Computing Solar Eclipses — Research

Reading list and reference matrix

workingupdated 2026-09-16
  • Read four documents first: Wright and Young 2024 for the state of the art, section 9 of the 1961 Explanatory Supplement for the formulas, Quaglia and colleagues 2021 for the solar radius and the edge sensitivity, and Herald 1983 for the limb correction 1 2 3 4.
  • Read three source files: Stellarium's SolarEclipseComputer.cpp, NASA's program.js, and the Swiss Ephemeris swecl.c. Together they cover elements, every global curve, local circumstances and the geometric alternative 5 6 7.
  • Download eight datasets: NASA's element CSV and ASCII catalogue, the SVS shapefiles, LDEM_128 and SLDEM2015, a terrestrial DEM with its geoid, DE440 with its lunar PCK, and the USNO ΔT files.
  • The Explanatory Supplements and the NASA technical publications are free on archive.org and eclipse.gsfc.nasa.gov. Meeus's Elements of Solar Eclipses and the 2013 Supplement are not, and are cited only through implementations that transcribe them.

Papers and books, in reading order

Order Source Grade What it uniquely provides Note
1 Wright and Young 2024, AJ 168:163 1 peer-reviewed The raster method, the limb-profile construction with bin count and refresh rule, the limb test, the broken-annular criterion, the SPICE calls, the radius survey Open access, CC BY. Sections 4 and 5 are implementable as written
2 Explanatory Supplement 1961, chapter 9 2 peer-reviewed Every formula for elements, global circumstances and local circumstances, with worked examples for 1961 February 15 Free OCR on archive.org; the shortest complete statement
3 Explanatory Supplement 1992, chapter 8 8 peer-reviewed The vector restatement, the flattening auxiliaries, the recommendation of direct root-finding, the warning list on ephemeris consistency, rotation, centre of figure, limb and refraction Free on archive.org; OCR garbles some equations
4 Quaglia, Irwin, Emmanouilidis and Pessi 2021, ApJS 256:36 3 peer-reviewed The eclipse solar radius 959.95″ ± 0.05″, duration-versus-radius curves at the central line and at a limit, the comparison of Irwin's model with Occult and Solar Eclipse Maestro, a fully topocentric limb-based method arXiv 2107.09416
5 Herald 1983, JBAA 93:241 4 peer-reviewed The contact-time correction from a limb profile, the limit displacement factor, the error budget of the Watts era ADS scan
6 Espenak and Meeus 2009, Five Millennium Catalog, NASA/TP-2009-214174 9 primary The enumeration method, the ephemerides and truncation, the two kk values, the ΔT model with its correction, the type classification with counts, Saros tables With the 2006 Canon, NASA/TP-2006-214141 10
7 Espenak and Anderson 2001 bulletin, NASA/TP-1999-209484 11 primary The lunar limb profile and graze zone sections, the kk history, the elevation factor, the Lusaka worked correction Any bulletin from 1994 to 2009 has the same sections
8 Meeus, Astronomical Algorithms, chapter 54 12 trade The approximate enumeration and classification with the thresholds 0.36, 0.9972, 1.5433, 0.0047, 0.00464 1991 edition free on archive.org as chapter 52
9 Stephenson, Morrison and Hohenkerk 2016, Proc. R. Soc. A 13 peer-reviewed The current ΔT spline and parabola, the lengthening-of-day rate, the historical record's scatter Open access
10 Park, Folkner, Williams and Boggs 2021, AJ 161:105 14 peer-reviewed DE440 and DE441: LLR residuals, frame, the recommendation of DE440 for 1550 to 2650 With Williams, Boggs and Folkner 2013 for the PA and ME frames 15
11 Morrison and Appleby 1981, MNRAS 196:1013 16 peer-reviewed The systematic corrections to Watts' datum, needed only to reproduce historical bulletins ADS scan
12 Lamy and colleagues 2015, Solar Physics 290:2617 17 peer-reviewed The largest homogeneous eclipse radius dataset, 959.99″ ± 0.06″ from 17 light curves
13 Haberreiter, Schmutz and Kosovichev 2008, ApJ 675:L53 18 peer-reviewed Why the inflection-point radius exceeds the seismic radius by 0.33 Mm, the basis of the IAU nominal value arXiv 0711.2392
14 Prša and colleagues 2016, AJ 152:41 19 peer-reviewed What the IAU 2015 nominal radius is and is not The reason not to use astropy's constant
15 Fiala, Dunham and Sofia 1994 20 peer-reviewed The IOTA edge method for solar radius from beads, results 1715 to 1987
16 Guhl and Tegtmeier 2018 and Guhl 2023, Journal for Occultation Astronomy 21 22 trade Per-bead residual tables for 2017 and 2023 with Occult, LOLA and Kaguya The bead-level validation cases
17 Rozelot and Kosovichev 2026, arXiv 2605.23794 23 preprint The only review tabulating canonical, nominal, seismic and eclipse radii side by side

