How to find an eclipse around another planet

Last week, we talked about how moons in the outer solar system can see total eclipses as good as the ones we see on Earth. To recap, if you’re standing on one big round moon of a planet like Jupiter or Saturn, you can watch another big round moon just barely block out the Sun, the same way you can see the Moon just barely block out the Sun on Earth. From Earth, this is visible as one moon suddenly dimming as it enters the shadow of the other – one type of what’s called a “mutual event”. Which combinations of moons can see perfect eclipses? Geometrically, it’s a bit of a complicated question. You need the right combination of size and distance. Let’s take two of Jupiter’s big moons, Ganymede and Callisto, as an example. If they’re lined up next to each other on the same side of Jupiter, the closest possible distance between them is Callisto’s minimum distance from Jupiter (it’s “perijove”) minus Ganymede’s maximum distance from Jupiter (it’s “apojove”). This is 1.869 million km minus…