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On the Stability of Realistic Three-Body Problems

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Abstract:

We consider the system Sun—Jupiter—Ceres as an example of a planar, circular, restricted three-body problem and, after substituting the mass ratio of Jupiter/Sun (which is approximately 10-3) with a parameter , we prove the existence of stable quasi-periodic motions with frequencies close to the observed (average) frequencies reported in “The Astronomical Almanac” for . The proof is “computer-assisted”.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università dell'Aquila, 67100—Coppito, L'Aquila, Italy.¶E-mail: celletti@axscaq.aquila.infn.it, , , , , , IT

    Alessandra Celletti

  2. Dipartimento di Matematica, Università: di Roma Tre, Largo San Murialdo 1, 00146 Roma, Italy.¶E-mail: luigi@matrm3.mat.uniroma3.it, , , , , , IT

    Luigi Chierchia

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  1. Alessandra Celletti
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  2. Luigi Chierchia
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Received: 1 April 1996 / Accepted: 25 October 1996

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Celletti, A., Chierchia, L. On the Stability of Realistic Three-Body Problems . Comm Math Phys 186, 413–449 (1997). https://doi.org/10.1007/s002200050115

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  • DOI: https://doi.org/10.1007/s002200050115

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