Computing Solar Eclipses — Research

Open questions

workingupdated 2026-09-16
  • The code behind the SVS maps is unpublished. The paper's ten lines of SPICE calls and the released shapefiles are the only ground truth. A release would let the pipeline design be checked line by line 1.
  • The 2024 solar radius is unsettled by the data that could settle it. The IOTA reductions of the 2023 and 2024 bead videos are not yet published, and the 2024 limit observations collected by the Besselian Elements team have no published reduction 2 3.
  • Three sources are unavailable: Occult's help file, distributed only inside the Windows installer; Solar Eclipse Maestro's statement of its ephemeris and ΔT, which its help pages omit; and timeanddate's ephemeris, kk and ΔT source, which its accuracy page does not name. Jubier's browser calculator is public, and its constants are in the software note.
  • Two standard texts are cited only through implementations: Meeus's Elements of Solar Eclipses 1951-2200 and chapter 11 of the 2013 Explanatory Supplement.
  • Only the enumeration is independently reproduced. Meeus's series and Kluepfel's Saros formula are implemented and checked against the NASA catalogue; every Besselian, limb and terrain number is quoted from its source. The first act of any implementation is to reproduce the reference cases.

Ranked by how much a different answer would move the design

  1. The SVS source code, or an author statement of the 2024 run's ΔT, ephemeris and Earth DEM resolution. The paper names DE440 and the product pages name DE421; the ΔT is inside an Earth-orientation kernel; the map pixel size is unstated. The SVS API JSON for page 5123 would settle it. Until then the umbra_hi polygons are the ground truth and the stage 8 design is a reconstruction 1 4.

  2. A published reduction of the 2024 edge observations. Irwin and Quaglia's team collected limit observations in 2024, and IOTA's Solon, Maine recording is promised for the Journal for Occultation Astronomy. Either would decide whether 959.95″ or a value nearer 960.0″ is the default, which moves every edge-mode limit by up to 100 m 5 3.

  3. A quantitative SVS-against-Irwin comparison. Difference Irwin's 2024 limit polylines, or the Besselian Elements app's output, against SVS upath_hi at fixed longitudes. Dunham measured the Jubier-to-Irwin offset at 0.7 km; the SVS-to-Irwin offset is inferred, not measured 5 6.

  4. Occult 4's help file. It is distributed inside the Windows installer and holds the limb dataset, the datum radius, the solar radius default, the bead definition and the ΔT policy of the program the occultation community treats as the reference. Its 2 s offset from Irwin's model at Vale is unexplained without it 7 8.

  5. Herald 1983's error budget should be transcribed in full. The 1992 Supplement points to it for "the total effect and its components" of the limb. The centre-of-figure and limb-sampling terms remain unquantified 9 10.

  6. Meeus, Elements of Solar Eclipses 1951-2200. Its local-circumstances chapter, its sampling scheme, its treatment of nutation in μ and of the Sun's aberration. Photo Ephemeris and several ports rest on it, and it is cited only through them 11.

  7. Explanatory Supplement 2013, chapter 11. Whether the μ convention, the ellipsoid, the recommended kk or the height formulas changed from 1992, and the exact text of equations 11.56 to 11.94 that Stellarium transcribes 12 13.

  8. Morrison, Stephenson, Hohenkerk and Zawilski 2021 and HMNAO Table S15.2020. The current ΔT sigmas by year, to replace the 2004 rule in the error budget 14.

  9. Smith and colleagues 2010 and Barker and colleagues 2016. The LOLA centre-of-figure vector and the SLDEM2015 mean radius are secondary values, unconfirmed against the primary publications, neither of which is accessible 15 16.

  10. A refraction number. No published source quantifies the effect of standard refraction on first and fourth contact at Sun altitudes of 2° and 5° in seconds. A ray-traced test case would replace the bound derived in the Earth-and-time note 17.

  11. The undocumented NASA CSV columns PNS, UNS, NCN, nSer, nSeq, nJLE, which appear to encode limits and Saros sequence 18.

  12. Jubier's ephemeris and timeanddate's inputs. Jubier's 2024 page carries the Five Millennium Canon coefficients with his own ΔT of 69.1 s, and the limb correction is computed server-side (Watts charts when the libration in latitude exceeds 1.6°, Kaguya otherwise, per the client code), but no page states the ephemeris behind the server. timeanddate's accuracy page names neither its ephemeris, its kk nor its ΔT source 19 20 21.

Experiments that require no further sources

  • Reproduce one SVS 2024 umbra_hi polygon from SLDEM2015 with the limb test as written. This is the end-to-end check of stage 8, and the paper states the method in enough detail to perform it 6.
  • Run SPICE gfoclt_c with a pinpoint surface site, an ellipsoid Sun and a LOLA-derived DSK Moon, and compare its FULL interval with a limb-corrected C2 to C3 from Occult or Solar Eclipse Maestro. If it agrees to a second, a DSK Moon is a second route to a shaped limb 22.
  • Compute from LDEM the mean limb radius averaged over position angle and libration, and compare with 1738.09 km (k=0.2725076k = 0.2725076) and 1736.65 km (k=0.272281k = 0.272281). No published value exists 23.
  • Difference the SVS umbra_hi centre coordinates against Espenak's central line at the same instants to put the ephemeris-plus-ΔT difference in kilometres 24.

