They named them Callisto, Ganymede, Europa and Io.
They are now referred to as the Galilean moons.
Galileo recorded their orbits around Jupiter.
This was, in fact, the first time a planet was discovered as the center of motion, other than Earth.
Jupiter has sixty-three known satellites as of 2004.
This includes the four larger Galilean moons and many more small ones.
Some of them have never been named.
Jupiter is actually slowing down - very gradually - because of the tidal drag that the Galilean moons produce.
The same forces change the orbits of Jupiter's moons, forcing them ever farther from the planet.
Ganymede, Europa and Io have almost synchronous orbits.
Their orbits evolve together.
Callisto will also become part of this phenomenon, within about 300 million years.
The Galileo probe, which was seeking more facts about Jupiter, discovered that the planet has an intense belt of radiation between its rings and the highest layers of its atmosphere.
Jupiter has rings like Saturn, except that they are much smaller and fainter.
No one knew they existed until fairly recently - they were discovered when Voyager 1 scientists wanted a closer look.
Since then, the rings have been imaged in infra-red photography from Earth, and by Galileo.
While Saturn's rings are bright, Jupiter's rings are dark.
They are most probably composed of grains of rocky material.
And while Saturn's rings contain ice, Jupiter's seem not to.
Any particles within Jupiter's rings don't stay there for very long, due to magnetic and atmospheric drag.
Scientists don't know why Jupiter's rings are so dark while Saturn's are so bright.
In July of 1994, the Shoemaker-Levy 9 comet collided with Jupiter, and the visual results were spectacular.
Even with amateur telescopes, the effects were visible from Earth.
And the debris could still be seen for almost a year after the collision.
When Jupiter is in the night-time sky, as viewed from Earth, it is usually the brightest "star" visible.
Venus is brighter, but not usually visible in a sky that is dark.
The four moons of Jupiter are easy seen with binoculars.
The Great Red Spot and a few of Jupiter's bands can be seen with a small telescope.