Computing Eclipses, Occultations and Transits

Saturn and outer-planet satellites

workingupdated 2026-10-17saturnuranusplutosatellitesmutual-eventsringsphesat
  • Saturn's satellite phenomena are seasonal. Transits, eclipses by the globe and mutual events of Mimas to Titan cluster around the ring-plane crossings, which came in 1995, 2009 and 2025, 13.72 and 15.74 years apart 1 2 3.
  • The satellite ephemeris decides the prediction. Dourneau's theory, which Meeus chapter 46 condenses, is good to hundreds of kilometres. TASS 1.7 is good to tens of milliarcseconds. JPL's SAT441 and the NOE ephemerides of the Institut de mécanique céleste et de calcul des éphémérides (IMCCE) are better again 4 5 6.
  • Saturn needs a body model that the Moon never did. Its flattening is 0.098, and the rings range from nearly transparent, ring C, to nearly opaque, ring B. Horizons ignores both, and none of Horizons, SPICE and Stellarium models ring transmission 7 8 9 10 11.
  • Mutual events give the best ground-based astrometry of these satellites. They reached about 20 milliarcseconds at Saturn in 2009 and formal uncertainties below 0.01 arcseconds at Uranus in 2007 5 12.
  • The 1985 to 1990 Pluto-Charon events showed what light curves can measure, including radii, albedo maps and the orbit. They also showed how a neglected limb-darkening term biases the radii 13 14.

What this topic covers

This topic covers the satellite phenomena of Saturn and of the outer planets, with a short section on Mars. It describes the theories and ephemerides that place the satellites, in their dated versions, and quotes Meeus's ring and satellite formulas with their constants. It sets out the geometry of eclipses by an oblate planet and by its rings, and the conventions for the start, end and maximum of an event. It reports what the PHESAT, PHEURA and Pluto-Charon campaigns observed and how accurately. It also records which theory each common program evaluates. Jupiter's Galilean satellites share most of this geometry and are covered in the Jupiter satellite topic. The planetary ephemerides underneath are in the ephemerides note, and light-time and frames in the frames note.

Notes in this topic

  • Saturn's satellite theories and ring geometry: Dourneau, Harper and Taylor, TASS, NOE and SAT441 with their accuracy. It quotes Meeus chapters 45 and 46 with constants and test vectors, gives Saturn's figure and ring radii, and records which program uses which theory.
  • Phenomena and mutual events of Saturn's satellites: the event types, ring-plane crossing dates, shadow and light-time geometry, timing conventions, ring eclipses of Iapetus and ring transmission. It also covers the mutual-event photometric model, the 1980 to 2025 campaigns and the limits of public tools.
  • Uranus, Neptune, Pluto and Mars satellite events: the 2007 Uranian season with its two-model predictions and results, Triton, the 1985 to 1990 Pluto-Charon events, and Phobos and Deimos.

What this topic changes for the pipeline

The pipeline gains a satellite ephemeris layer on top of the planetary one, delivered as SPK files consistent with DE440. The body-shape layer gains an oblate primary and a ring annulus with a radial optical-depth profile, and the shadow code must handle a partially transparent occulter. The event search gains a seasonal gate on the saturnicentric or uranocentric latitudes of the Earth and the Sun. The event list must carry an uncertainty from the comparison of two independent satellite ephemerides, because events can appear or vanish between models.

