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'Solar eclipses on Jupiter' occur when any of the natural satellites of Jupiter pass in front of the Sun as seen from the planet Jupiter. For bodies which appear smaller in angular diameter than the Sun, the proper term would be a transit. For bodies which are larger than the apparent size of the Sun, the proper term would be an occultation.
There are 5 satellites capable of completely occulting the Sun; Amalthea, Io, Europa, Ganymede and Callisto. All of the others are too small or too distant to be able to completely occult the Sun, so can only transit the Sun. Most of the more distant satellites also have orbits that are strongly inclined to the plane of Jupiter's orbit, and would rarely be seen to transit.
When the four largest satellites of Jupiter, the Galilean satellites, occult the Sun, a ''shadow transit'' can be seen on the surface of Jupiter which can be observed from Earth in telescopes.
Eclipses of the Sun from Jupiter are not particularly rare, since Jupiter is very large and its axial tilt (which is related to the plane of the orbits of its satellites) is relatively small - indeed, the vast majority of the orbits of all 5 of the objects capable of occulting the Sun will result in a solar occultation visible from somewhere on Jupiter's surface.
Shadow transits have been observed since the time of Galileo, and predicted times for these events date to the mid Seventeenth Century. It was soon noticed that predicted times differed from observed times in a regular way, varying from up to ten minutes early to up to ten minutes late. The Danish astronomer Ole Roemer used these errors to make the first accurate determination of the speed of light, correctly realizing the variations were caused by the varying distance between Earth and Jupiter as the two planets moved in their orbits around the Sun.
The website skytonight.comcarries links to predictions for eclipses of Jovian moons and their shadow transits.