Computing Eclipses, Occultations and Transits

Phenomena of Jupiter's Galilean satellites

workingupdated 2026-10-17jupitergalilean-satelliteseclipsesoccultationstransitsmutual-eventsphemu
  • Five kinds of event, two geometries. Eclipses and shadow transits are decided from the Sun. Occultations and transits are decided from the Earth. Mutual events need the Earth or the Sun in the satellites' orbital plane, which happens for about a year every 5.9 years 1 2.
  • The theory changed from analytical to numerical. Sampson (1921) and Lieske's E-series served until the Institut de mécanique céleste et de calcul des éphémérides (IMCCE) switched to Lainey's L1 for 2015 and to the NOE solution from 2023. JPL's JUP365 (2021, with DE440) is the current SPICE kernel 3 4.
  • The classical computation is two cones and an oblate Jupiter, with separate light-time rules for the Sun path and the Earth path, and a phase correction of up to 6 minutes 5.
  • Published times are mid-events in TT: half flux for an eclipse, bisection for the rest. The first or last visible speck is 1 to 15 minutes away, depending on the satellite 3 6.
  • Mutual events give some of the most accurate ground-based astrometry, 5 to 50 milliarcseconds, or 15 to 150 km, through a photometric model of the satellites' surfaces fitted to each light curve 2 7.
  • The history matters to the pipeline. Io's eclipses gave the first finite speed of light in 1676, and the light-time they revealed, 33 to 53 minutes, enters every prediction 8 9.

What this topic covers

This topic covers how the phenomena of Jupiter's four large moons are predicted. It covers the theories of motion and the ephemeris files, with dates, versions and accuracy. It gives the shadow and disc geometry with Jupiter's flattening, the light-time rules and the phase correction. It defines what a published "start" or "end" means and how Jupiter's atmosphere blurs an eclipse. It describes the published tables and the software, and states the theory each one uses. Finally it covers mutual events: when they happen, the PHEMU campaigns from 1973 to 2021, the photometric models and the astrometric accuracy they reach.

Notes in this topic

  • Theories and ephemerides: Sampson, the Sampson-Lieske theory and E5, Lainey's L1 and NOE, JPL's JUP310 and JUP365, Meeus's two methods with formulas, and which program uses which.
  • Eclipses, occultations, transits and shadows: the four satellite-Jupiter phenomena, shadow cones, flattening, light-time, the phase correction, timing conventions, the atmosphere, published products, accuracy, and Rømer.
  • Mutual events: equinox geometry, the PHEMU campaigns, prediction, photometric models, reduction to astrometry and the accuracy achieved.

What this topic changes for the pipeline

The pipeline needs a satellite ephemeris layer next to the planetary one, versioned as a pair such as DE440 with JUP365. The shadow-cone code must accept an oblate occulting body whose projected outline depends on the jovicentric declination. It must keep the Sun-side and Earth-side light-time paths apart. The contact solver needs a mid-event mode, half flux or bisection, because that is what the reference tables publish. Mutual events add a photometric stage, the overlap of two textured discs under a limb-darkened Sun, which no part of the solar eclipse pipeline needs. Saturn's satellite phenomena follow the same pattern and are covered in their own topic.

References

  1. 1primary IMCCE Natural Satellites Data Center, Guide for the phenomena of the natural planetary satellites Read in full. Definitions, half-flux timing convention, the 10 km per second of time rule, time-scale advice.
  2. 2peer-reviewed Saquet, E., Emelyanov, N., Robert, V., Arlot, J.-E. et al. (2018). The PHEMU15 catalogue and astrometric results of the Jupiter's Galilean satellite mutual occultation and eclipse observations made in 2014-2015. MNRAS 474, 4730-4739 Read in full from the UNESP repository copy. Campaign statistics 1985 to 2015, the photometric model, the Emelyanov reduction equations, NOE-5-2010-GAL and JUP310 residuals.
  3. 3primary IMCCE, /pub/ephem/satel/phenjupiter/README (2021 September) Read in full. Event codes, TT time scale, mid-event convention, the theory used for each range of years (G-5 to 2014, L1 2015 to 2022, Lainey 2021 after), and the TT-UT table.
  4. 4primary NAIF, generic_kernels/spk/satellites/jup365.cmt (BVS/NAIF, 2021-03-14) Read the header. JUP365.26 global fit, DE440 planets, 1600 to 2200, RADIUS 71492 km, Chebyshev interpolation error 16 m, GM values. The .bsp is 1,136,581,632 bytes.
  5. 5peer-reviewed Thuillot, W. (1983). Theorie des phenomenes des satellites galileens de Jupiter: une representation par les polynomes de Tchebychev. Astronomy and Astrophysics 127, 63-67 Pages 1 to 3 read from the ADS scan (in French). Source of the cone equations with an ellipsoidal Jupiter, the phase correction of 3 min (Io) and 6 min (Callisto), the light-time rules, the Chebyshev form and its 51 s maximum error.
  6. 6trade Westfall, J. E. (2006). Timing the eclipses of Jupiter's Galilean satellites. ALPO observing instructions Read pages 1 and 2. Table of penumbral widths, ingress and egress durations and eclipse durations; the 1 to 2 minute offset of visual timings from mid-event predictions; comparison standard E-2.
  7. 7peer-reviewed Catani, L. M., Assafin, M., Morgado, B. E. et al. (2023). The 2021 mutual phenomena involving the Galilean satellites of Jupiter and the inner satellite Thebe. MNRAS, doi:10.1093/mnras/stad3006 (arXiv:2310.00807) Read in the arXiv version. Read sections 1 and 4 to 8. DE440 plus JUP365, Oren-Nayar reflectance, solar limb darkening of Hestroffer and Magnan, chi-square fit of about 900 simulated curves per event, 5 mas (15 km) average uncertainty.
  8. 8peer-reviewed Bobis, L. and Lequeux, J. (2008). Cassini, Romer and the velocity of light. Journal of Astronomical History and Heritage 11, 97-105 Read pages 97 to 99. Longitude use of Jovian eclipses, Cassini's 1668 ephemerides, the 15 s and half-minute timing accuracies, the 22 August 1676 announcement and the 7 December 1676 publication.
  9. 9company Keys, S. (2013). meeus/v3/jupitermoons/jupitermoons.go, Go implementation of Astronomical Algorithms chapter 44 (MIT licence) Read in full. Third-party reimplementation. Source of the quoted low-accuracy method (Positions) and of the E5 method with differential light-time constants 17295, 21819, 27558, 36548 and perspective divisor 2095. The package documents its validation by tests that reproduce Meeus's worked examples.

In this section

Theories and ephemerides of the Galilean satellitesThe satellite theories behind Jupiter-moon predictions, from Sampson's tables and Lieske's E5 to Lainey's NOE and JPL's JUP365, with Meeus's formulas.workingEclipses, occultations, transits and shadow transitsHow the four satellite-Jupiter phenomena are computed, from shadow cones and Jupiter's flattening to light-time, timing conventions, published tables and accuracy.workingMutual events of the Galilean satellitesHow mutual eclipses and occultations of Jupiter's moons are predicted, modelled and reduced to astrometry, from the 1973 campaign to PHEMU21 and 2026-27.working