|MadSci Network: Physics|
Some of the people who have to take the Earth's movement into account are the hunters of extrasolar planets. They use Doppler shifts to look for very tiny deviations in the velocity of other stars, and therefore have to subtract out the motion of the Earth. While the detailed motion of the Earth is fairly complicated (if one takes into account the gravitational influence of all the other planets, tidal effects, rotation, etc.), it so happens that the Earth's motion can still be modelled very accurately.
For some of the extrasolar planets that they've discovered, the stars are only moving back and forth at about 10 meters per second (as a result of the gravitational perturbation from the orbiting planet). Certainly, to see this level of precision, one has to take into account the motion of the Earth. If this wasn't taken into account, the doppler shift imparted by the Earth's motion would dominate the analysis.
Try the links in the MadSci Library for more information on Physics.