References

  1. 1primary Nicholson, P. D. et al., PDS Ring-Moon Systems Node, Saturn RPX 1995-1996 Dear Colleague letter (overview.html) Read in full. Sun ring-plane crossing 1995 Nov 19, Earth crossings 1995 May 21, 1995 Aug 11 and 1996 Feb 11, about 2 hours advance of the crossing over 15 years from ring-plane precession, and the 80 km (about 0.01 arcsecond) post-fit residuals of the 1980 mutual events.
  2. 2primary NASA/JPL/Space Science Institute, Photojournal PIA10563, Shadows on the Move Read 2026-10-17 (the photojournal.jpl.nasa.gov/catalog/PIA10563 address redirects here). States that the Sun crosses Saturn's ring plane on 2009 Aug 10.
  3. 3trade British Astronomical Association, Saturn, Uranus and Neptune Section, Saturn 2025 Apparition Notes Read 2026-10-17. Earth ring-plane crossing 2025 Mar 23, Sun crossing 2025 May 6, and dated observations of Titan shadow transits at 16-day steps from May to September 2025, plus Tethys, Dione and Rhea transits.
  4. 4peer-reviewed Dourneau, G. (1993). Orbital elements of the eight major satellites of Saturn determined from a fit of their theories of motion to observations from 1886 to 1985. Astronomy and Astrophysics 267, 292-299 ADS scan read through OCR. Source of the 22,000 observed coordinates, the element tables (Mimas epoch JD 2411093.0, L0 127.64 degrees, n 381.994497 degrees per day, e 0.01905, t0 1866.39), and the stated uncertainties of 350 to 500 km for satellites II to VI, 800 to 1000 km for Mimas and Iapetus, 2500 km for Hyperion, and 50 to 100 km from the 1980 mutual events.
  5. 5peer-reviewed Arlot, J.-E., Emelyanov, N. V., Lainey, V. et al. (2012). Astrometric results of observations of mutual occultations and eclipses of the Saturnian satellites in 2009. Astronomy and Astrophysics 544, A29 Read in full from the HAL PDF (CC BY 4.0). Source of the observation counts 14, 66 and 33 for 1980, 1995 and 2009, the photometric model E(t) = K S(X, Y), the O-C residuals against TASS 1.7, Lainey and SAT351, and the NOE-6-2011-MAIN accuracy statement.
  6. 6primary NAIF, generic_kernels/spk/satellites/sat441.cmt (SPKMERGE log and SATEPHGEN summary for SAT441.24, created 2022-01-29) Read in full. Bodies 601 to 609, 612 to 614, 632, 634 and 699, span 1749 Dec 29 to 2250 Jan 5, planetary ephemeris DE440, model SATORBINT, Chebyshev interpolation error 7.5 m, RADIUS 60,330 km as the harmonic reference radius, ring mass terms RINGM1 to RINGM4.
  7. 7primary Williams, D. R., NASA NSSDCA, Saturn Fact Sheet Read 2026-10-17. Equatorial radius 60,268 km and polar radius 54,364 km at the 1 bar level, flattening 0.09796, J2 16,298 x 10^-6, tropical period 10,746.94 days, obliquity 26.73 degrees.
  8. 8primary Williams, D. R., NASA NSSDCA, Saturnian Rings Fact Sheet Read 2026-10-17. Ring edge radii (C inner 74,658 km, B inner 91,975 km, B outer 117,507 km, A inner 122,340 km, A outer 136,780 km), optical depths (C 0.05 to 0.35, B 0.4 to 2.5, Cassini Division 0 to 0.1, A 0.4 to 1.0) and thicknesses.
  9. 9primary JPL Horizons System Manual Read live. Observer table quantities, DE440/DE441, satellite eclipse circumstances; no solar eclipse product.
  10. 10primary NAIF CSPICE gfoclt_c documentation Official documentation read 2026-09-30. Detailed Input accepts ELLIPSOID+ELLIPSOID, ELLIPSOID+POINT, DSK+POINT. POINT requires ANY; exceptions 9 and 14 reject the proposed DSK+finite-Sun FULL search. Cached HTML SHA256 7aef5446d1b4a396bbed8eaba1201da94a2aa118fcaa757a063b7080abf33d3a.
  11. 11company Stellarium, src/core/modules/Planet.cpp at commit 77d52ea34a6b6c78dc544938c3903b6fcf314e93 Read getCandidatesForShadow and the shadow uniform setup. Shadow casters are the parent, own satellites and sibling satellites, each treated as a sphere of its equatorial radius, at most four per body.
  12. 12peer-reviewed Christou, A. A., Lewis, F., Roche, P. et al. (2009). Observational detection of eight mutual eclipses and occultations between the satellites of Uranus. Astronomy and Astrophysics 497, 589-594 Abstract read in the arXiv version (arXiv:0902.4582); journal DOI 10.1051/0004-6361/200811523 from Crossref. Fifteen light curves with five instruments of 0.4 to 10 m, eight events detected, formal uncertainties below 0.01 arcsecond, and a systematic lag of observed mid-times behind predictions.
  13. 13peer-reviewed Binzel, R. P., Tholen, D. J., Tedesco, E. F., Buratti, B. J., Nelson, R. M. (1985). The Detection of Eclipses in the Pluto-Charon System. Science 228, 1193-1195 Abstract read through Crossref. First eclipses in 1985 January and February, events at 3.2-day intervals for 5 to 6 years, then none for about 120 years.
  14. 14peer-reviewed Young, E. F. and Binzel, R. P. (1994). A New Determination of Radii and Limb Parameters for Pluto and Charon from Mutual Event Lightcurves. Icarus 108, 219-224 Not read. Described through PHEMU Technical Note 9 (about 4 per cent radius discrepancy with the 1988 stellar occultation, attributed to neglected limb darkening).

In this section

Saturn's satellite theories and ring geometryWhich theories and ephemerides place Saturn's satellites, how Meeus chapters 45 and 46 compute ring aspect and satellite positions, and which constants matter.workingPhenomena and mutual events of Saturn's satellitesHow eclipses, occultations, transits, ring eclipses and mutual events of Saturn's satellites are predicted, when they occur, and what PHESAT observed.workingUranus, Neptune, Pluto and Mars satellite eventsHow the 2007 Uranian mutual events and the 1985 to 1990 Pluto-Charon events were predicted and observed, with notes on Triton, Phobos and Deimos.working