Code, in reading order

Order Code Licence What to read it for Constants
1 Stellarium src/core/SolarEclipseComputer.cpp 5 GPL-2.0 Elements from an ephemeris, central line, limits, outlines, rise and set curves, KML export, with 2013 Supplement equation numbers in comments kk 0.2725076 and 0.272281, Sun 696,000 km, Earth 6378.1366 km
2 NASA JavaScript Solar Eclipse Explorer program.js 6 GPL-2+ The 1961 local-circumstances method in 1,200 lines: observer constants, hour angle with ΔT, Newton iteration for contacts, magnitude branches, lens obscuration, P and V b/a=0.99664719b/a = 0.99664719, a=6378140a = 6378140 m, ΔT/13713.44
3 Swiss Ephemeris swecl.c 7 AGPL or paid The geometric alternative: eclipse_where for the central point, eclipse_how and eclipse_when_loc for topocentric contacts with a bracketed search, an explicit error budget in the comments Moon 3476.3 km, Sun 1,392,000 km, factor 0.99916 for interior contacts
4 Astronomy Engine 24 MIT A second independent enumerator in five languages, shadow axis against a dilated sphere Sun 695,700 km, Moon 1737.4 km
5 Eclipse-Engine 25 AGPL-3.0 Rasterised obscuration contours, antimeridian and pole pitfalls, the 15.041″/s ΔT rule Elements fitted to DE440s, fitting code unpublished
6 tomasrojasc/eclipse-2026 26 none stated The only open LOLA bead construction, with the correct orientation kernel, for one eclipse LDEM_16, moon_pa_de421
7 tahze0/solar-eclipse-explorer 27 MIT A template for catalogue-scale validation against the NASA CSV 0.26 percent median width error over 300 eclipses
8 Eclipse-Engine, 2027 visualiser and besselian 28 29 30 mixed Compact ellipsoid formulations in JavaScript and Python, three-time validation against NASA tables WGS84, k2=0.272281k_2 = 0.272281

Datasets

Dataset Owner Format and size Use Source
Besselian elements CSV, 11,898 rows, 54 columns NASA GSFC CSV, 5.95 MB Regression fixture for stage 3; carries t0t_0 and ΔT but not kk or the ephemeris 31
Five Millennium ASCII catalogue NASA GSFC text, 11,898 rows Fixture for stages 2 and 3: types, γ, magnitude, Saros 32
SVS 2017, 2023 and 2024 shapefiles and cities JSON NASA SVS zipped shapefiles, KML, JSON Ground truth for limb-and-terrain umbra polygons at 1 s and for city contact times 33 34
LOLA LDEM_128 NASA PDS PDS3 IMG, 2.12 GB, 128 ppd, 237 m Development limb dataset; 0.13″ per cell 35
SLDEM2015 and polar LDEM tiles NASA PDS PDS3 IMG, 512 ppd, 60 m, 3 to 4 m vertical Production limb dataset with polar coverage above 60° 36
SRTM GL1 or Copernicus GLO-30, with EGM96 or EGM2008 NASA LP DAAC, ESA HGT or cloud-optimised GeoTIFF Terrain stage; orthometric heights need the geoid 37 38
de440s.bsp, moon_pa_de440_200625.bpc, moon_de440_250416.tf (the 2025 revision of the moon_de440_200625.tf the paper cites) NAIF SPK 31 MB, binary PCK, frame kernel Ephemeris and lunar orientation in the ME frame 39 40
deltat.data, deltat.preds, finals.all USNO, IERS text ΔT measured and predicted with errors, UT1 and polar motion 41 42 43
Watts charts, VizieR VI/122 CDS table Only to reproduce pre-2009 bulletins, with the Morrison and Appleby corrections 44

