First observation that the Sun and Jupiter (and friends) move around a common barycenter?
This idea would be a direct reduction from Newton's laws of motion.  In his Principia he states "Hence the common centre of gravity of the earth, the sun, and all the planets, is to be esteemed the centre of the world".  So that would be the first evidence of the Sun moving outside of a geocentric universe.  Of course he wouldn't have known about Uranus and Neptune at the time.