In 1821 Alexis Bouvard published a book with tables of the orbits of Jupiter, Saturn and Uranus and future predictions of the orbits. The real orbit of Uranus deviated from the calculations which was the starting point of an investigation which eventually led to the discovery of Neptun.

I am wondering how he performed the calculation, which I presume is not just Keppler Orbits, but including some pertubation from the know planets (correct me if I understand that wrong). Usually nowadays you would do pertubation calculations in the Hamilton-Jacobi framework, but since Jacobi just started college in 1821 it has not been invented yet (I presume).

So anybody knows how exactly these calculation were done at that time?


1 Answer 1


Perturbation theory begins with Newton who tried to explain the motion of the Moon (this is the object in the solar system whose motion deviates most from Keplerian orbits). Newton essentially failed, and more advanced methods of perturbation theory were developed in 18th century, main contributions are due to d'Alembert, Clairaut, Euler and Mayer. This resulted in the tables of Moon motion which had accuracy sufficient for navigation (that is an error of fraction of a minute over several years). Same ideas were applied to the large planets, of which the most conspicuous case is the 3-body problem Sun-Jupiter-Saturn. The perturbation theory is too technical to be explained here (see the reference below), but the modern notions of Hamilton-Jacobi framework slowly evolved in the process of this development of perturbation theory. This is a general pattern: scientists solve concrete problems, and only after that their methods are generalized into some general framework.

Ref. Curtis Wilson, The Great Inequality of Jupiter and Saturn: from Kepler to Laplace, Arch. Hist. Exact Sci., 33, 1/3, 1985, 15-290. Contains a popular not very technical historical exposition of perturbation theory, as it developed in the investigation of Jupiter and Saturn.

  • $\begingroup$ Thanks. You state that the pertubation theory is too technical to be explained here (the technical part is what interests me most) and see reference below. But for the reference below you say it is no lt technical. Could you explain? $\endgroup$
    – lalala
    Apr 13 at 18:57
  • $\begingroup$ The reference is 275 pages long. Do you want me to explain it here?? For full explanation, read the paper of Bouvard. $\endgroup$ Apr 14 at 5:10

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