Computing Solar Eclipses — Research

Earth model and time scales

workingupdated 2026-09-15earth-figuredelta-trefractiontime-scales
  • Use WGS 84 and never a sphere. The three modern ellipsoids differ by 3 m in equatorial radius, but feeding a geodetic latitude into spherical formulas misplaces the observer by up to 21 km 1 2.
  • Terrain moves a path limit by hcot⁡Asin⁡Dh \cot A \sin D, 577 m per 1000 m of elevation at a 60° Sun and 5.7 km at 10°. NASA SVS is the only predictor that puts every observer on the terrain, and it measured up to 3 km of umbra shift in 2017 3 4.
  • ΔT enters only through μ, and one second of it moves every longitude by 465cos⁡ϕ465\cos\phi metres. The 2006 Espenak and Meeus polynomial was 1.4 to 2.3 s high for 2024, which is 0.5 to 0.8 km at latitude 40° 5 6.
  • Refraction is left out of contact times, and that is right above a 5° Sun. A common lift of both disks cancels, leaving seconds at first and last contact below 5° and under a second at second and third contact 3 5.
  • The elements are built from apparent places. Using a geometric Sun displaces the shadow axis by 20.5 arcseconds, which is 38 km on the ground 5.

What this topic covers

Three notes on the parts of an eclipse computation that concern the Earth rather than the Sun and Moon: the ellipsoid and the observer's coordinates, terrain and the elevation datasets, the rotation of the Earth and the ΔT models that describe it, and the atmospheric and frame corrections that sit between an ephemeris and a contact time.

Notes in this topic

  • Earth figure and terrain: the ellipsoid behind ρsin⁡ϕ′\rho\sin\phi' and ρcos⁡ϕ′\rho\cos\phi', what a sphere costs, how observer height moves the path limits, what NASA SVS did with SRTM for 2017 and 2024, the free elevation datasets, and the geoid question.
  • ΔT and Earth rotation: the definition TT − UT1, where it enters the elements, the Morrison and Stephenson and Stephenson, Morrison and Hohenkerk models, the Espenak and Meeus polynomials and their tidal-acceleration correction, IERS and USNO data, prediction uncertainty by lead time, the values each predictor used for 2017 and 2024, leap seconds, polar motion and sidereal time.
  • Refraction, light-time and frames: why refraction is left out of contact times and why that is mostly right, the almanac and Stellarium formulas, apparent places and the 38 km aberration trap, TT versus TDB, and the table of every effect with its size and who includes it.

What this topic changes for the pipeline

The pipeline needs a terrain stage between the global Besselian solution and the published path polygons, a ΔT provider with three regimes and a stated uncertainty, and an "apparent places" contract on the ephemeris interface. Every published coordinate needs a stated datum and every published path needs the ΔT value stamped on it. The recurring finding is one of scale: getting the Sun's aberration or the Earth's flattening wrong costs tens of kilometres, terrain costs kilometres at the limits, and a ΔT prediction error costs hundreds of metres, while the geoid, polar motion, the nutation model, TDB and refraction above 5° together cost less than the metre-level error of the ephemeris itself 7.

References

  1. 1primary World Geodetic System 1984 (NGA Office of Geomatics) Read. Defining parameters a = 6378137.0 m, 1/f = 298.257223563, omega = 7292115 x 10^-11 rad/s, GM = 3.986004418 x 10^14 m3/s2; EGM2008 to degree 2159 with a 2.5-minute geoid grid, EGM96 to degree 360 with a 15-minute grid.
  2. 2peer-reviewed Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac (HMSO, 1961) Section 6 (figure of the Earth: Hayford spheroid, the S and C functions) and Section 9B (eclipses: observer coordinates, Bessel's parametric-latitude device, rising and setting curves without refraction). Read from the archive.org OCR text kept in var/downloads/es1961_djvu.txt.
  3. 3primary Total Solar Eclipse of 2001 June 21, F. Espenak and J. Anderson, NASA/TP-1999-209484 Read from the PDF text kept in var/downloads/TP209484_2001.txt. States that predictions use centre-of-mass positions with no refraction or limb corrections, that local circumstances are at sea level unless the elevation is known, and defines the elevation factor tan(90-A) sin(D) for shifting the path limits.
  4. 4primary NASA SVS 4517: Umbra Shapes (E. Wright) Read from the Wayback Machine snapshot of 2025-12-10. Explains the limb-profile point-cloud method, states that observer elevations come from SRTM, and that the western-US elevations in 2017 shift the umbra toward the Sun's azimuth by as much as 3 km.
  5. 5peer-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.
  6. 6primary 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.
  7. 7peer-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.

In this section

Earth figure and terrainThe ellipsoid behind ρ sin φ' and ρ cos φ', what a sphere or a wrong ellipsoid costs, how observer height moves the path, which elevation datasets the predictors use, and whether anyone corrects for the geoid.workingΔT and Earth rotationHow TT − UT1 enters the Besselian elements, the ΔT models from Morrison and Stephenson to the IERS series, how far off a prediction is one to a hundred years ahead, and what each predictor used for 2017 and 2024.workingRefraction, light-time and framesWhether refraction belongs in contact times and paths, what the almanac formulas are and how big the effect is, why apparent places and consistent aberration matter far more, the TT versus TDB question, and a table of every effect with its size and who includes it.working