(Terrestrial data from the NASA eclipse web site )The busiest period for the Galilean mutual eclipses is between 16 and 20 June, when there are nine eclipses.
One of the more interesting eclipses occurs just two weeks beforehand: Callisto eclipses Io on 3 June, and during the early partial phase Io is also eclipsed by Jupiter!
In 2009—2010 there will be 140 mutual eclipses among the Galilean moons — Io, Europa, Ganymede and Callisto — while there will be 164 mutual eclipses among the first seven major moons of Saturn: Mimas, Enceladus, Tethys, Dione, Rhea, Titan and Hyperion.
Although the Uranian mutual eclipses began in 2007 and will continue until 2010, only 5 eclipses of the 180 total occur during 2009—2010.
Eclipses between the major moons of Jupiter and Saturn are occurring this year.
The circumstances of these eclipses are compared to terrestrial solar eclipses.
In addition, about 25 minutes before the start of the eclipse, Europa occults Io as viewed from Earth.
Every planet with multiple moons has them, at the equinoxes.For example, among the four Galilean moons 12 different eclipses are possible (e.g.Io eclipses Europa, Europa eclipses Io, Io eclipses Ganymede, etc).During this eclipse the rings of Saturn obscure a large fraction of the Sun's corona.(Michael Carroll, conception of the total mutual eclipse of Mimas by Tethys on as viewed from the surface of Mimas.