Families of periodic orbits in the three-body problem

Details Families of periodic orbits in the three-body problem Families of periodic orbits in the three-body problem

Nov 1974

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974cemec..10..375h&link_type=abstract

Celestial Mechanics, vol. 10, Nov. 1974, p. 375-388.

Computer Science

Numerical Analysis

24

Celestial Mechanics, Orbital Mechanics, Periodic Functions, Three Body Problem, Angular Momentum, Numerical Analysis, Tables (Data)

Scientific paper

It is shown by a general argument that periodic solutions of the planar problem of three bodies (with given masses) form one-parameter families. This result is confirmed by numerical investigations: two orbits found earlier by Standish and Szebehely are shown to belong to continuous one-parameter families of periodic orbits. In general, these orbits have a nonzero angular momentum, and the configuration after one period is rotated with respect to the initial configuration. Similar general arguments show that in the three-dimensional problem, periodic orbits also form one-parameter families; in the one-dimensional problem, periodic orbits are isolated.

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