The global flow of the hyperbolic restricted three-body problem

Physics

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Scientific paper

Two mass points of equal masses m 1 = m 2 > 0 move under Newton's law of attraction in a non-collision hyperbolic 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 remains on the line L. The hyperbolic restricted 3-body problem is to describe the moton of m 3. Our main result is the characterization of the global flow of this problem.

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