The theory of the Trojan asteroids. V

Details The theory of the Trojan asteroids. V The theory of the Trojan asteroids. V

May 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985cemec..36...19g&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 36, May 1985, p. 19-45.

Astronomy and Astrophysics

Astronomy

3

Asteroids, Celestial Mechanics, Lagrangian Equilibrium Points, Trojan Orbits, Kinematics, Periodicals, Series Expansion, Three Body Problem, Asteroids, Trojan Asteroids, Theoretical Studies, Long-Period Comets, Orbits, Motion, Celestial Mechanics, Astronomy, Three-Body Problem, Kinematics, Calculations

Scientific paper

E. W. Brown conjectured (1911) that the family of the long-periodic orbits in the Trojan case of the restricted problem of three bodies terminates in an asymptotic orbit passing through the Lagrangian point L3 at t = ±∞. In 1977 the author showed that such an orbit deviates from L3 by the epicyclic term mg(±∞). It is shown here that g(±∞) ≠ 0, so that the Brown conjecture regarding L3 is false. Contrary to what Brown believed, there is an entire family of homoclinic orbits, doubly asymptotic to short-periodic orbits around L3. The kinematics of the homoclinic family is investigated here in some detail.

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