It's commonly known that the center of gravity of our solar system is not the suns axis, and, that the same goes for other orbital systems like Pluto and Charon, and so on. When was it discovered that our sun has an orbit around a barycenter?
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$\begingroup$ This doesn't answer your question, but Kepler's Laws of Planetary Motion are the first instance I can think of (off the top of my head) where the concept of "a common center" exists. However, you could argue that the concept of epicycles also had the Sun revolving around an empty point. Just as a note, make sure you're not confusing revolution with rotation. The sun revolves around the barycenter (sort of -- it's more complicated than that though), but rotates on its own axis. $\endgroup$– user21Oct 17, 2018 at 4:29
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$\begingroup$ the question isn't when it was discovered or entered public consciousness that planets revolve around the sun, it is a bit of a leap to go from that to that the sun is revolving a barycenter of the solar system as a whole $\endgroup$– pol0Oct 17, 2018 at 4:34
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1$\begingroup$ @barrycarter isn't Kepler first law incompatible with your statement? Or is "the Sun at one focus" not what Kepler actually wrote (genuine question)? $\endgroup$– ProfRobOct 17, 2018 at 6:35
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2$\begingroup$ @barrycarter Thinking... The best way to think about a small planet's orbit is as an orbit with the Sun at the focus with a secondary (smaller amplitude) orbit with a 12-year period around the Sun-Jupiter barycentre superimposed. I am withdrawing my suggestion that if you modelled Mercury's orbit as an approximate ellipse that the SSB would be the best focus. This would be exactly true for 2-bodies, is approximately true for Jupiter, but is not true for >2 bodies where a third body is much more massive. $\endgroup$– ProfRobOct 17, 2018 at 19:57
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1$\begingroup$ @uhoh I think you have misinterpreted. It is quite the opposite. Mercury has an 88 day orbit essentially with the centre of the Sun at one focus (actually the Sun-Mercury barycentre). If you look on longer timescales the Sun then orbits the solar system barycentre. $\endgroup$– ProfRobOct 19, 2018 at 12:02
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Newton explained the motions of planets in the solar system in Principia in 1687.
This amongst many other things "defines the very slow motion of the Sun relative to the solar-system barycenter;" (https://en.m.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica ).
Since Newton came up with the ideas of gravity and barycentres, surely this is the answer? (Though, I note there is some debate that the inverse square law may have been around and discussed during the previous decade).
Ideas that the Sun moved were of course commonplace before then.
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$\begingroup$ Not when the theory was discovered, asking more for when the actual motions were mapped. Aristarchus and so on had detailed the theory as well. Today, online, I can see detailed maps of the suns orbit around the barycenter, when did that begin to enter the scene? $\endgroup$– pol0Oct 17, 2018 at 7:36
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1$\begingroup$ You should ask that then @pol0. Currently your question doesn't say that $\endgroup$ Oct 18, 2018 at 22:05