NASA wants to minimize any chance that Galileo might hit Europa -- for that is one of the very few other places in the Solar System with a serious chance of possessing either past or present-day microbial life, and Galileo was not sterilized before launch.
It was designed to endure Jupiter's ferocious radiation belts -- a very destructive environment for solid-state electronics -- for a two-year orbital mission.
But at the end of that time, having shown virtually no sign of radiation damage, it was then given the go-ahead for an additional two-year extended mission during which it carried out eight flybys of Europa and then two daring incursions into the inner regions of the radiation belts -- where they are over a dozen times more intense than at Europa -- in order to fly by Io and make the observations that had to be cancelled during its first Io flyby on the day of its arrival at Jupiter due to the tape recorder problem.
During that second mission, it again came through in good -- though not perfect -- shape, despite having to endure one unexpected and mysterious "storm" of radiation during one orbit last August that was several times more intense than any such dose anyone had ever anticipated.
The temporary radiation-caused electronic "safing" events that fouled up two of its eight Europa flybys were successfully eliminated by new software in time for the Io flybys; other new software worked around radiation-caused problems with its attitude-sensing gyros; and the only science instruments to suffer were the UV spectrometer (which finally failed completely) and the near-IR mapping spectrometer (whose spectral scanning ability suffered a breakdown that has ruined its ability to map the composition of surface materials, although it can still make detailed temperature maps).
Since it was still ticking, it was given permission for a further one-year extension of its mission, which it has now half completed -- making one more flyby each of Io, Europa and Ganymede, and showing absolutely no sign of further damage.
It is now partway through a very elongated orbit around Jupiter -- far outside the dangerous part of the radiation belts -- which will take it fully 20.7 million kilometers from the planet.
It will finally return to Jupiter's vicinity for another Ganymede flyby on Dec. 28 -- while that moon is shrouded in the darkness of an eclipse by Jupiter, in order to study the surprisingly bright auroras generated by Ganymede's own unexpected magnetic field.
Only two days later, it will monitor one part of Jupiter's huge magnetosphere at the same time that the Cassini Saturn spacecraft makes a distant flyby of Jupiter and makes simultaneous measurements of another part of the magnetosphere, providing great new insights into the complex "weather patterns" of that magnetosphere.