In a flash of intuition, he had it: the new stars near Jupiter were actually moons, orbiting the planet as our moon orbits us.
It is running out of fuel for its thrusters, and once that has gone its path will be at the whim of the gravitational fields of Jupiter and its moons.
And new software, plus the ability to vary the projected sizes and brightnesses of planets and moons, makes it possible to simulate the sky from anywhere in the solar system: to see earthrise from Mars, for example, or to watch Jupiter's moons rise and set from a vantage point just above the gas giant's cloud-tops.
Galilei discovered the moons of Jupiter in, mebbe 1608, 1610, something like that.
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He saw the moons of Jupiter objects that circled another heavenly body in direct disobedience of the church's teaching.
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Robotic explorers have found evidence of water, a key ingredient for life on Mars and on the moons of Jupiter.
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But the best reason that we have to believe in the moons of Jupiter is that no one has to be prepared to die for them in order for them to be real.
Of course Galileo made great use of the telescope, and his discoveries--that Jupiter has its own moons, that the Milky Way is made of stars, that Venus has phases just like the moon--were turning points.
The ocean on Earth is thought to have been where life started, so these discoveries have led optimists to wonder whether the moons of Jupiter, rather than the deserts of Mars, may yield the first signs of extraterrestrial life.
Galileo, which has spent the past two years studying Jupiter and its four largest moons, will now concentrate on Europa's icy crust.
Astrobiologists are optimistic about Europa, one of Jupiter's four large moons.
If the question is life - and that's one of the most profound questions we can ask, he says - the answer is almost certainly not Mars or an asteroid, but rather the icy moons orbiting distant planets like Saturn and Jupiter.
Galileo's most remarkable discoveries, however, and the ones that dictated that it would eventually follow the probe's fiery fate, were made not about Jupiter itself, but (appropriately) about the four large Jovian moons discovered by Galileo Galilei, the 17th-century astronomer after whom the craft was named.
Because Jupiter's axis of rotation does not quite line up with its magnetic axis, the moons that orbit the planet feel such a fluctuating magnetic force.
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