QUESTION:
Why is the Jupiter flyby so distant?Wouldn't going closer pick up more
speed and get Cassini to Saturn sooner?

ANSWER from Brian Rush on October 28, 1999:
In determining the optimal trajectory, many factors have to
be balanced.
 
If Cassini passed more closely to Jupiter it could get to
Saturn's orbit more quickly, but it would arrive at a place
in the orbit ahead of Saturn.

To pass by Jupiter more closely AND head towards an earlier
part of Saturn's orbit, to meet Saturn, would require Cassini to
come at Jupiter from a different angle. That, in turn, wouldn't
be possible without losing one or more of the previous
flybys (2 of Venus and 1 of Earth).

There would be no easy way to have the 4 flybys currently planned,
AND flyby Jupiter more closely, AND arrive right at Saturn. There
might be a complicated way to do that, but that would require more
trajectory maneuvers with the main engines, using much
more fuel (maybe even more than the spacecraft can carry),
losing the advantage of the flybys in the first place (which
is to gain acceleration without using more fuel).

Thus, all stages of a trajectory have to be looked at together,
and the best combination chosen, even if one part does not
seem ideal.  The location and date of the launch must also be
taken into account. This whole procedure is called Trajectory Optimization,
and is an area studied extensively by Mission Designers and Navigators.