The global flow of the parabolic restricted three-body problem

Details The global flow of the parabolic restricted three-body problem The global flow of the parabolic restricted three-body problem

Sep 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004cemda..90...13c&link_type=abstract

Celestial Mechanics & Dynamical Astronomy, Volume 90, Issue 1-2, pp. 13-33

Astronomy and Astrophysics

Astronomy

2

Global Flow, Restricted Three-Body Problem, Sitnikov Problem

Scientific paper

We have two mass points of equal masses m 1=m 2 > 0 moving under Newton's law of attraction in a non-collision parabolic orbit while their center of mass is at rest. We consider a third mass point, of mass m 3=0, moving on the straight line L perpendicular to the plane of motion of the first two mass points and passing through their center of mass. Since m 3=0, the motion of m 1 and m 2 is not affected by the third and from the symmetry of the motion it is clear that m 3 will remain on the line L. The parabolic restricted three-body problem describes the motion of m 3. Our main result is the characterization of the global flow of this problem.

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