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A barycenter is the common center of mass of an orbiting system. Here is a illustrative gif from wikipedia:

enter image description here

The first mention of something like a barycenter that I could find is in a translation of Newton’s Principia, published in 1687, proposition 12, theorem 12:

https://en.wikisource.org/wiki/The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookIII-Prop2.

This includes the quote that: “the common centre of gravity of Jupiter and the sun will fall upon a point a little without the surface of the sun” which to me demonstrates a clear understanding and articulation of the idea of a barycenter. Does anyone know of an earlier clear reference to a barycenter?

Related: What are Kepler's laws (as he wrote them)?

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  • $\begingroup$ Please, why downvote this question? $\endgroup$
    – Connor Garcia ♦
    Feb 17, 2021 at 21:44

2 Answers 2

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I'm pretty sure Newton was the first to apply the notion of the barycentre to celestial motion, although the concept of a centre of mass may predate him.

Before Newton, there was a very strong demarcation between celestial motion and terrestrial motion, inherited from the Greek philosophers like Aristotle. (Similar philosophies applied outside the Western world). Celestial bodies had a celestial nature, and moved according to celestial principles, eg, they were perpetually in motion, and that motion was composed of perfect circles. Bodies on the Earth obeyed a different set of laws appropriate to their earthly nature. The essential quality of the earth element is to move towards the centre of the universe and to not otherwise move, unless something else interferes. So terrestrial objects didn't move unless they fell, or were pushed in some way, and would soon stop moving.

Newton did a lot of great scientific and mathematical work, but his outstanding insight was that a single scheme could describe both terrestrial motion and celestial motion. And that is the "core" point of the anecdote about Newton seeing the falling apple. Prior to Newton, the very idea of attempting to apply mundane mechanics to the heavens would have seemed strange to most natural philosophers, if not downright blasphemous.

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    $\begingroup$ Yeah, it always surprised me that Newton didn’t get into as much trouble as Galileo. $\endgroup$
    – Pierre Paquette
    Feb 16, 2021 at 22:01
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    $\begingroup$ @PierrePaquette That could be a fascinating topic to discuss, but it would take far too much space than is practical in a comment thread. ;) IMHO, Galileo's troubles were really more political than religious, per se. $\endgroup$
    – PM 2Ring
    Feb 16, 2021 at 22:12
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    $\begingroup$ @PierrePaquette That's a question for the history of Math and Science if you want detail, but it's an interesting bit of history. Galileo essentially called the Pope and other religious men of power who basically lived in his back yard "fools" and he published in Italian, not Latin, so anyone could read it (or have it read to them). Newton published in Latin, so the "common man" wouldn't read his work and 54 years had passed since Galileo's excommunication. Science had become more accepted in that time. Also, England had separated from the Catholic Church for over a century. $\endgroup$
    – userLTK
    Feb 16, 2021 at 22:40
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    $\begingroup$ @userLTK It's complicated. ;) For a condensed summary of what happened with Galileo, please see ncbi.nlm.nih.gov/pmc/articles/PMC2564400 $\endgroup$
    – PM 2Ring
    Feb 16, 2021 at 23:24
  • $\begingroup$ From what I remember, Galileo sort of got himself into trouble. If I remember rightly, the story is that he left a region where he was totally safe because he disliked teaching and moved to an institution in an area where he was vulnerable because the job had no teaching duties. $\endgroup$
    – Hollis Williams
    Feb 17, 2021 at 22:08
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The concept of "center of mass" in the form of the center of gravity was first introduced by Archimedes of Syracuse.

As far as the center of an orbiting system is concerned, the Antikythera mechanism is an ancient Greek hand-powered orrery, and the oldest known example of such a device, used to predict astronomical positions and eclipses for calendar and astrological purposes decades in advance. It materilize with gears the, then in use geometric models, based on epicycle with equants which are figures similar to your nice illustrative gif.

Similar, with the exception that the big circle (the sun) and the small circle (the planet) were exchanged. It was not because the greek did believe that the sun was orbitiong around the earth [that's a meaningless question for computation], but because it was a good way to take into account in the model the difference of speed (2nd Kepler law) with gears that cannot be elliptical. So there were no reason to make all the equans equal, and make them equal to the sun-earth distance, as Copernic did, simplifiying at cost of accuracy.

In antiquity, accuracy was much more important (for navigation, for oracle, and for religious feast) than explanation. So, if the epicycle, deferents and equants were of common use by Ptolemy, and if Archimedes did estimates the weight of the celestial bodies, it was not before the distinction between Weight and Mass, done by Newton, that the equant could be identified with the center of mass of an orbiting system.

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