Reference products for validation

Level Case Values Tolerance Source
1 1961 February 15, 08h ET ϕ=+44∘18′.3\phi = +44^{\circ} 18'.3, λ=−29∘20′.9\lambda = −29^{\circ} 20'.9, duration 158.6 s last printed digit on the same elements 45
1 2017 August 21 greatest eclipse, EclipseWise 18:26:40.3 TD, width 114.7 km, duration 2m40.12s, DE405, ΔT 68.8 s 0.1 s, 0.1 km 46
2 Lusaka 2001 June 21, smooth Moon C2 13:09:19.3 UT, C3 13:12:32.8 UT 0.5 s 47
3 Lusaka with limb corrections +4.0 s at C2, −1.2 s at C3 1 s (Watts against LOLA) 47
4 Vale, Oregon, 2017, 711 m C2 17:25:34.3, C3 17:26:06.9 UTC at 959.63″; limit distance 1200 m falling under 400 m at 960.00″ 2 s, 100 m 3
4 Stephenville, Texas, 2024 observed C2 18:39:06.6, C3 18:39:20.3 UTC, 13.7 s 3 s with true limb and 959.95″; about 24 s expected at 959.63″ as a negative control 48
5 Thermopolis 2017 and Cape Range 2023 bead tables 16 events each with axis angles and times 1 s per event at the derived radius correction 21 22

Where the raw notes go deeper

Each topic folder ends with a "Sources compared" table and a "What a developer should do" section. The foundations and local circumstances notes quote the formulas; the lunar limb and SVS notes quote the algorithm; the software note has the thirty-row repository matrix; the validation note has the five-level protocol in full.

