On the plane form and symmetry of asymptotic solutions in the restricted three-body problem

Details On the plane form and symmetry of asymptotic solutions in the restricted three-body problem On the plane form and symmetry of asymptotic solutions in the restricted three-body problem

Feb 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978sva....22...88l&link_type=abstract

(Astronomicheskii Zhurnal, vol. 55, no. 1, 1978, p. 156-163.) Soviet Astronomy, vol. 22, Jan.-Feb. 1978, p. 88-91. Translation.

Astronomy and Astrophysics

Astronomy

2

Asymptotic Methods, Lagrangian Equilibrium Points, Librational Motion, Orbit Calculation, Three Body Problem, Analytic Functions, Convergence, Elliptical Orbits, Liapunov Functions, Poincare Spheres

Scientific paper

It is shown that the asymptotic solutions for the libration points in the restricted three-body problem are planar and are situated in the plane of motion of the primary bodies. Moreover, they are symmetric with respect to a line joining the primary bodies. This is a consequence of the symmetry of the solutions to the restricted three-body problem, which is demonstrated for the restricted elliptical three-body problem.

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