QUESTION:
Why is Galileo's energy before and after its approach to Io is not
conserved?  Is it possible that the angular momemtum is responsable for this
energy saving ?  If it is, can you send me some values of speed for
different moment of Galileo's trajectory before and after it's passage ''in
front'' of Io?

ANSWER from Lou D'Amario on February 16, 1996:
Energy is being conserved in the gravity-assist flyby that Galileo has
with the satellite Io. The law of conservation of energy applies to the
entire "system"  under consideration. The system in this case includes
Galileo and Io.  Therefore, the sum of the kinetic energies of Galileo and
Io must be the same before and after the flyby. Galileo can have a greater
energy after the flyby if Io's energy is reduced by the same amount. Since
Io has essentially an infinite mass (as compared to Galileo), the
reduction in the speed of Io in its orbit is extremely small. For Galileo,
the gravitational attraction of Io causes the speed to decrease from
30.289 kilometers per second (before the flyby) to 30.132 kilometers per
second (after the flyby). Galileo's mass at the Io flyby was 1967
kilograms. With that information, you can compute the energy change. Why
don't you ask your students to calculate how much Io slowed down given
that it would have to loose the same amount of kinetic energy?