An approximate solution to the energy change of a circular binary in a parabolic three-body encounter

Details An approximate solution to the energy change of a circular binary in a parabolic three-body encounter An approximate solution to the energy change of a circular binary in a parabolic three-body encounter

Nov 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987mnras.229..333h&link_type=abstract

Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 229, Nov. 15, 1987, p. 333-344. Research supported by t

Statistics

Applications

10

Approximation, Binary Stars, Energy Transfer, Orbit Calculation, Parabolic Bodies, Three Body Problem, Circular Orbits, Dynamic Stability, Eccentric Orbits, Perturbation Theory

Scientific paper

Parabolic encounters between a circular binary and a third body of similar mass are studied. Numerical orbit calculations, about 18,000 in total, are compared with predictions from perturbation theory. Even though the perturbation theory is not strictly applicable near the stability boundary, the functional forms from the theory can be used, and the unknown coefficients can be fit from the numerical data. In this way analytic functions are constructed, valid near the stability boundary, which give the relative energy change of the binary Delta E/E and its final eccentricity e as a function of the seven initial parameters of the problem. The accuracy of the functions are studied; the expression for the energy change is found to be good for most of the phase space, while eccentricity function behaves less satisfactorily. Applications to the stability of hierarchical triple systems are discussed.

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