Abstract
The main goal of this paper is to give an approximation to initial conditions for ejection-collision orbits with the more massive primary, in the planar elliptic restricted three body problem when the mass parameter µ and the eccentricity e are small enough. The proof is based on a regularization of variables and a perturbation of the two body problem.
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References
Abramowitz, M. and Stegun, I.: 1965, Handbook of Mathematical Functions, New York: Dover.
Brouwer, D. and Clemence, G.M.: 1961, Methods of Celestial Mechanics, Academic Press.
Chenciner, A. and Llibre, J.: 1988, ‘A Note on the Existence of Invariant Puctured Tori in the Planar Circular Restricted Three-Body Problem’, Ergod. Th. and Dynam. Sys. 8, 63–72.
Devaney, R.L.: 1978, ‘Collision Orbits in the Anisotropic Kepler Problem‘, Inventiones Math. 45, 221–251.
Devaney, R.L.: 1979–80, Singularities in Classical Mechanical Systems, Ergod. Th. and Dynam. Sys. I (Proceedings special year), A. Katok (ed.), Birkhauser, Basel. Maryland, pp. 211–339.
Llibre, J. and Pinyol, C.: 1990, ‘On the Elliptic Restricted Three-Body Problem’, Celestial Mechanics and Dynamical Astronomy 48, 319–345.
Llibre, J. and Simó, C.: 1980, ‘Oscillatory Solutions in the Planar Restricted Three-Body Problem’, Math. Ann. 248, 153–184.
McGehee, R.: 1974, ‘Triple Collision in the Collinear Three-body Problem’, Inventiones Math. 27, 191–227.
Martínez, R. and Pinyol, C.: 1994, ‘Parabolic Orbits in the Elliptic Restricted Three-Body Problem’, J. Diff. Equations 111, 299–339.
Szebehely, V : 1967, Theory of Orbits, Academic Press.
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This work was partially supported by DGICYT grant number PB90-0695.
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Pinyol, C. Ejection-collision orbits with the more massive primary in the planar elliptic restricted three body problem. Celestial Mech Dyn Astr 61, 315–331 (1995). https://doi.org/10.1007/BF00049513
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DOI: https://doi.org/10.1007/BF00049513