QUESTION:
Why wasn't a Hohmann transfer orbit used to get Galileo into the
Jovian sphere of influence (SOI)?

ANSWER from Lou D'Amario on January 10, 1996:
Prior to the Space Shuttle Challenger accident, Galileo was scheduled
to be launched in May 1986 on a "direct" Earth-to-Jupiter transfer.
In the world of interplanetary mission analysis, a "direct" transfer
is a trajectory that does not use gravity-assist flybys. The direct
transfer that Galileo would have used (if it had been launched in 1986)
was very close to a Hohmann transfer.

After the Challenger accident occurred, NASA decided that it would not
be safe to use the liquid-fueled Centaur upper stage in the Shuttle.
(The upper stage is a separate rocket motor attached to an interplanetary
spacecraft that boosts the spacecraft out of Earth orbit to get it
going on its interplanetary transfer.) The loss of the Centaur upper
stage meant that Galileo could no longer use a direct (nearly Hohmann)
transfer to get to Jupiter. The reason for this is that the Centaur
was the most powerful upper stage available -- and the only one that
could give Galileo enough speed to fly a direct transfer to Jupiter.

The upper stage that Galileo could use was called the Inertial Upper
Stage (or IUS). The IUS could only give Galileo enough speed to get
to Venus or Mars. So the mission designers working on Galileo looked
for a way to get Galileo to Jupiter by going to Venus first and then
using gravity assist flybys to boost its speed. After much work, the
Venus-Earth-Earth Gravity Assist (VEEGA) trajectory was discovered.
The net effect of the single Venus and two Earth flybys is to add
about 9 kilometers per second to Galileo's speed as it leaves the Earth
after the second Earth flyby. That's what is required to go directly
to Jupiter. Not surprisingly, the final leg of the VEEGA trajectory,
from the second Earth flyby to Jupiter, is nearly a Hohmann transfer.