Comment Re:Wouldn't it be cool... (Score 2, Informative) 116
You said they might just need to use a bit more fuel to correct, but the story also mentions that that they went to great lengths to preserve as much fuel as possible, so i still wonder if they needed to use relativity or not...
Random variation in solar activity, random outgasing of surfaces, and random light pressure effects on decaying surface patterns/paints should totally swamp any relativity effects.
There are also experimentally observed effects that have no current explanation. Perhaps they are just noise, perhaps not. The topics you need to search for are Flyby Anomaly and Pioneer Anomaly. That will give you enough background on the scale of unknown orbital forces to compare with the theoretical effects of relativity calculations.