Previous article Next article Restrictions on the Motion of the Three-Body ProblemDonald G. SaariDonald G. Saarihttps://doi.org/10.1137/0126072PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractIt is shown in the three-body problem of Newtonian mechanics that there exist values of the constants of motion which define regions in physical space where motion cannot occur.[1] Jean Chazy, Sur l'allure du mouvement dans le problème des trois corps quand le temps croı⁁t indéfiniment, Ann. Sci. École Norm. Sup. (3), 39 (1922), 29–130 MR1509241 CrossrefGoogle Scholar[2] Harry Pollard and , Donald G. Saari, Singularities of the n-body problem. I, Arch. Rational Mech. Anal., 30 (1968), 263–269 10.1007/BF00281534 MR0231565 0174.26904 CrossrefISIGoogle Scholar[3] Donald G. Saari, Expanding gravitational systems, Trans. Amer. Math. Soc., 156 (1971), 219–240 MR0275729 0215.57001 CrossrefISIGoogle Scholar[4] Donald G. Saari, On oscillatory motion in gravitational systems, J. Differential Equations, 14 (1973), 275–292 10.1016/0022-0396(73)90048-X MR0664946 0277.70003 CrossrefISIGoogle Scholar[5] Aurel Wintner, The Analytical Foundations of Celestial Mechanics, Princeton Mathematical Series, v. 5, Princeton University Press, Princeton, N. J., 1941xii+448 MR0005824 0026.02302 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Stability of the coplanar planetary four-body systemResearch in Astronomy and Astrophysics, Vol. 20, No. 9 | 1 Sep 2020 Cross Ref On an analogy in the restricted and general three-body problemsAdvances in Space Research, Vol. 64, No. 5 | 1 Sep 2019 Cross Ref Hill stability of the coplanar four-body problem with a binary subsystemMonthly Notices of the Royal Astronomical Society, Vol. 469, No. 3 | 7 June 2017 Cross Ref On a new inequality in the planar three-body problemAstrophysics and Space Science, Vol. 361, No. 6 | 30 May 2016 Cross Ref Analytical criteria of Hill stability in the elliptic restricted three body problemAstrophysics and Space Science, Vol. 358, No. 2 | 22 July 2015 Cross Ref The Hill stability of low mass binaries in hierarchical triple systemsCelestial Mechanics and Dynamical Astronomy, Vol. 107, No. 1-2 | 14 May 2010 Cross Ref Stability criteria for hierarchical triple systemsCelestial Mechanics and Dynamical Astronomy, Vol. 100, No. 2 | 3 January 2008 Cross Ref Third Body Perturbations of Double StarsVisual Double Stars: Formation, Dynamics and Evolutionary Tracks | 1 Jan 1997 Cross Ref A search for planets in binary star systems: A new type of approachEarth, Moon and Planets, Vol. 54, No. 3 | 1 Sep 1991 Cross Ref ReferencesThe Three-Body Problem | 1 Jan 1990 Cross Ref From rotations and inclinations to zero configurational velocity surfaces, II. The best possible configurational velocity surfacesCelestial Mechanics, Vol. 40, No. 3-4 | 1 Sep 1987 Cross Ref Studies in the Stability of Hierarchical Dynamical SystemsStability of the Solar System and Its Minor Natural and Artificial Bodies | 1 Jan 1985 Cross Ref From rotations and inclinations to zero configurational velocity surfaces I. A natural rotating coordinate systemCelestial Mechanics, Vol. 33, No. 4 | 1 Aug 1984 Cross Ref The effect of orbital eccentricities on the shape of the hill-type analytical stability surfaces in the general three-body problemCelestial Mechanics, Vol. 32, No. 3 | 1 Mar 1984 Cross Ref Asymptotic Approach to Mirror Conditions as a Trapping Mechanism in N-Body Hierarchical Dynamical SystemsDynamical Trapping and Evolution in the Solar System | 1 Jan 1983 Cross Ref Asymptotic Approach to Mirror Conditions as a Trapping Mechanism in N-Body Hierarchical Dynamical SystemsInternational Astronomical Union Colloquium, Vol. 74 | 12 April 2016 Cross Ref TheN-body problem of celestial mechanicsCelestial Mechanics, Vol. 14, No. 1 | 1 Mar 1976 Cross Ref Qualitative Methods and Results in Celestial MechanicsLong-Time Predictions in Dynamics | 1 Jan 1976 Cross Ref On the final evolution of the n-body problemJournal of Differential Equations, Vol. 20, No. 1 | 1 Jan 1976 Cross Ref Hill regions for the general three-body problemCelestial Mechanics, Vol. 12, No. 2 | 1 Sep 1975 Cross Ref The angle of escape in the three body problemCelestial Mechanics, Vol. 9, No. 2 | 1 Apr 1974 Cross Ref Volume 26, Issue 4| 1974SIAM Journal on Applied Mathematics687-832 History Submitted:08 February 1973Published online:12 July 2006 InformationCopyright © 1974 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0126072Article page range:pp. 806-815ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics