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Answers to the question How did Kepler determine the orbital period of Mars? describing careful observations centuries ago got me thinking.

What was the first analysis of observations that directly demonstrated that the Sun and the outer giant planets were moving around a common barycenter rather than all planets rotating around a fixed Sun?

I am not sure if First observation that the movement of a planet or asteroid in its orbit was affected by another planet? is a completely separate question, or if this confirmation happened all at once, but I've currently asked it separately.

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    $\begingroup$ @Max0815 any statement about things moving in orbits is incorrect so some degree, this is understood in orbital mechanics. Even a non-keplerian, non-newtonian n-body numerical simulation of the solar system doesn't include gravitational effects from things outside the solar system. As soon as you say the word "orbit" you've started down the rabbit hole of approximations. $\endgroup$
    – uhoh
    Commented Feb 25, 2019 at 4:46
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    $\begingroup$ Hey @Max0815 Here's the swirly diagram of the solar system barycentre that uhoh mentioned. astronomy.stackexchange.com/a/28036/16685 $\endgroup$
    – PM 2Ring
    Commented Feb 25, 2019 at 6:45
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    $\begingroup$ @uhoh I'll need to look more into this. More complicated than I thought xD. $\endgroup$
    – Max0815
    Commented Feb 26, 2019 at 20:14
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    $\begingroup$ @uhoh I don't know anything about this topic, and I can't to seem to find a source on this topic other than articles saying the barycenter is 1.07 solar radii. $\endgroup$
    – Max0815
    Commented Feb 27, 2019 at 23:56
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    $\begingroup$ @Max0815 The 1.07 is only for the Sun-Jupiter system. The other large planets (Saturn, Uranus, Neptune) are not as heavy as Jupiter but they are farther out and the combined motion moves the Sun almost 2 solar radii at maximum. $\endgroup$
    – uhoh
    Commented Feb 28, 2019 at 0:04

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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.

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  • $\begingroup$ Thanks for your answer, but as I also mentioned in this comment I've asked for the first observation rather than the first realization. $\endgroup$
    – uhoh
    Commented Sep 1, 2019 at 20:41
  • $\begingroup$ You'll want to update the question then or post a new one, this one specifically asks for analysis of observations. $\endgroup$
    – Greg Miller
    Commented Sep 1, 2019 at 21:53
  • $\begingroup$ ...that directly demonstrated that the Sun and the outer giant planets were moving around a common barycenter. I have a hunch that the answer to my question will coincide with the first measurement of the mass of the Sun or more likely, the ratio of the masses of Jupiter and the Sun. If you'd like to specifically cite his analysis of solar parallax then that could be an answer, though it seems he was so far off it was probably just wrong. But just saying "Newton said in a book that they go around a common center" isn't enough. $\endgroup$
    – uhoh
    Commented Sep 1, 2019 at 23:44
  • $\begingroup$ just fyi, while the bounty expires in about 15 hours, there's a further 24 hour "grace period". $\endgroup$
    – uhoh
    Commented Sep 1, 2019 at 23:51
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    $\begingroup$ "Analysis of observations" and "Observations" are different things. Newtons entire Principia is about showing how his laws of motion fit to prior observations, just one conclusion of which is the solar system barrycenter. It sounds like you're looking for something else, so good luck. $\endgroup$
    – Greg Miller
    Commented Sep 2, 2019 at 1:29

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