eclipsemap

Real: every body's semi-major axis, eccentricity, orbital inclination, orbital period, physical radius, and axial tilt come from NASA/JPL planetary and satellite fact sheets. The eclipse math — angular sizes, umbra/penumbra shadow cones, total vs. annular vs. partial classification — is the same geometry real eclipse prediction uses, just without the higher-order perturbation corrections professional ephemerides add.

Simplified: this is a two-body Keplerian propagator (each body orbits its parent on a fixed ellipse), not a live n-body ephemeris. Each moon's starting orbital phase is an arbitrary-but-fixed value, not looked up from a real "where is Io right now" feed — so exact predicted dates drift from reality within roughly an orbit or so, even though the mechanism, frequency, and character of each eclipse type is physically real. A few high-inclination moons (Triton, Charon, the Uranian moons) use an approximated "effective inclination" derived from their parent planet's real axial tilt rather than a precisely-oriented equatorial plane, so eclipse-season timing is illustrative even though the underlying "seasons happen at all, decades apart" behavior is real.

a few real facts the simulator doesn't need to compute to be true

• Jupiter's Galilean moons are so close and so large relative to Jupiter's tiny (5.2 AU away) sun that their shadow-transits are true total eclipses at Jupiter's cloud tops, happening several times a week — sometimes two moons at once.
• Phobos is too small and too close to ever fully cover Mars's sun — every Phobos crossing is a fast, tiny partial transit. Curiosity and Perseverance have both photographed real ones.
• Pluto and Charon ran a real five-year mutual eclipse season from 1985–1990 (that's how Charon's exact size was first measured) because Pluto is tipped over ~120° on its axis. The next season isn't due until roughly 2103–2109.
• Uranus is tipped 98° on its side, so its moons orbit almost perfectly edge-on to the sun. Uranus's last equinox was in 2007; its next is 2049 — that's when Uranian moon-on-moon eclipses cluster.
• Venus transits the sun (as seen from Earth) in pairs eight years apart, separated by over a century otherwise — the last pair was 2004 and 2012; the next isn't until 2117. Mercury is more frequent, about 13–14 times a century; its next transits are 2032 and 2039.