Abstract
The Stability of the Solar System as hierarchical dynamical system is investigated with analytical methods i) by using the topological stability criterion of the general 3-body problem for 3-body subsystems ii) by exploiting the hierarchical arrangement of the whole system to develop a new perturbation theory containing as smallness parameters both mass and distance ratios. At the first order in these parameters we get, for the inner Solar System, a minimum lifetime of ~108y. Most of the results presented here are discussed in detail in Milani and Nobili (1982,1983a,1983b) which we shall refer to as Paper I, II and III, respectively.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Cohen, C.J., Hubbard, E.C. and Oesterwinter, C. (1973), Astr.Pap. Ephem. 22, 1.
Janizek, P.M., Seidelmann, P.K. and Duncombe, R.L. (1972), A.J. 77, 764.
Kresák, L. (1979), in “Asteroids” (T.Gehrels ed.), Univ. of Arizona, Tucson, 289.
Farinelia, P., Milani, A., Nobili, A.M. and Valsecchi, G.B. (1980) Icarus 44, 810.
Milani, A. and Nobili, A.M. (1983), “On Topological Stability in the General 3-Body Problem”, Celestial Mechanics, 31, 213.
Milani, A. and Nobili, A.M. (1983a), “On the Stability of Hierarchical 4-Body Systems”, Celestial Mechanics, 31, 241.
Milani, A. and Nobili, A.M. (1983b) “The Depletion of the Outer Asteroid Belt”, submitted to the Astronomical Journal.
Nacozy, P.E. (1977), Celestial Mechanics, 16, 77.
Roy, A.E. (1979), in “Instabilities in Dynamical Systems” (V.Szebehely ed.), Reidel Pu. Co., Dordrecht, p.177.
Walker, I.W., Gordon Emslie, A. and Roy, A.E. (1980), Celestial Mechanics 22, 371.
Walker, I.W. and Roy, A.E. (1981), Celestial Mechanics, 24, 195.
Wisdom, J. (1982), A.J. 87, 577.
Wisdom, J. (1983), Icarus 56, 51.
Szebehely, V. (1967), “Theory of Orbits”, Academic Press, N.Y. London.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 D. Reidel Publishing Company, Dordrecht, Holland
About this paper
Cite this paper
Milani, A., Nobili, A.M. (1984). On the Stability of the Solar System as Hierarchical Dynamical System. In: Berger, A. (eds) The Big Bang and Georges Lemaître. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6487-7_19
Download citation
DOI: https://doi.org/10.1007/978-94-009-6487-7_19
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-6489-1
Online ISBN: 978-94-009-6487-7
eBook Packages: Springer Book Archive