On the restrited three-body problem when the mass parameter is small

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Abstract

We study some aspects of the restricted three-body problem when the mass parameter μ is sufficiently small. First, we describe the global flow of the two-body rotating problem, μ=0, and we use it for the analysis of the collision and parabolic orbits when μ≳0. Also we show that for any fixed value of the Jacobian constant and for any ε>0, there exists a μ0>0 such that if the mass parameter μ∈[0,μ0], then the set of bounded orbits which are not contained in the closure of the set of symmetric periodic orbits has Lebesgue measure less than ε. © 1982 D. Reidel Publishing Co.
Original languageEnglish
Pages (from-to)83-105
JournalCelestial mechanics
Volume28
Issue number1-2
DOIs
Publication statusPublished - 1 Sep 1982

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