On the Restricted ThreeBody Problem when the Mass Parameter is Small
Abstract
We study some aspects of the restricted threebody problem when the mass parameter μ is sufficiently small. First, we describe the global flow of the twobody 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 ɛ>0, there exists a μ_{0}>0 such that if the mass parameter μ∈[0,μ_{0}], 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 ɛ.
 Publication:

Celestial Mechanics
 Pub Date:
 October 1982
 DOI:
 10.1007/BF01230662
 Bibcode:
 1982CeMec..28...83L
 Keywords:

 Existence Theorems;
 Three Body Problem;
 Collisions;
 Manifolds (Mathematics);
 Mass;
 Orbits;
 Two Body Problem;
 Astronomy