EJECTION—COLLISION Orbits and Invariant Punctured Tori in a Restricted FOUR-BODY Problem

Details EJECTION—COLLISION Orbits and Invariant Punctured Tori in a Restricted FOUR-BODY Problem EJECTION—COLLISION Orbits and Invariant Punctured Tori in a Restricted FOUR-BODY Problem

May 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998cemda..71....1m&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 71, Issue 1, p. 1-14 (1998).

Astronomy and Astrophysics

Astronomy

Restricted Problem, Invariant Tori, Ejection&Ndash, Collision Orbits, Ejection–Collision Orbits

Scientific paper

We study the motion of an infinitesimal mass point under the gravitational action of three mass points of masses μ, 1-2μ and μ moving under Newton's gravitational law in circular periodic orbits around their center of masses. The three point masses form at any time a collinear central configuration. The body of mass 1-2μ is located at the center of mass. The paper has two main goals. First, to prove the existence of four transversal ejection-collision orbits, and second to show the existence of an uncountable number of invariant punctured tori. Both results are for a given large value of the Jacobi constant and for an arbitrary value of the mass parameter 0<μ≤1/2.

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