Computing Eclipses, Occultations and Transits

Occultations by planets and minor bodies

workingupdated 2026-10-17stellar-occultationasteroidtnoplanetsgaiasoraoccultmutual-occultation
  • The shadow of a body against a star is a cylinder. Its width on the fundamental plane equals the body's diameter, and on the ground it widens as the diameter divided by the sine of the star's altitude 1 2.
  • Prediction is limited by astrometry, not geometry. The path's 1-sigma lines sit one cross-track uncertainty outside each edge, and 1 milliarcsecond is 0.7253 km per astronomical unit of distance 3 4.
  • Gaia changed the error from hundreds of kilometres to fractions of a path width. Occultation astrometry reduced against Gaia EDR3 fits orbits at about 10 milliarcseconds, against 30 to 50 with older catalogues 5 6.
  • Reduction models diffraction, star size and exposure, then fits chords. The light-curve model of SORA (Stellar Occultation Reduction and Analysis) and Herald's ellipse, circle and shape-model fits are the documented methods 1 7.
  • The method found rings and atmospheres. Uranus's rings in 1977, Pluto's atmosphere in 1988, and rings around Chariklo, Haumea and Quaoar 8 9 10 11 12.
  • Planet-planet occultations are eclipse geometry with a planet as the source. The last was Venus and Jupiter in 1818, and the next is the same pair in 2065 13 14.

What this topic covers

This topic covers occultations of stars by bodies other than the Moon: asteroids, trans-Neptunian objects, Centaurs, the giant planets and their satellites, and the rare occultations of one planet by another. It gives the fundamental-plane geometry of the shadow path and the formulas that SORA and Herald's Occult-based reductions use. It quantifies the uncertainty budget from the star catalogue and the orbit before and after Gaia, and describes how light curves are modelled and chords fitted. It also records what the method has found and how the prediction services fit together. Lunar occultations are in Lunar occultations.

Notes in this topic

  • Prediction geometry and astrometry: the cylinder shadow on the fundamental plane, the event search, the path and 1-sigma lines, the star and ephemeris error budget, Gaia and occultation astrometry, timing, and the software and services.
  • Light curves, chords and results: the diffraction, star-size and exposure model, sub-exposure timing, chord fitting with ellipses, circles and shape models, and the results for asteroids, TNOs and rings.
  • Planets, satellites and mutual planetary occultations: SPICE-based predictions for the giant planets, Titan and Triton, satellite astrometry from occultations, and the geometry and lists of planet-planet occultations.

What this topic changes for the pipeline

The Besselian stage generalises: the source can be the Sun, a star at infinity or a planet, and the occulter can be the Moon, a minor body or a planet. For a star the shadow axis is fixed and the shadow radius is the body's radius. The pipeline gains three stages that eclipse work does not need: star-catalogue propagation with Gaia space motion, orbit covariance mapped to a cross-track uncertainty, and an inverse reduction from timed chords back to a size, shape and astrometric position.

