Computing Solar Eclipses — Research

Open questions

workingupdated 2026-09-30
  • The code behind the SVS maps is unpublished. The paper's SPICE examples and released shapefiles provide public reference products. Observed contacts supply independent checks. 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.
  • Some program inputs lack a complete public description. Occult's installed help is needed for its input policy. The cited Solar Eclipse Maestro help does not specify its ephemeris and ΔT, and timeanddate's accuracy page does not name its ephemeris, kk or ΔT source. Jubier's client constants are documented in the software note 4 5 6.
  • Two standard texts are cited only through implementations: Meeus's Elements of Solar Eclipses 1951-2200 and chapter 11 of the 2013 Explanatory Supplement.
  • The end-to-end limb-and-terrain pipeline needs numerical validation. Catalogue comparisons are available for Meeus's series and Kluepfel's Saros formula. The other stages need the named table, contact and polygon fixtures before they can claim product accuracy 7 8.

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. The umbra_hi polygons are reference products, and the stage 8 design is a reconstruction 1 9.

  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. These reductions would help test the radius and detection conventions. A change of 0.05 arcseconds is about 100 m in the cited edge geometry, rather than a universal bound for every path limit 10 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 10 11.

  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 4 12.

  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. Transcribe its original components and compare them with the modern centre-of-figure and limb-sampling terms already tabulated in the error budget 13 14.

  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 15.

  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 16 17.

  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 18.

  9. Smith and colleagues 2010 and Barker and colleagues 2016. The LOLA centre-of-figure vector and the SLDEM2015 mean radius are secondary values, reported secondhand and unconfirmed against the primary publications 19 20.

  10. A refraction number. The cited sources do not quantify a general physical contact-time shift at Sun altitudes of 2 and 5 degrees. A specified atmosphere and ray-traced finite-distance geometry are needed before assigning a correction. A common angular remapping of both limbs alone preserves contact 21.

  11. The undocumented NASA CSV columns PNS, UNS, NCN, nSer, nSeq, nJLE, which appear to encode limits and Saros sequence 22.

  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 23 24 6.

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 11.
  • Compare a LOLA-derived DSK silhouette with the profile-based test. gfoclt_c supports DSK paired with POINT and the ANY condition. It does not support a DSK Moon paired with an ellipsoid Sun for FULL or ANNULAR intervals. Finite-disc contacts need a separate limb-containment implementation. Use two ellipsoids with gfoclt_c for a smooth baseline 25.
  • 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). The sources compared here do not give this observer-and-libration average 26.
  • 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 27.

References

  1. 1peer-reviewed Wright, E. and Young, C. A. 2024, A Raster-oriented Method for Creating Eclipse Maps, AJ 168, 163 Original publisher PDF preserved in Wayback snapshot 2024-11-19. Sections 4-6 and Appendix A checked 2026-09-30. 0.02 degree bins imply about 600 m along the Moon, not Earth edge accuracy. Printed broken-annular criterion needs common angular normalisation. PDF SHA256 5c07500302a852e21439b0cfe8b4a94c423fd92ca3315918818009d4cbf26447. CC BY 4.0.
  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. 4company 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.
  5. 5company Jubier: Solar Eclipse Maestro for MacOS X Fetched with curl. Version 1.9.0v1 (2019-06-09), donationware, Baily's beads preview, camera control, macOS up to Mojave only.
  6. 6company 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.
  7. 7trade 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.
  8. 8trade van Gent R. H., A Catalogue of Eclipse Cycles, list of eclipse cycles Read live 2026-09-15 via curl and text extraction. Source of the Kluepfel 1985 algorithm for the Saros number from the lunation number, the lunation-number offsets (Brown -953), the odd/even node rule, series lengths 1226 to 1550 years, and the k = m I + n S statement. Verified against all 11,898 NASA rows.
  9. 9primary 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.
  10. 10trade 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.
  11. 11primary 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.
  12. 12peer-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.
  13. 13peer-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.
  14. 14peer-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.
  15. 15survey 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.
  16. 16primary 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.
  17. 17peer-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.
  18. 18peer-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).
  19. 19peer-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.
  20. 20peer-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.
  21. 21peer-reviewed Explanatory Supplement to the Astronomical Almanac, P. K. Seidelmann ed. (University Science Books, 1992) Sections 2.553, 3.244, 3.283, 3.351, 3.352, 7.3, 8.12, 8.342, 8.353, 8.362 and 8.363 read from archived original OCR. Section 8.363 reread on 2026-09-30: the OCR gives a negative longitude correction and labels longitude eastward, followed by table interpolation. Typeset page 467 is not confirmed here. This transcription is not used for the independently derived NASA/JSEX fixed-TT east-longitude sign. Downloaded HTML/OCR capture SHA256 f43edb6c9a5c287a00ba87d8f5a27090be75ddd4e026ff009fe8449dae834e9d.
  22. 22primary 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.
  23. 23company 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.
  24. 24company 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.
  25. 25primary NAIF, CSPICE gfoclt_c documentation Read Detailed_Input and Exceptions 9 and 14 on 2026-09-30. Finite-disc FULL/ANNULAR/PARTIAL supports two ellipsoids. DSK requires a POINT partner and ANY. ELLIPSOID Sun with DSK Moon is unsupported.
  26. 26primary 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).
  27. 27primary 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.