On 7 December 1995, Galileo arrived at Jupiter and completed the first spacecraft to orbit Jupiter.
It was launched 6 years earlier and had as mission to study the Jovian system, Jupiter and its 4 moons (Io, Europa, Ganymede and Callisto):
The Galilean moons. From left to right, in order of increasing distance from Jupiter: Io, Europa, Ganymede, Callisto
The Journey To Jupiter
Galileo was originally planned for launch in 1986 with the Centaur-G liquid hydrogen fuelled booster. That rocket was powerful enough to take the Galileo directly to Jupiter.
But because of the Space Shuttle Challenger disaster in early 1986 the launch was pushed back and new safety protocols were instated.
That led to the postponing of the launch until 1989 by the Space Shuttle Atlantis, with a less powerful booster stage. One that wasn't powerful enough to make the direct trip.
To get there, they used a technique called the gravitational slingshot.
And the journey to Jupiter was going to require various gravitational slingshots to have additional velocity to reach its destination: the Venus-Earth-Earth Gravity Assist or VEEGA.
This means that the spacecraft flies by a planet and uses it's gravity to increase its speed. In this case it flew by Venus once and Earth twice to develop enough momentum to get to Jupiter.
Galileo's Final Destination
Galileo remained active for 8 years, sending data about the Jupiter and its moons. And then on 12 September 2003, its orbit was altered so it would enter the planet's atmosphere and burn up.
This was done to avoid contamination because the spacecraft hadn't been sterilised before launching,