Flat central configurations of four planet motions
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The flat central configurations of four planet motions are investigated with Wu's elimination method. We obtain 12 collinear central configurations and a necessary condition for determining flat but noncollinear central configurations. We also prove that the number of central configurations in planet motions of 4 bodies is finite under the condition that the masses and angular velocity of the planets do not satisfy any algebraic relations.
Key wordsCentral configuration Wu elimination
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- 1.A. Wintner, The Analytical Foundations of Celestial Mechanics, Second Printing, Princeton Univ. Press, Princeton, 1947.Google Scholar
- 2.Wu Wen-tsiin, Central Configurations in Planet Motions and Vortex Motions, MM Research Preprints No. 13(1995) 1–14.Google Scholar
- 3.F. R. Moulton, The Straight Line Solutions for the Problem of n-bodies, Annals of Math. 12 (1910) 1–17.Google Scholar
- 6.Wu Wen-tsiin, Basic Principles of Mechanical Theorem Proving in Geometries, Volume 1: Part on Elementary Geometries, Science Press, Beijing (in Chinese), 1984; English edition, Springer, Wien New York, 1994.Google Scholar