Geodesic
Two-dimensional configuration in the three-dimensional problem of four gravitating bodies
Russian journal of nonlinear dynamics, Tome 1 (2005) no. 2, pp. 215-232.

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The paper concerns the behavior of four gravitating bodies. Three bodies have zero mass and are referred to “planet”. The fourth body (the “Sun”) is a massive gravitating center. The conditions under which the four bodies lie in one plane are discussed. These conditions are shown to be deeply connected with arithmetic and geometric characteristics of “planets” motion.
Keywords: flattening moment, gravitating bodies, motion of planets
Mots-clés : torus. 
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     author = {G. A. Galperin},
     title = {Two-dimensional configuration in the three-dimensional problem of four gravitating bodies},
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G. A. Galperin. Two-dimensional configuration in the three-dimensional problem of four gravitating bodies. Russian journal of nonlinear dynamics, Tome 1 (2005) no. 2, pp. 215-232. http://geodesic.mathdoc.fr/item/ND_2005_1_2_a4/