QUESTION:
When will the Global Surveyor vehicle reach the point where Mars' 
gravity exceeds Earth's? How fast will it be going at that point?

ANSWER from Eric Graat on April 16, 1997:
On May 16, 1997 the gravitational influence of Mars on MGS will
begin to exceed that of the Earth's on MGS; however, both the
Earth's and Mars's gravitational forces are dwarfed by the Sun's
at this time.  The Sun's gravitational influence on MGS is about
100,000 times greater than the gravitational influences of either
the Earth or Mars.

On that date, the speed of MGS with respect to the Sun is ~23.25 
km/s (~52010 miles/hour).

The gravitational influence on MGS of Mars will dominate on about
September 9, 1997, three days from the planned encounter and orbit
insertion.