Many satellites are found rotating around Jupiter in a ring, of which Io, Europa, Ganymede and Calisto are four important satellites. In 1610 Galileo was the first scientist to discover them hence is called Galilean satellites. Of the various satellites in solar system Ganymede is the largest among all. Planet Mercury is also small as compared to it.
The importance of Galilean satellites is in its period of rotation. Especially the rotation of Io, Europa and Ganymede is very much systematic. Io is very close to Jupiter for one rotation it takes 1.769 days. Europa completes one rotation around Jupiter in 3.551 days and Ganymede completes one rotation in 7.155 days and comes back to its original position. It is noticed from the rotation period of all these 3 satellites, that, when Io completes two rotations, Europa completes one rotation. And when Europa completes two rotations Ganymede completes one rotation. Thus the three satellites are rotating with respect to each other in synchronous rotation.
Laplace a famous scientist has expressed a simple equation for Galilean scientist which is given as,
Period of rotation of Io - Period of rotation of Europa + Period of rotation of Ganymede = 0
Due to this synchronous rotation, Io, Europa and Ganymede never come on the same side of Jupiter. When Europa and Ganymede are on the same side of Jupiter then Io is on their opposite side. When Io is at the extreme point in its orbit of rotation, Europa is at the lowest point and they meet. When Europa is at its maximum point in its orbit, it meets with Ganymede at that point wherever it is in its orbit
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