Computing Solar Eclipses — Research

Earth model and time scales

workingupdated 2026-09-30earth-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 evaluates terrain height at each mapped observer, and it measured up to 3 km of umbra shift in 2017 3 4.
  • ΔT places the shadow on the rotating Earth through μ, according to the element set's recorded convention, 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.
  • Nominal geometric contacts omit refraction. A common one-to-one mapping of both limbs preserves contact and containment. The cited sources do not establish a general physical contact-time correction near the horizon 3 5.
  • Classical elements use apparent places. Light-time and observer aberration are separate corrections. A 20.5-arcsecond inconsistency corresponds to about 38 km at lunar distance, rather than a guaranteed shift between two consistent formulations 5 7.

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: the geometric-contact convention and separate atmospheric visibility treatment, 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. Geoid-height mistakes can reach hundreds of metres at low solar altitude. Polar motion and inconsistent nutation can reach tens of metres. These terms need consistent treatment even when terrain, lunar limb and solar-radius choices dominate the path-edge comparison 5 8 3.

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, 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.
  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. 7primary NAIF, Aberration Corrections Required Reading, revision 2020 May 26 Original documentation read on 2026-09-30. Reception light-time uses the target at emission and observer at reception; observer-velocity aberration is a separate correction. Supports the reduction contract, not a universal 100-metre solar-light-time residual.
  8. 8primary The IAU Resolutions on Astronomical Reference Systems, Time Scales, and Earth Rotation Models, G. H. Kaplan, USNO Circular 179 (2005) Read from the PDF (var/downloads/circ179.txt). Equation 2.6 for TDB - TT (0.001657 s leading term), the statement that using TT for TDB errs by under 2 ms and under 1 mas for the Moon, the equation of the equinoxes with amplitude about 1 s, and the statement that the IAU 2000 resolutions change quantities only at the level of tens of milliarcseconds.

In this section

Earth figure and terrainObserver reduction formulas, ellipsoid choices, elevation datasets and geoid questions behind terrain-aware solar eclipse path calculations.workingΔT and Earth rotationHow ΔT connects terrestrial time to Earth rotation in eclipse prediction, with historical models, IERS data and forecast uncertainty.workingRefraction, light-time and framesRefraction, apparent positions, aberration, light-time and TT versus TDB in eclipse calculations, with documented effects and implementation choices.working