Abstract
This paper gives analytical formulas to express the changes in orbital elements due to a close encounter between two particles of a ring or between two small satellites of a planet. The study is performed in the frame of the Hill's problem, extended to fully take into account the eccentricities. The Lie's transform method is used to average the Hamiltonian, particularized to two types of encounters: the ones with small impact distance (coorbitals) and those with a large one (shepherds).
Similar content being viewed by others
References
Delhaise, F. and Moons, M.: 1988, ‘Effects of a Non-Circular Shepherd upon a Planetary Ring’, in A.E. Roy, (ed.) Long Term Dynamical Behaviour of Natural and Artificial n-Body Systems, NATO Advanced Study Institute Series, Kluwer.
Dermott, S.F. andMurray, C.D.: 1981, ‘The Dynamics of Tadpole and Horseshoe Orbits. I. Theory,Icarus,48, 1–11.
Goldreich, P. andTremaine, S.: 1979, ‘Towards a Theory for the Uranian Rings’,Nature,277, 97–99.
Goldreich, P. andTremaine, S.: 1980, ‘Disk-Satellite Interactions’,Astrophys. J.,241, 425–441.
Hénon, M. andPetit, J. M.: 1986, ‘Series Expansions for Encounter-Type Solutions of Hill's Problem’,Celestial Mechanics,38, 67–100.
Moons, M. and Delhaise, F.: 1988, ‘Développements récents en planétologie dynamique’, Comptes-rendus de la table ronde de planétologie, Aussois, septembre 1987, D. Benest et C. Froeschlé, (ed.), Observatoire de Nice.
Petit, J. M. andHénon, M.: 1986, ‘Satellite Encounters’,Icarus,66, 536–555.
Showalter, M. R. andBurns, J. A.: 1982, ‘A Numerical Study of Saturn's F-Ring’,Icarus,52, 526–544.
Spirig, F. and Waldvogel, J.: 1985, ‘The Three-Body Problem with Two Small Masses : a Singular-Perturbation Approach to the Problem of Saturn's Coorbiting Satellites’, in V. Szebehely, (ed.), Stability of the Solar System and its Minor Natural and Artificial Bodies, NATO Advanced Study Institute Series, C. Reidel.
Yoder, C. F., Colombo, G., Synott, S. P. andYoder, K. A.: 1983, ‘Theory of Motion of Saturn's Coorbiting Satellites’,Icarus,53, 431–443.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Moons, M., Delhaise, F. & Depaepe, E. Elliptical Hill's problem (large and small impact parameters). Celestial Mechanics 43, 349–359 (1987). https://doi.org/10.1007/BF01234579
Issue Date:
DOI: https://doi.org/10.1007/BF01234579