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. 2peer-reviewed Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac (1961), section 9B Eclipses and Transits Read in full (OCR text). Definitive almanac formulation: fundamental plane, point Z, x y z, mu from ephemeris sidereal time, sin f1 sin f2 with tabulated numerators for k = 0.272274, 0.2724807, 0.272281 and 0.2724880, c1 c2 l1 l2, sign convention, observer coordinates, ephemeris meridian 1.002738 ΔT, worked example 1961 Feb 15.
  3. 3peer-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.
  4. 4peer-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.
  5. 5company Stellarium src/core/SolarEclipseComputer.cpp Read from a sparse clone at commit 69888f4 (2026-09-14). 2,183 lines. Besselian elements, k and s constants, Explanatory Supplement references, KML and PNG map export.
  6. 6primary JSEX program.js (JavaScript source of the Solar Eclipse Explorer) Source read in full (36.8 KB, downloaded 2026-09-15). GPL v2+. Contains the local-circumstance algorithm, the observer geocentric constants and the crude refraction handling.
  7. 7company Swiss Ephemeris swecl.c (eclipse routines) Read from a depth-1 clone at commit 9083a12 (2026-09-14), SE_VERSION 2.10.03. Functions eclipse_where, eclipse_how, eclipse_when_loc and their constants and comments.
  8. 8peer-reviewed Seidelmann, P. K. (ed.), Explanatory Supplement to the Astronomical Almanac (1992), chapter 8 Eclipses of the Sun and Moon, sections 8.31 to 8.36 Read sections 8.31 to 8.333 in OCR text. Rotation-matrix form 8.322-3, unit vectors 8.322-5, mu = Greenwich apparent sidereal time minus a, cone equations 8.323-1 to 8.323-7, summary of elements 8.324, practical note 8.325, observer coordinates and flattening auxiliaries 8.331 to 8.333. Ellipsoid a = 6378.137 km, f = 1/298.257 from equation 3.244-1. Chapter author not shown in the scan.
  9. 9primary 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).
  10. 10primary 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.
  11. 11primary Espenak, F. and Anderson, J. (1999). Total Solar Eclipse of 2001 June 21. NASA/TP-1999-209484 Read from the local PDF text. Sections Mean Lunar Radius, Lunar Limb Profile and Limb Corrections to the Path Limits: Graze Zones. Source of the two k values, equations [8] and [9], the Lusaka worked example, Table 6 path corrections, the 5 to 10 km graze zone and the interior/exterior graze definitions.
  12. 12trade 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.
  13. 13peer-reviewed Measurement of the Earth's rotation: 720 BC to AD 2015, F. R. Stephenson, L. V. Morrison and C. Y. Hohenkerk, Proc. R. Soc. A 472, 20160404 (2016) Full text read via the Europe PMC XML (PMC5247521), saved as var/downloads/smh2016.txt. Parabola -320.0 + (32.5 +/- 0.6)((year-1825)/100)^2 s, lod +1.78 +/- 0.03 ms/cy observed against +2.3 +/- 0.1 ms/cy tidal, DE430 tidal acceleration -25.82 arcsec/cy^2, spline knots at 5 and 3 year intervals after 1800, IERS TAI-UT1 used as control 1962 to 2015.
  14. 14peer-reviewed Park, Folkner, Williams, Boggs (2021). The JPL Planetary and Lunar Ephemerides DE440 and DE441. Astronomical Journal 161, 105 Open-access HTML read through the fetch tool's extraction, not the PDF. Spans, geodetic precession on librations, LLR to 2020 March, 20 cm early and 1.3 cm recent rms, ICRF3, libration angles stored in the files, DE440 for modern data and DE441 for historical.
  15. 15primary 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).
  16. 16peer-reviewed Morrison, L. V. and Appleby, G. M. (1981). Analysis of lunar occultations III. Systematic corrections to Watts' limb-profiles for the Moon. MNRAS 196, 1013-1020 Read in full from the ADS scan (OCR text). Source of the harmonic correction formula, the 1737.97 km datum radius, the +0.04 arcsec radius term, the -0.18 arcsec latitude shift, the -0.09 arcsec ellipticity, the +0.50 arcsec sin Q centre-of-figure term, and the 0.4 arcsec peak error.
  17. 17peer-reviewed Lamy, P., Prado, J.-Y., Floyd, O., Rocher, P., Faury, G. and Koutchmy, S. (2015) A novel technique for measuring the solar radius from eclipse light curves: results for 2010, 2012, 2013, and 2015. Solar Physics 290, 2617 Seventeen photometer light curves at 540 nm with Kaguya limb profiles: 959.99 ± 0.06 arcseconds (696,246 ± 45 km). Abstract read on the Springer page; full text paywalled.
