The first approximate resolution of the three-body problem in celestial mechanics

CLAIRAUT, Alexis Claude.

Théorie de la lune, déduite du seul principe de l'attraction réciproquement proportionnelle aux quarrés des distances.

Paris: Dessaint & Saillant, 1765.

2nd Edition. Hardcover. Very Good. Item #001995

4to (252x200 mm), [1-3] 4 [5] 6-7 [8], [1] 2-161 [1] pp. and folding plate with diagrams. Contemporary French calf with 5 raised bands, gilt in compartments and with red morocco label (hinges cracked, extremities worn, boards rubbed), red-dyed edges, marbled endpapers, text only very minor spotted and age-toned. ----

DSB III, p.283. SECOND EDITION (the first in France of both papers unified). First published in 1752, this discourse won the annual prize at the Russian Imperial Academy. "In 1743 Clairaut read before the French Academy a Paper entitled 'L'orbite de la lune dans le systeme de M. Newton,' Newton was not fully aware of the movement of the moon's apogee, and therefore the problem had to be reexamined in greater detail. However, Clairaut - and d'Alembert, and Euler, who were also working on this question - found only half of the observed movement in their calculations. It was then that Clairaut suggested completing Newton's law of attraction by adding a term inversely proportional to the fourth power of the distance... The minimal value of the term added soon made Clairaut think that the correction - all things considered - could apply to the calculations but not to the law... Clairaut found toward the end of 1748... that in Newton's theory the apogee of that moon moved over a time period very close to that called for by observations. This is what he declared to the French Academy on 17 May 1749. This first approximate resolution of the three-body problem in celestial mechanics culminated in the publication of the Théorie de la lune in 1752 and the Tables de la lune in 1754." (DSB III, p. 283).

Sold