Horseshoe periodic orbits in the restricted problem of three bodies for a sun-Jupiter mass ratio

Details Horseshoe periodic orbits in the restricted problem of three bodies for a sun-Jupiter mass ratio Horseshoe periodic orbits in the restricted problem of three bodies for a sun-Jupiter mass ratio

Nov 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981a%26a...103..288t&link_type=abstract

Astronomy and Astrophysics, vol. 103, no. 2, Nov. 1981, p. 288-294.

Astronomy and Astrophysics

Astrophysics

16

Jupiter, Three Body Problem, Sun, Orbits, Periodicity, Mass, Shape, Computer Techniques, Data, Procedure, Asymmetry, Diagrams, Evolution, Periods, Theoretical Studies, Celestial Mechanics, Motion

Scientific paper

Segments of seven families of symmetric horseshoe periodic orbits of the restricted three body problem for a sun-Jupiter mass ratio have been numerically determined. Each family is found to have a region consisting of smooth horseshoe shaped orbits with the family evolving to orbits acquiring loops on both sides of the smooth horseshoes. The general evolution of these families is discussed and one in particular (Rabe's horseshoe is a member of this family) is described in more detail with the aid of computer plots of orbits in this family. The smooth horseshoes do not continuously evolve along one family but are members of many distinct families. The change in shape of the smooth horseshoe orbits is examined as they have closer approaches to Jupiter. Each family has a bifurcation with an asymmetric family of periodic orbits. The initial conditions and other quantities describing these bifurcation orbits are given. Starting from these orbits the initial segments of the asymmetric families has been determined.

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