QUESTION:
How fast can the Galileo spacecraft go without using it's engines often 
and how fast is it going right now?

ANSWER from Robert Haw on December 21, 1995:
The Galileo spacecraft does not use its thrusters (engines) to increase its
speed.  They are used primarily to *slow* Galileo and also to change the
*direction* it is travelling.  That is, if we determine that Galileo is going
somewhere we don't want it to, we will adjust its path (trajectory) in order
to return it to the path we want it to follow.  

Galileo was endowed with all the velocity (speed) it required when it left
Earth.  In this sense, Galileo is like a bullet fired from a gun, and not
at all like an automobile travelling across the country.

Galileo, however, is a little special because it left Earth three times, not
just once.  The rocket booster that pushed Galileo out of Earth orbit 
initially did not have the energy to push Galileo fast enough.  So what 
happened was this:  Galileo had to 'dance' around the inner solar system, 
passing Venus once and Earth twice (after launch) in order to pick up 
additional speed.  And all without using its engines.  It's a little bit 
like swinging a sling around your head in order to propel the rock a long 
way.  That's how Galileo got going fast enough without even using its 
engines (the booster is not considered a part of Galileo).

Galileo left Earth for the last time travelling with a velocity of 9 km/s
(20,250 mph).  The fastest Galileo will ever travel occurred just as the 
spacecraft encountered Io, one of Jupiter's moons that Galileo passed by
during its approach to Jupiter.  The spacecraft was travelling at a velocity
of 24.1 km/s (54,225 mph) at that time.  The reason it's travelling faster
now than when it left Earth (without using its engine to speed up) is 
because of Jupiter's enormous gravity force -- that's what accelerated Galileo 
to its high speed.  

We used the main engine to slow Galileo down as we passed behind Jupiter, 
enabling the spacecraft to enter into orbit around that planet (rather than 
flying away never to return).  The speed of Galileo right now (Dec 21) is 
4.4 km/s (9,900 mph).  During the next two years as the remaining part of the
mission, the satellite tour, unfolds, Galileo will reach speeds of 8 km/s
(18,000 mph).