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The global flow of the parabolic restricted three-body problem


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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Correspondence to Josep M. Cors.

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Cors, J.M., Llibre, J. The global flow of the parabolic restricted three-body problem. Celestial Mech Dyn Astr 90, 13–33 (2004).

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  • global flow
  • restricted three-body problem
  • Sitnikov problem