FYI that would be (G * M1) in the equation above. Of course it's not just the mass of the Sun that counts, but the mass of everything else in the solar system too. However since the mass of all the rest is small compared to the mass of the sun, it need not bee known to the same precision as the total effective mass , and I suspect the net (G*M) is known to the required precision, in fact I'd bet on it, else there would not be all this who-hah. The astronomers understand those equations much better than most of us, I say most, because I suspect some of us are astronomers or astrophysicts, orbit mechanics specialists and so forth. (but not me, I do airplanes and such)
Since the craft is ten billion miles away from our Sol (I think that was the number - is that 11 light years?), it is outside the solar system. So we need the mass and distance from the stars in the neighborhood. If it is accelerating then it may be attracted to something ahead of it or to the side. Or its path may be curving if it is out of the plane of the galaxy. Seems to me that this error is really pretty small...