References

  1. 1peer-reviewed Wright, E. and Young, C. A. 2024, A Raster-oriented Method for Creating Eclipse Maps, AJ 168, 163 The paper. Read in full from the Wayback capture of the IOP PDF dated 2024-11-19 (iopscience.iop.org/article/10.3847/1538-3881/ad6b23/pdf), extracted with pdftotext. CC BY 4.0. Sections 4 and 5 give the limb-profile construction and the limb test; Appendix A gives the SPICE calls.
  2. 2trade Dunham, D. (2024) April 8th total solar eclipse, the ultimate lunar occultation, updated 2024 May 6 (IOTA) IOTA's 2024 campaign page: Jubier's map uses the 1976 radius, Irwin's 959.95 ± 0.05 limit, the 0.7 km and 10 s corrections, the 2 km umbral-depth rule, and IOTA's retraction of radius variation. Read via curl on 2026-09-15.
  3. 3trade Irwin, J. and Quaglia, L. 2024, Technical Details of the true-limb Eclipse Path Determination, Besselian Elements Page text plus the parameter table image tech_parameters.png (DE440, IAU2006A with EOP, 959.95 arcsec, 1738.091 km, SLDEM2015/LDEM128, Earth2014, EGM96, proprietary EclipseView). Page read via fetch tool, image viewed directly.
  4. 4primary NASA SVS 5123, The 2024 Total Solar Eclipse (2023, updated 2024-04-07) 2024 map page with the same method statement and shapefile list; download path /vis/a000000/a005100/a005123/2024eclipse_shapefiles.zip. Read from Wayback capture 2024-05-06.
  5. 5trade Dunham (2024), April 8th Total Solar Eclipse, the Ultimate Lunar Occultation, IOTA page updated 2024 May 6 Full HTML read from a saved copy (var/downloads/iota.jhuapl.edu_TSE20240408.htm.html). Solon, Maine site 3 km north of the predicted southern limit, 43 s of totality, beads over a minute each side. Compares Jubier's and Irwin's limits and recommends umbral depth of at least 2.0 km. States IOTA's revised view that its earlier solar-radius variations were observational error.
  6. 6primary NASA SVS, 2024eclipse_shapefiles.zip (78.6 MB) Downloaded from Wayback capture 2025-02-12 and parsed: umbra_hi 6741 records at 1 s 17:56:00 to 19:48:20 UTC with 12 attributes; umbra_lo 1181 at 10 s; center, duration, ppath, ppath01, upath_hi, upath_lo; all .prj GCS_WGS_1984.
  7. 7company Occult v4 (David Herald) home page Fetched with curl 2026-09-15. Feature list, C#/.NET 4.5, 42 data files, installer sizes. Eclipse-specific help is inside the Windows help file and was not read.
  8. 8peer-reviewed Quaglia, Irwin, Emmanouilidis & Pessi (2021), Estimation of the Eclipse Solar Radius by Flash Spectrum Video Analysis, ApJS 256:36 Full PDF read (var/downloads/quaglia2021_flash_spectrum_ApJS.txt). Flash-spectrum video from a site a few hundred metres inside the 2017 southern limit near Vale, Oregon. S = 959.95 +/- 0.05 arcsec. Gives sensitivity of duration and limit distance to solar radius, and compares Irwin's model with Occult and Solar Eclipse Maestro.
  9. 9peer-reviewed Herald, D. (1983). Correcting predictions of solar eclipse contact times for the effects of lunar limb irregularities. Journal of the British Astronomical Association 93, 241-246 Read in full from the ADS scan (page images). The displacement-curve method: h = 960 (M-1)(1-cos P), r = 0.97 M n arcsec per second, radial rate r cos(PA-N), the path-limit factor 1.863 km per arcsec times sqrt(sin^2 D / sin^2 a + cos^2 D), the limiting magnitudes for total and annular eclipses, and the error budget.
  10. 10peer-reviewed Seidelmann (ed.) (1992), Explanatory Supplement to the Astronomical Almanac, chapter 8 Eclipses of the Sun and Moon Local scan text read (var/downloads/es1992_djvu.txt). History of the two k values, limb effects of up to two seconds per contact on the central line, and the annotated reference to Herald 1983.
  11. 11survey Jean Meeus, "Elements of Solar Eclipses 1951-2200" (Willmann-Bell, 1989) Not read. The book's local-circumstances chapter is known here only through Jubier's acknowledgement that it supplied the algorithms of his calculator, Photo Ephemeris' method statement, and Bill Gray's review. Its formulation is the Explanatory Supplement one.
