Flat central configurations of four planet motions
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
Unable to display preview. Download preview PDF.
- 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