Abstract
Hill-type stability surfaces are computed for the general hierarchical three-body problem for non-zero eccentricities of the initial osculating orbits. Significant differences are found between them and the one obtained for initial zero eccentricities. Application is made to the triple subgroups of the Solar System; in particular it is found that no analytical guarantee of Hill-type stability can be given to any of the satellites against solar perturbations.
Similar content being viewed by others
References
Dole, S. H.: 1961,Am. Rocket Soc. J. 2, 214.
Easton, R. W.: 1971,J. Diff. Eq. 10, 371.
Easton, R. W.: 1975,J. Diff. Eq. 19, 258.
Harrington, R. S.: 1972,Celest. Mech. 6, 322.
Harrington, R. S.: 1977,Astron. J. 82 753.
Horedt, G. P.; Pop, P., and Ruck, H.: 1977,Celest. Mech. 16, 209.
Marchal, C.: 1971,Astron. Astrophys. 10, 278.
Marchal, C. and Saari, D. G.: 1975,Celest. Mech. 12, 115.
Nacozy, P. E.: 1976,Astron. J. 81, 787.
Nacozy, P. E.: 1977,Celest. Mech. 16, 77.
Roy, A. E.: 1979, in V. G. Szebehely (ed.),Instabilities in Dynamical Systems, D. Reidel Publ. Co., Dordrecht, Holland, p. 177.
Saari, D. G.: 1974,SIAM J. Appl. Math. 26, 806.
Smale, S.: 1970a,Invent. Math. 10, 305.
Smale, S.: 1970b,Invent. Math. 11, 45.
Szebehely, V. G. and Zare, K.: 1977,Astron. Astrophys. 58, 145.
Walker, I. W., Emslie, A. G., and Roy, A. E.: 1980,Celest. Mech. 22, 371.
Walker, I. W. and Roy, A. E.: 1981,Celest. Mech. 24, 195.
Walker, I. W. and Roy, A. E.: 1983,Celest. Mech. 29, 117.
Zare, K.: 1976,Celest. Mech. 14, 73.
Zare, K.: 1977,Celest. Mech. 16, 35.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Valsecchi, G.B., Carusi, A. & Roy, A.E. The effect of orbital eccentricities on the shape of the hill-type analytical stability surfaces in the general three-body problem. Celestial Mechanics 32, 217–230 (1984). https://doi.org/10.1007/BF01236601
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01236601