Computing Eclipses, Occultations and Transits

Lunar occultations

workingupdated 2026-10-17occultationsbesseliangrazeiotaoccultdelta-t
  • An occultation of a star is an eclipse with a cylindrical shadow. On the fundamental plane the Moon's shadow is a circle of fixed radius k=0.2725k = 0.2725 Earth radii, given by elements at conjunction in right ascension 1 2.
  • The limits of an occultation are where the star's track is tangent to the limb. Near them a graze is seen. There the prediction is a limb profile and a height-corrected line on the ground, not a time 3 4.
  • A planet is an occulted disc. Its contacts are those of an eclipse of one disc by another, with the planet's radius replaced by a perpendicular that depends on phase 3.
  • Star positions and the limb are no longer the limit. With Gaia positions and LOLA heights, typical residuals are under 0.04 arcseconds and most predictions agree with video timings to 0.3 s 5.
  • Three centuries of timings measure ΔT. The archive from 1623, reduced with DE440 and LOLA, gives ΔT for each timing from its residual and rate 6 7.

What this topic covers

This topic covers the computation of lunar occultations of stars and planets. It gives the Explanatory Supplement's elements and station reduction for a star, with the coefficients and limits that the almanac offices published. It describes how the prediction programme passed from HM Nautical Almanac Office and the US Naval Observatory to ILOC and then IOTA. Grazing occultations are covered as limb-profile products: limit lines, profiles, the observer-height shift and station placement. The limb datasets themselves are in Lunar limb profile. For planets the topic gives Chauvenet's reduction to the eclipse case. It then follows the star catalogues from Robertson's ZC through XZ to Gaia, double stars, and stellar diameters from diffraction. Last, it covers the reduction of timings to residuals, Morrison's analyses, the personal equation, ΔT from the archive, and the error budget of a prediction.

Notes in this topic

What this topic changes for the pipeline

The eclipse pipeline gains a star target and a cylinder mode. The ephemeris layer must take a catalogue star with its epoch and space motion. The element stage must accept l1=l2=kl_1 = l_2 = k and zero cone angles, and the local solver must report kncosψkn\cos\psi, which is kk times the radial limb rate, and the cusp angle. The limb stage is shared unchanged, but the event position angle must be good to 0.01 degrees. Limit lines for stars become graze products with a profile and a terrain step. A reduction stage that turns an observed time into an O−C residual and its rate makes the pipeline usable for validation against the 1623 to present archive.

References

  1. 1peer-reviewed Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac (1961, reprint with 1973 added notes), section 10 Occultations, pp. 277-305 Read in full from the archive.org OCR text. Source of the occultation Besselian elements (T, H, Y, x', y'), the formulas for x and y and their rates, the station reduction with f, g and kn cos psi, the position angle, the a and b coefficients, the limiting parallels, the prediction limits, the k values 0.2725, 0.2724953 and 0.2725026, the reduction to delta-sigma, the limb correction arguments and section F on planetary occultations. Some equations are damaged in the OCR text.
  2. 2peer-reviewed Seidelmann, P. K. (ed.), Explanatory Supplement to the Astronomical Almanac (1992), section 9.4 Occultations (pp. 494-498), section 8.12 on k, and section 4.51 on historical UT1 Read sections 9.41, 9.42, the k paragraph of 8.12 and 4.51 in the archive.org OCR text. Source of equations 9.41-2 to 9.41-9 for the shadow on the Earth and the visibility map, the planetary occultation condition 9.42-1, the statement that ILOC in Tokyo reduced timings, and the 1982 adoption of k = 0.2725076 to conform to occultation work. Equation 9.41-8 is partly illegible in the scan.
  3. 3primary Chauvenet, W., A Manual of Spherical and Practical Astronomy, Vol. I (1863), chapter on Eclipses, Arts. 288 to 296 Read Arts. 288 to 291 and the cone-angle precepts in OCR text (garbled in places). Original almanac form of Bessel's method: point Z as the Sun seen from the Moon's centre, equations (482) for x y z, principal plane of reference, log k = 9.435000, c = z ± k/sin f, l = c tan f.
  4. 4trade Nugent, R. (ed.) (2007). Chasing the Shadow: The IOTA Occultation Observer's Manual. International Occultation Timing Association Read chapter 4 (software), chapter 5 (grazes: geometry, elevation correction, limit-line shift, Occult graze profile, station placement, central graze time, double stars). Written by IOTA practitioners about their own methods.
  5. 5company Herald, D. (2016-11-20). Update to Occult and Observations Read (curl). States that a position-angle error of up to 0.2 deg in the traditional method corrupted the limb correction, and that with the LOLA lunar limb (Occult download #26) most occultation predictions are within 0.3 s of observation.
  6. 6primary Herald, D. and Gault, D. et al. (2022). VizieR VI/132C, Archive of lunar occultation observations (1623 to the present), doc.txt and ReadMe Read doc.txt in full and the ReadMe column list. Source of the custody history (HMNAO 1943, ILOC 1981 to 2008, IOTA from 2008), the observation counts and correction statistics, the reduction basis (DE440, Gaia EDR3 for most stars, deltaT splines, WGS84 conversion, polar motion, refraction, LOLA limb in a P,D frame at 0.01 degree spacing), and the default personal equations.
  7. 7peer-reviewed Stephenson F. R., Morrison L. V., Hohenkerk C. Y. (2016) Measurement of the Earth's rotation: 720 BC to AD 2015, Proc. R. Soc. A 472, 20160404 Open-access copy read 2026-09-15. Quoted: +1.8 ms/cy lod trend versus +2.3 ms/cy tidal, the parabola Delta T = -320.0 + 32.5 ((year-1825)/100)^2 s, the roughly 1500-year oscillation, DE430 acceleration -25.82 arcsec/cy^2, the untimed-eclipse method and the cubic spline fit.

In this section

Besselian elements for lunar occultationsHow almanac offices and IOTA predict lunar occultations of stars, from the cylindrical shadow and conjunction elements to station times, coefficients and limits.workingGrazing occultations and the lunar limbHow grazing occultations are predicted, how limb profiles and observer height move the limit line, and how expeditions place observers.workingPlanets, star catalogues and the reduction of occultationsHow planet occultations, star catalogues, double stars and diffraction enter occultation work, and how timings are reduced to residuals and ΔT.working