  18. 18peer-reviewed Haberreiter, M., Schmutz, W. and Kosovichev, A. G. (2008) Solving the discrepancy between the seismic and photospheric solar radius. ApJ 675, L53 Inflection point lies 0.347 ± 0.006 Mm above tau5000 = 1 and 0.333 ± 0.008 Mm above tauRoss = 2/3; photospheric radius 695.66 Mm. Abstract read on arXiv and Semantic Scholar.
  19. 19peer-reviewed Prša, A. et al. (2016) Nominal values for selected solar and planetary quantities: IAU 2015 Resolution B3. AJ 152, 41 Defines the nominal solar radius 6.957e8 m and explains that it is the rounded Haberreiter et al. value 695,658 ± 140 km at Rosseland optical depth 2/3. Full arXiv PDF read.
  20. 20peer-reviewed Fiala, A. D., Dunham, D. W. and Sofia, S. (1994). Variation of the solar diameter from solar eclipse observations, 1715-1991. Solar Physics 152, 97-104 Read pages 97-102 from the ADS scan. Describes the IOTA edge-observation method (Sofia, Dunham and Fiala 1979), its dependence on Watts data, and Table II of solar-radius corrections per eclipse relative to 959.63 arcsec.
  21. 21trade Guhl & Tegtmeier (2018), Baily's Beads Observations during the Total Solar Eclipse 2017 August 21, Journal for Occultation Astronomy 2018-3, pp. 19-21 Full PDF read (var/downloads/JOA2018_3.txt). Two IOTA/ES stations, Thermopolis WY 700 m inside the northern limit and Cape Girardeau MO region. Bead-by-bead radius residuals reduced with Occult 4.5.3.0 using LOLA and Kaguya.
  22. 22trade Guhl (2023), Baily's Beads Observation during the Hybrid Solar Eclipse 2023 April 20, Journal for Occultation Astronomy 2023-4, pp. 12-15 Full PDF read (var/downloads/JOA2023_4.txt). Northern limit of the total segment, Cape Range, Western Australia. Sixteen bead timings, mean correction +0.38 arcsec, result 960.01 +/- 0.12 arcsec.
  23. 23preprint Rozelot, J.-P. and Kosovichev, A. (2026) Sharper Than Ever: Do Modern Observations Pin Down the Solar Radius to Converge on New Standards? arXiv:2605.23794 Review tabulating canonical, seismic, photospheric, eclipse and nominal radii with km and arcsecond values and a proposed glossary. Full PDF read. Contains a typo giving the canonical value as 965.63.
  24. 24company Cross D., Astronomy Engine, source file source/c/astronomy.c (MIT) Source read in full via the GitHub API (13,061 lines). Quoted functions: CalcShadow, Astronomy_SearchGlobalSolarEclipse, GeoidIntersect, EclipseKindFromUmbra with the 0.014 km bias, PruneLatitude 1.8 degrees, constants EARTH_MEAN_RADIUS_KM 6371.0, MOON_MEAN_RADIUS_KM 1737.4, MOON_POLAR_RADIUS_KM 1736.0. README read for the accuracy claim and VSOP87 statement.
  25. 25company RHerAle/Eclipse-Engine (eclipseradar.com engine) Read live. Besselian geometry, elements fitted to DE440s, terrain skyline from DEM and OSM, AGPL-3.0, last push 2026-09-14.
  26. 26company tomasrojasc/eclipse-2026 Read live. Skyfield with DE421, LOLA LDEM_16 limb profile, moon_pa_de421 orientation, Baily's beads per bead; 84 tests; no licence stated.
  27. 27company tahze0/solar-eclipse-explorer Read live. Reconstructs all 11,898 Canon eclipses from the NASA CSV; path width median error 0.26 percent; MIT; last push 2026-09-08.
  28. 28company RHerAle/Eclipse-Engine, js/besselian.js and README (eclipseradar.com, AGPL-3.0) Read the README summary and the source file (var/downloads/rherale_besselian.js). WGS84 flattening, Delta T shift at 1.002738*15 arcsec/s, central line at 6-s steps, limits perpendicular to ground-relative motion with 5 iterations and the 5 km low-latitude remark, outlines at 181 angles to convergence, obscuration grid 640x320x121 and contour refinement to 0.5 km, antimeridian and pole handling. Validation only against the project's own Python chain.
  29. 29company enrique7mc/solar-eclipse-2027, src/eclipse.js and README Read the README summary and the source (var/downloads/enrique_eclipse.js). NASA elements, f=1/298.257, k2=0.272281, Delta T=71.7 s, mu shift 0.00417807 deg/s, line-ellipsoid quadratic, sweep-envelope limits, 90-point outline, two-circle obscuration formula, bisected central duration; check script agrees with the NASA path table to ~1 km and 0.1 s.
  30. 30company aravpanwar/besselian, README Read the README summary. k1=0.272488, k2=0.272281, Delta T=76.0 s for 2027, longitude shift Delta T*15/3600 deg (~32 km), exact centreline solve, greatest eclipse versus greatest duration differ by ~215 km and 0.6 s, checks against NASA numbers.
  31. 31primary 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.
  32. 32primary 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.
