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Stable Orbits in the Circular Plane Restricted Three-Body Problem*

Published online by Cambridge University Press:  12 April 2016

Daniel Benest*
Affiliation:
Observatoire dg Nice

Abstract

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We investigate by numerical exploration the extended regions of stability for retrograde satellites when the mass of the less massive body increases up to μ = 0.5. A preliminary study is made of the characteristic and stability properties of the families of periodic orbits; then the general case of non-periodic orbits is considered. Those numerical explorations show that for stable large non-periodic orbits, the motion can be decomposed into a fast “reference motion” and slow libration; we study theoretically this libration in Hill’s case for which the “reference motion” is elliptic.

Resumen

Resumen

Se investigan por exploración numérica las regiones extendidas de estabilidad para satélites retrógrados cuando la masa del cuerpo poco masivo crece hasta μ = 0.5. Se hace un estudio preliminar de las características y propiedades de estabilidad de las familias de órbitas periódicas. En seguida se considera el caso general de órbitas no periódicas. Dichas exploraciones numéricas muestran que para grandes órbitas aperiódicas el movimiento se puede descomponer en un “movimiento de referencia” rápido y una libración lenta. Estudiamos esta libración teóricamente en el caso de Hill, por el cual el “movimiento de referencia” es elíptico.

Type
Session 5
Copyright
Copyright © Otto G. Franz and Paris Pismis 1977

Footnotes

*

Figures 2, 3 and 6c have been reproduced from Astron. and Astrophys., 1974, 32, 39. Figures 4a-h, 5, and 6d-n from Astron. and Astrophys., 1975, 45, 353 published by Springer-Verlag Berlin-Heidelberg-New York on behalf of the Board of Directors, ESO.

References

Benest, D. 1974, Astron. and Astrophys., 32, 39.Google Scholar
Benest, D. 1975, Astron. and Astrophys., 45, 353.Google Scholar
Benest, D. 1976, Celes. Mech., 13, 203.CrossRefGoogle Scholar