henry (06/30/82)
Actually, Galileo's position for Neptune is considered quite accurate, partly because it is given with respect to the accurately-known position of Jupiter and partly because the way Galileo recorded his observations tended to cancel out some important observational errors. In fact, if Galileo had had setting circles on his telescope, he might have been the discoverer of Neptune. It is clear from his notes that he recognized Neptune as an anomalous object. But he got only a few chances at observations during the time when he could get Jupiter and Neptune in his telescope simultaneously, and without setting circles he had no way of finding a non-naked-eye object without a naked-eye object like Jupiter as a reference. The interest in Galileo's position is because his fairly-accurate position in fact is not quite consistent with the "standard" orbital elements of today. The orbit of Neptune is not really known terribly accurately, and the Galileo sighting (plus some later ones) strongly suggests that either the standard orbital elements are wrong or else an undiscovered planet is perturbing Neptune's orbit. For more details on all this, there was an article in Scientific American in the last year or so. The authors were the people who discovered the Galileo sighting. Sorry, I don't have the exact date handy.