and one CSV of Besselian polynomial elements for the same eclipses, both from the Five Millennium Canon, are the acceptance test set for any enumerator 2 3.
  • The Five Millennium Catalogue uses a pair of lunar radii. k=0.2724880k = 0.2724880 for all partial and penumbral contacts and k=0.272281k = 0.272281 for all umbral and antumbral ones. The single IAU value 0.2725076, which IMCCE uses, misclassifies beaded annular eclipses as total 4 5.
  • Type is decided by the umbral radius at the surface, not on the fundamental plane. Evaluating it at greatest eclipse and at both ends of the central line is what separates the three hybrid classes and the 94 non-central eclipses of five millennia 4 6.
  • ΔT, not the ephemeris, sets the accuracy floor. The catalogue's own statement is that the lunar ephemeris stays below map resolution even at −1999-1999, while the standard error in ΔT exceeds 265 s before +0001 and after +2300, which is more than a degree of longitude 7.

What this topic covers

The three questions a developer meets before any path or contact time is computed. Which new moons produce an eclipse at all, by a closed-form series, an ephemeris minimum-distance search or a full Besselian computation. What type each one is, from the inequalities in γ\gamma and the umbral radius, including the central, non-central and hybrid classes and the meaning of every column a catalogue prints. And where a trustworthy list already exists, in what format, with its ephemeris, its ΔT model and its lunar radius stated.

Notes in this topic

  • Enumerating eclipses: the Meeus approximate search, the ephemeris-based search, the method behind the Five Millennium Canon, Saros and Inex numbering, and the accuracy limits set by ΔT.
  • Types and classification: the inequalities in γ\gamma and uu that separate partial, annular, total, hybrid, central and non-central eclipses, and the definition of every quantity a catalogue lists.
  • Canons and data products: NASA GSFC, IMCCE, HMNAO, EclipseWise, Jubier, Occult, machine-readable files, open-source enumerators, and the older canons from Oppolzer to Mucke and Meeus.

What this topic changes for the pipeline

Enumeration is solved and cheap, so the pipeline runs a Meeus pre-filter into a Besselian stage rather than building a search of its own. Classification is not a post-processing label: it depends on kk and on where along the path the umbral radius is evaluated, so the enumeration stage carries only a provisional type and the final type is assigned in the Besselian stage. Every exported row carries a provenance record naming the ephemeris, the ΔT model and the kk pair, because the only widely mirrored element set carries no statement of its own constants.

References

  1. 1trade Meeus J. (1991) Astronomical Algorithms, first edition, Willmann-Bell, Chapter 52 Eclipses Read from the Internet Archive OCR text (chapter 52 in the 1991 edition, chapter 54 in the 1998 edition). Source of the |sin F| > 0.36 rule, the corrections to the time of maximum, P, Q, W, gamma, u, the thresholds 0.9972, 1.0260, 1.5433, 0.0047, 0.00464, the partial-magnitude formula and the stated accuracy of 0.36 min mean and 1.1 min maximum for 1951 to 2050. Graded trade as a recognised practitioner's own algorithm text.
  2. 2primary NASA GSFC, Five Millennium Catalog of Solar Eclipses, ASCII table 5MKSEcatalog.txt (2008 Oct 07) Downloaded (1.38 MB, 11,908 lines) and parsed: all 11,898 rows, type counts 4200/3956/3173/569, type-code tallies, per-century counts, gamma ranges per class, and the Kluepfel Saros formula and the Meeus chapter 54 method were verified against it.
  3. 3primary NASA GSFC, Besselian elements for all 11,898 eclipses of the Five Millennium Canon, CSV export Downloaded (5.95 MB, 11,899 lines). Header read: catalog columns plus t0, cubic x and y, quadratic d, mu, l1, l2, tan f1, tan f2, tmin -3 to tmax +3 h, and six undocumented trailing columns PNS, UNS, NCN, nSer, nSeq, nJLE.
  4. 4primary Espenak F., Meeus J. (2009) Five Millennium Catalog of Solar Eclipses: -1999 to +3000 (Revised), NASA/TP-2009-214174 Read in full as PDF text (20,579 lines). The main method source: column definitions (1.2), VSOP87D and truncated ELP-2000/82 (1.3), n-dot -25.858 and correction c (1.4), k = 0.2724880 and 0.272281 (1.5), Delta T polynomials (2.7), uncertainty (2.8), statistics (3), Saros and Inex (5).
  5. 5primary IMCCE and Observatoire de Paris, Le canon de l'IMCCE : les parametres physiques Read live 2026-09-15 via curl. Solar semidiameter 15'59.63", k = 0.2725076, equatorial radius 6,378,140 m, e^2 = 0.00669438, 1/f = 298.257.
  6. 6company Astrodienst, Swiss Ephemeris source swecl.c (AGPL or commercial) Source read via the GitHub API (6,428 lines). Quoted: constants DSUN, DMOON, DEARTH, the eclipse_where central and non-central tests, the K lunation seed, the dt bracketing search, and the annular-total detection by sign change of the core diameter.
  7. 7primary Espenak F., Meeus J. (2006) Five Millennium Canon of Solar Eclipses: -1999 to +3000, NASA/TP-2006-214141 Read in full as PDF text (2,625 lines). Sections 1.3 to 1.6 give ephemerides, secular acceleration, k values and the map-accuracy statement with the reference-gore example for -1996 Oct 04. Note the Text10 link on the NASA publication page returns 404, Text11 is the live file.

In this section

Enumerating eclipsesThree ways to list every solar eclipse in a period, the method and constants behind the NASA Five Millennium Canon, Saros and Inex numbering, and the accuracy ceiling set by ΔT.workingTypes and classificationThe inequalities in gamma and the umbral radius that separate partial, annular, total, hybrid, central and non-central eclipses, and the definition and derivation of every quantity a catalogue lists per eclipse.workingCanons and data productsWhere the eclipse lists live, in what format, with which ephemeris and ΔT, which open-source code enumerates eclipses, and what the older canons from Oppolzer to Mucke and Meeus contain.working