  33. 33primary NASA SVS 5073: The 2023 and 2024 Solar Eclipses: Map and Data Read from a Wayback Machine snapshot (2025) because svs.gsfc.nasa.gov refused connections. Lists the shapefile and KML contents and the data sources (SRTM, LRO, DE421).
  34. 34primary 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.
  35. 35primary PDS Geosciences Node. LRO LOLA GDR label ldem_128.lbl (LRO-L-LOLA-4-GDR-V1.0, V3.0) Read. 128 pix/deg, 236.901 m/pix, A_AXIS_RADIUS 1737.4 km, OFFSET 1737400, SCALING_FACTOR 0.5, 16-bit, MEAN EARTH/POLAR AXIS OF DE421, data 2009-07-13 to 2016-11-29.
  36. 36primary PDS Geosciences Node. SLDEM2015 label sldem2015_128_60s_60n_000_360_float.lbl (V2.0) Read. 128 pix/deg, 0.236901 km/pix, A_AXIS_RADIUS 1737.4 km, PC_REAL 32-bit in km, MEAN EARTH/POLAR AXIS OF DE421, GRGM900B gravity for geolocation, heights -8.717 to +10.778 km, coverage 60S to 60N.
  37. 37primary SRTM Version 3.0 User Guide (NASA JPL and LP DAAC) Read from the PDF (var/downloads/srtm_guide.txt). Heights are metres referenced to the WGS84/EGM96 geoid; the true spatial resolution of the 1 arc-second data is 50 to 80 m; the LP DAAC 3 arc-second product averages 3x3 posts; voids are filled with ASTER GDEM2, GMTED2010 and NED.
  38. 38primary Copernicus DEM (COP-DEM) collection description, Copernicus Data Space Ecosystem Read. EEA-10, GLO-30 and GLO-90 from TanDEM-X 2011 to 2015 (WorldDEM), vertical reference EGM2008, absolute vertical accuracy under 4 m at 90 percent linear error, GLO-30 and GLO-90 free with attribution, DOI 10.5270/ESA-c5d3d65.
  39. 39primary NAIF generic planetary SPK summaries (aa_summaries.txt) Read. Exact start and end epochs of de430, de431, de432s, de435, de438, de440, de440s, de441 parts, de442 and de442s.
  40. 40primary NAIF lunar frame kernel moon_de440_250416.tf Read. MOON_PA_DE440 and MOON_ME_DE440_ME421 definitions, TKFRAME angles (67.8526, 78.6944, 0.2785) arcsec about axes (3,2,1), 0.02886 deg = 875 m, DE440 ME vs DE421 ME at most 53.4 cm over 2000-2040.
  41. 41primary deltat.data: monthly determinations of TT - UT1 (USNO) Read on 2026-09-15. 2017 Aug 1: 68.8373 s; 2017 Sep 1: 68.8477 s; 2024 Apr 1: 69.1983 s; 2024 May 1: 69.2018 s; last row 2026 Apr 1: 69.1330 s.
  42. 42primary deltat.preds: long-term predictions of TT - UT1 (USNO) Read on 2026-09-15. Columns MJD, year, TT-UT1, UT1-UTC, error. 2025.0: 69.04 +/- 0.088 s; 2026.0: 69.05 +/- 0.189 s; 2028.0: 69.34 +/- 0.486 s; 2030.0: 69.97 +/- 0.768 s.
  43. 43primary IERS Bulletin A, Vol. XXXIX No. 037 (10 September 2026) Read. UT1-UTC = 0.000946 s on MJD 61287, TAI-UTC = 37 s since 2017 Jan 1, no leap second in December 2026, DUT1 = 0.0 s from 2026 Apr 9, polar motion x = 0.20025 arcsec and y = 0.33395 arcsec, prediction accuracies for UT1-UTC of 1.4, 2.4, 3.2 and 4.0 ms at 10, 20, 30 and 40 days.
  44. 44primary VizieR catalogue VI/122: The Marginal Zone of the Moon (Watts 1963), digitised by HMNAO and USNO, documentation file Read in full. Gives the record layout of WATTS.TXT, the libration grid (L -9 to +9, B -8 to +8 in 0.2 deg steps), 1800 Watts-angle points per block, the +0.21 deg Watts-angle offset, the 1.564 versus 1.542 deg inclination correction, the accuracy codes, and the photograph sequences 1927 to 1956.
  45. 45peer-reviewed HMNAO and USNO (1961), Explanatory Supplement to the Astronomical Ephemeris, section 9 examples Local scan text read (var/downloads/es1961_djvu.txt). Worked examples 9.2 to 9.9 for the eclipse of 1961 February 15, usable as hand-checkable reference cases.
  46. 46company Espenak, Total Solar Eclipse of 2017 Aug 21, EclipseWise prime page Read via WebFetch summary. DE405, Delta T = 68.8 s, k = 0.2725076 (penumbra) and 0.2722810 (umbra), central duration 02m40.12s, path width 114.7 km.
  47. 47primary Espenak & Anderson (2001), Total Solar Eclipse of 2001 June 21, NASA TP-2001-209484 Local text read (var/downloads/TP209484_2001.txt). DE200/LE200, Watts corrections of 0.4 arcsec, graze-zone accuracy +/- 0.3 arcsec, advice to stay 1 km inside the interior limit, Elev Fact terrain factor, consumer GPS +/- 100 m, worked Lusaka limb-correction example.
  48. 48trade Besselian Elements team, Experimentally Testing Eclipse Maps Accuracy (2024) Read via WebFetch summary. Stephenville, Texas, 2024 April 8. Observed totality 13.7 s (C2 18:39:06.6, C3 18:39:20.3 UTC) versus six predictions from 12.9 s (Irwin) to 65 s (timeanddate). Authors' own experiment, so trade grade.