QUESTION:
I know Newton's Laws are most often used to calculate and correct 
trajectories when spacecraft are sent to the planets.  But I would like 
to know if it is ever necessary to use Einstein's relativity for these 
calculations.  If so, what would be a typical mission requiring this 
refinement?  Is this necessary on Mars missions?

ANSWER from Charles Whetsel on May 6, 1997:
We do account for relativity in our calculations, but not in the 
manner you might expect.  The trajectories that we use to travel 
between earth and Mars don't carry the spacecraft nearly fast enough 
for relativity to be a major effect on the trajectory itself.  There 
are, however two areas where relativity makes a very tiny, but 
noticable effect.

The first of these has to with the way in which the gravity field of a
planet is foreshortened due to the fact the planet is moving in a 
fairly fast trajectory around the sun.  Once we are in orbit around 
Mars, we will account for this effect by modelling the fact that the 
gravity field on the leading edge of Mars' orbit (as it moves around 
the Sun) is not symmetric with the gravity field on the trailing edge 
(opposite to Mars's velocity).

A second effect of relativity can be observed during certain parts of 
the mission when the earth and Mars are on opposite sides of the Sun 
from each other.  Since one of the main methods by which we determine
the position of the spacecraft involves measuring delays in the path 
length of the radio signal that we send to the spacecraft, the 
gravitational bending of the radio beam (as it passes near the Sun) 
can cause a noticable delay in the signal, which makes Mars (and our
spacecraft in orbit around Mars) appear to be at a different position from where it really is.

You asked if it is "necessary" for us to refine our calculations based 
on relativity, and I guess the short answer probably should be "No."  
We could probably do our jobs just fine without making these
refinements, but when we collect real data and compare it to the models 
both with and without relativistic effects, the ones with the 
relativistic effects do a better job of fitting the data, so we use 
those instead!