Exchange and Capture in the Planar Restricted Parabolic 3-Body Problem

Martha Alvarez-Ramírez (), Joaquín Delgado and Josep Maria Cors ()
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Martha Alvarez-Ramírez: UAM-Iztapalapa, Departamento de Matemáticas
Joaquín Delgado: UAM-Iztapalapa, Departamento de Matemáticas
Josep Maria Cors: Universitat Politécnica de Catalunya, Departament de Matemàtiques

A chapter in New Advances in Celestial Mechanics and Hamiltonian Systems, 2004, pp 1-28 from Springer

Abstract: Abstract Two attracting bodies m 1,m 2 move in parabolic orbits and a third massless body mo = 0 moves in the plane under the attraction of the primaries. We obtain the equations of motion of the massless particle in a rotating-pulsating coordinate system where the primaries remain fixed. Introducing an appropriate time scaling we obtain two invariant subsystems corresponding to final evolutions as time goes to±∞. We show that the set of initial conditions leading to parabolic escape of the infinitesimal mass is the union of invariant manifolds of dimension 3 and 4 and tend asymptotically to a central configuration. We also give a new criterion based in the Jacobi function analogous to the circular case, to guarantee elliptic capture. This criterion seems to be distinct from criteria introduced by Merman [1954] for the hyperbolic and parabolic restricted problems. We review Kocina’s example of exchange where the infinitesimal mass mo comes from infinity forming a bounded binary with m2 and escapes forming a bounded binary with m 1, and obtain new classes of orbits of symmetric exchange.

Keywords: 3-body problem; capture orbit; exchange orbit (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-9058-7_1

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DOI: 10.1007/978-1-4419-9058-7_1

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