Saari's conjecture for the restricted three-body problem

Details Saari's conjecture for the restricted three-body problem Saari's conjecture for the restricted three-body problem

Mar 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007cemda..97..211r&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 97, Issue 3, pp.211-223

Astronomy and Astrophysics

Astronomy

Celestial Mechanics, Restricted Three-Body Problem, Saari&Rsquo, S Conjecture, Bkk Theory

Scientific paper

Saari’s conjecture adapted to the restricted three-body problem is proven analytically using BKK theory. Specifically, we show that it is not possible for a solution of the planar, circular, restricted three-body problem to travel along a level curve of the amended potential function unless it is fixed at a critical point (one of the five libration points.) Due to the low dimension of the problem, our proof does not rely on the use of a computer.

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