References

  1. 1peer-reviewed Gomes-Júnior, A. R., Morgado, B. E., Benedetti-Rossi, G. et al. (2022). SORA: Stellar Occultation Reduction and Analysis. MNRAS 511, 1167-1181 (arXiv:2201.01799) Read in full from the arXiv LaTeX source. Source of the closest-approach equations (Assafin et al. 2010 geometry), the shadow velocity, the magnitude-drop equation, the Fresnel scale f = sqrt(lambda D / 2), the star radius at the body, the exposure length r_t = V_S t_exp, the timing uncertainty sigma_t = sigma_LC t_exp / Delta f, the tangent-plane equations 6 to 9, the 0.021 s light-time and the chord and ellipse chi-square. Its printed albedo equation omits the factor 0.4 that the code applies.
  2. 2company Preston, S. Steve's Asteroid Update: HELP / FAQ page (asteroidoccultation.com), last updated 2019-06-11 Read. Source of the Occult plot conventions: the path width as diameter divided by the sine of the star altitude, the dashed 1-sigma lines and the 68 and 95 per cent interpretation, the uncertainty ellipse, the Rank definition and the RUWE note.
  3. 3peer-reviewed Tanga, P. and Delbo, M. (2007). Asteroid occultations today and tomorrow: toward the GAIA era. A&A 474, 1015-1022 (arXiv:0801.2684) Read the sections on astrometric accuracy from the arXiv LaTeX source. Source of sigma_path = sqrt(sigma_CEU^2 + sigma_star^2), the efficiency factor p = 2 theta / sigma_path, the pre-Gaia catalogue errors (FK6 1 mas, Hipparcos 10 mas, Tycho-2 70 mas, UCAC2 20 mas), the 0.5 arcsec ephemeris and 350 km statement, and the 15 per cent success rate of 2005.
  4. 4company riogroup/SORA, Stellar Occultation Reduction and Analysis, version 0.3.3, commit 63a1b2d of 2026-08-03 Code read: sora/prediction/core.py (occ_params and prediction), sora/prediction/occmap.py (xy2latlon and the path and 1-sigma lines), sora/lightcurve/utils.py (calc_fresnel, bar_fresnel, calc_magnitude_drop), sora/lightcurve/core.py (occ_model), sora/occultation/utils.py (calc_geometric_albedo) and sora/occultation/fitting.py (fit_ellipse). The authors document their own library, so the grade is company.
  5. 5peer-reviewed Ferreira, J. F., Tanga, P., Spoto, F., Machado, P. and Herald, D. (2022). Asteroid astrometry by stellar occultations: accuracy of the existing sample from orbital fitting. A&A 658, A73 (arXiv:2201.03892) Read from the arXiv text. Source of the pre-Gaia residual level of 30 to 50 mas, the Gaia EDR3 level near 10 mas, the factor of about 5 reduction, the 10 mas FWHM of the residual core, the 3 to 4 mas along-track error level, the RUWE analysis and the statement that 61 per cent of events are single-chord.
  6. 6trade Dunham, D. W. et al. (2024). 2024 Occultations of Bright Stars by Main-Belt Asteroids. RASC Observer's Handbook supplement Read (pdftotext). States that the 2024 orbital elements are from JPL Horizons and star data from Gaia DR3 in Occult's catalogue, that path locations are uncertain by a few tenths of a path width, and that improved predictions are now distributed only through OccultWatcher.
  7. 7peer-reviewed Herald, D., Gault, D., Anderson, R. et al. (2020). Precise astrometry and diameters of asteroids from occultations: a data set of observations and their interpretation. MNRAS 499, 4570-4590 (arXiv:2010.06086) Read sections 1 to 6, 8 and 10 to 11 from the arXiv LaTeX source. Source of the reduction on the fundamental plane with Besselian elements and a cubic shadow motion, the inverse Besselian astrometry steps, the single-chord uncertainty rules, the weights 5, 4, 3 and 1, the ellipse-fit treatment of misses, the 40 mas and 40 km pre-Gaia statement, the 586 events of 2019, the Gaia DR2 bright-star frame rotation and the 10 ms timing goal.
  8. 8peer-reviewed Elliot, J. L., Dunham, E. and Mink, D. (1977). The rings of Uranus. Nature 267, 328-330 Only the publisher's preview paragraph was read. It states that five brief occultations of SAO 158687 before and after the occultation by Uranus on 1977 March 10 indicate at least five rings, observed from the Kuiper Airborne Observatory with 10 ms integrations.
  9. 9peer-reviewed Meza, E., Sicardy, B., Assafin, M. et al. (2019). Pluto's lower atmosphere and pressure evolution from ground-based stellar occultations, 1988-2016. A&A 625, A42 (arXiv:1903.02315) Abstract and introduction read. Source of the 1985 glimpse and 1988 June 9 confirmation of Pluto's atmosphere, the eleven occultations of 2002 to 2016 and the monotonic pressure increase from 1988 to 2016.
  10. 10peer-reviewed Braga-Ribas, F., Sicardy, B., Ortiz, J. L. et al. (2014). A ring system detected around the Centaur (10199) Chariklo. Nature 508, 72-75 (arXiv:1409.7259) Read the main text and table captions from the arXiv text. Source of the 3 June 2013 event, ring radii 391 and 405 km, widths 6.6 and 3.4 km, optical depths 0.38 and 0.06, the 10 Hz Danish 1.54 m light curve, the 9846 km per arcsec scale, and the ring model convolved with Fresnel diffraction, bandwidth, stellar radius and integration time.
  11. 11peer-reviewed Ortiz, J. L., Santos-Sanz, P., Sicardy, B. et al. (2017). The size, shape, density and ring of the dwarf planet Haumea from a stellar occultation. Nature 550, 219-223 (arXiv:2006.03113) Read the main text from the arXiv text. Source of the 2017 January 21 event, the limb ellipse 1704 by 1138 km, the ring at 2287 km radius and 70 km width, the opening angle 13.8 degrees and the density upper limit of 1885 kg per cubic metre.
  12. 12peer-reviewed Pereira, C. L., Sicardy, B., Morgado, B. E. et al. (2023). The two rings of (50000) Quaoar. A&A 673, L4 (arXiv:2304.09237) Abstract read. Source of the 2022 August 9 event with nine chords, the limb semi-major axis 579.5 km and oblateness 0.12, the Q1R radius 4057 km and the second ring at 2520 km, both outside the classical Roche limit.
  13. 13company Gray, B. (Project Pluto). Assorted celestial events: mutual planetary events, -1000 to +6000 Read. The author documents his own search: VSOP theory, times in TD, Gregorian dates, an event listed if at some point on Earth one disc overlaps another, an average rate of about one per 35 years, and the list including 1818 January 3 21:52 and 2065 November 22 12:45 TD.
  14. 14unsourced Bogan, L. Mutual Planetary Occultations Past and Future: their observation circumstances (web page) Read. Summarises Albers 1979 and adds events computed with Guide 7.0. Gives the Venus-Jupiter events of 1570, 1818, 2065 and 2123 with times, elongations, diameters and geocentric separations, and the Mercury events to 2133.

In this section

Prediction geometry and astrometryHow the shadow path of an asteroid, TNO or satellite occultation is computed on the fundamental plane, and how Gaia changed its uncertainty.workingLight curves, chords and resultsHow occultation light curves are modelled for diffraction, star size and exposure, how chords are fitted, and what the method has found.workingPlanets, satellites and mutual planetary occultationsHow occultations of stars by the giant planets, Titan, Triton and the Galilean moons are predicted, and how planet-planet occultations are found.working