On Brown's conjecture

Details On Brown's conjecture On Brown's conjecture

Oct 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..31..115h&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 31, Oct. 1983, p. 115-122.

Mathematics

13

Celestial Mechanics, Jupiter (Planet), Orbital Mechanics, Solar Orbits, Three Body Problem, Asymptotes, Jacobi Integral, Manifolds (Mathematics), Mass Ratios, Orbit Perturbation, Systems Stability

Scientific paper

The author examines the conjecture made by Brown (1911) that in the restricted three body problem, the long period family of periodic orbits around L4, ends on a homoclinic orbit to L3. By numerical integration he establishes that for the mass ratio Sun-Jupiter such a homoclinic orbit to L3 does not exist but that there exists a family of homoclinic orbits to periodic orbits around L3.

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