QUOTE (centsworth_II @ Feb 29 2008, 08:00 PM)
According to one of Emily Lakdawalla's Planetary Society Blog entries,
at least some relativistic effects are already accounted for in spaceflight.Accounting for general relativity at Mercury
"It turns out that general relativity is routinely accounted for in
spacecraft navigation.... the NASA navigation software developed
at JPL....incorporates the Ted Moyer formulations for navigation
which includes mathematical expressions that describe the effects
of general relativity."
I can also vouch for this about General Relativity. Back in the '70s when I worked briefly at JPL I wrote a numerical integration program to calculate planetary positions and conjunctions (as a hobby). This was based on information from DE96 (the latest JPL ephemeris at the time) and some other references. Like the procedure used in DE96, I included in my program explicit terms that correct for GR and utilized them for all the planets out to Saturn. This was the basis for my Sky and Telescope article in March 1979.
EDIT: Some additional comments to this discussion.
1) I think Mercury has more of an effect partly due to its eccentric orbit, thus the precession of its perihelion is more noticeable compared to the case of a circular orbit.
2) The uncertainty of the Gravitational Constant is much greater than the uncertainty of the spacecraft orbits. The corresponding masses are also uncertain, but the combination of G and M still can be stated with higher precision.
3) I wonder if the JPL ephemerides would/should account for frame dragging (as noted in post #1), or something simple like forces generated by Earth's magnetic field?