Jupiter's Moons: Where You Can Watch Gravity Do Its Thing
Why the Jovian System is a Good ‘Gravity Laboratory’
Most of the gravitationally driven phenomena in the Solar System are slow. The Moon takes a month to go through its phases; the planets take anywhere from 3 months to 164 years to complete an orbit; and the known Kuiper Belt objects take anywhere from about 250 to over 11,000 years to complete an orbit. You sure cannot see them do much in a night's observing.
Not so the Galilean Moons of Jupiter. With binoculars you can see that they are in very different positions every night. With a telescope and a webcam, you can detect movement of the inner moons in 20 min. Eclipses occur more than once every 2 days, although not necessarily at night from a given position on Earth. Over an evening you can often watch the paths of a pair of moons cross. The one that was nearer to Jupiter ends up being the further.
Some of the Saturn's moons are also fast movers, but they are twice as far away and therefore much harder to see. They are at the limit...