  12. 12primary USNO Astronomical Applications Department, The Explanatory Supplement to the Astronomical Almanac (page describing the 2013 third edition) Read. States the third edition is a complete revision of 1992 and links errata. Used only for the status of chapter 11. The 2013 chapter itself was not read.
  13. 13peer-reviewed Urban, S. E. and Seidelmann, P. K. (eds), Explanatory Supplement to the Astronomical Almanac, 3rd edition (2013), chapter 11 Eclipses of the Sun and Moon Not read. Known through Stellarium's citations of equations 11.56, 11.60, 11.65, 11.78, 11.81, 11.82, 11.89 and 11.94 for the zeta(Q) closed form and the maximum-at-horizon iteration.
  14. 14peer-reviewed Morrison, Stephenson, Hohenkerk & Zawilski (2021), Addendum 2020 to Measurement of the Earth's rotation: 720 BC to AD 2015, Proc. R. Soc. A 477, 20200776 Not read (HTTP 403). Known only through citations in the ytliu0/DeltaT README and Hayakawa et al. 2026. Provides spline fits to 2025 and a tabulated uncertainty (HMNAO Table S15.2020).
  15. 15peer-reviewed Smith, D. E. et al. (2010). Initial observations from the Lunar Orbiter Laser Altimeter (LOLA). Geophysical Research Letters 37, L18204 Not read (publisher and mirrors returned 403 or 405). The centre-of-mass to centre-of-figure offset of 1.9347 km toward 7.12 N, 202.38 E and the 10 m radial, 100 m spatial grid accuracy are taken from a search summary and should be verified against the paper.
  16. 16peer-reviewed Barker, M. K., Mazarico, E., Neumann, G. A., Zuber, M. T., Haruyama, J. and Smith, D. E. (2016). A new lunar digital elevation model from the Lunar Orbiter Laser Altimeter and SELENE Terrain Camera. Icarus 273, 346-355 Not read (publisher returned 403). The 512 pix/deg resolution, the 3 to 4 m vertical accuracy, the 1737.4 km reference and the 1737.1512 km mean radius are taken from the PGDA product page, the ODE help page and a search summary of the abstract.
  17. 17peer-reviewed Explanatory Supplement to the Astronomical Almanac, P. K. Seidelmann ed. (University Science Books, 1992) Sections 2.553 (Stephenson and Morrison 1984 parabolas), 3.244 (terrestrial coordinates, MERIT 1983 ellipsoid), 3.283 (low-precision refraction, 34 arcmin horizontal refraction), 3.351 and 3.352 (IAU 1976 ellipsoid, GMST), 7.3 (apparent places include aberration), 8.12, 8.342, 8.353, 8.362 and 8.363 (eclipses: apparent places, shadow radius at height, height above the geoid, refraction as a refinement, the delta-T longitude correction). Read from the archive.org OCR text in var/downloads/es1992_djvu.txt.
  18. 18primary 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.
  19. 19company Jubier: 2024 April 8 Total Solar Eclipse Interactive Google Map Fetched with curl 2026-09-15 (WebFetch refused). The page embeds its own Besselian element array with ΔT = 69.1 s and lists the JavaScript files it loads.
  20. 20company Jubier: EclipseCalculatorGM3_xSE.js (Solar Eclipse Calculator for Google Maps v3) Source read (198 KB, downloaded 2026-09-15). Change log 2007 to 2016, constants, k1/k2 ratio, Watts and Kaguya limb correction hooks, refraction and elevation handling.
  21. 21company timeanddate.com: Accuracy of Eclipse Times (Bikos) Read from a Wayback Machine snapshot (2025) because the live site returned 403. States sea-level assumption, no limb profile, ΔT and solar radius caveats.
  22. 22primary NAIF, CSPICE gfoclt_c documentation Read. Occultation types FULL, ANNULAR, PARTIAL, ANY; shapes ELLIPSOID, POINT, DSK; aberration corrections NONE, LT, CN, XLT, XCN; step size must be shorter than the shortest event; SPICE_GF_CNVTOL convergence; example finds the December 2001 solar eclipse from the geocentre.
  23. 23primary Williams, Boggs, Folkner (2013). DE430 Lunar Orbit, Physical Librations, and Surface Coordinates. JPL IOM 335-JW,DB,WF-20130722-016 Read in full from the PDF. 18,548 LLR ranges 1970-2012, 1.9 cm wrms, DE430 vs DE421 half a milliarcsecond, PA and ME frame definitions, the DE430 rotation Rx(-0.285") Ry(-78.580") Rz(-67.573"), 1" = 8.42 m, LOLA mean radius 1737.151 km (Neumann 2013).
  24. 24primary Path of Total Solar Eclipse of 2024 Apr 08 (NASA GSFC eclipse web site, Espenak) Read. Column headers, 120-second rows, Limits row, footnote Delta T = 70.6 s. First rows quoted verbatim in the data-products note.