QUESTION:
What is the current estimate for the Earth flyby altitude?

ANSWER from FAQ on June 3, 1999:
Before Cassini was launched, we reported that the swingby
altitude would be at least 800 km (500 miles). That actual
flyby altitude, however, depends on Cassini's launch date.
Since Cassini was launched on October 15 (as opposed to the
originally planned launch date of October 6) the actual
swingby altitude will be about 1173 km (729 miles).