Abstract
The gravitational problem of three bodies is treated in the case when the masses of the participating bodies are of the same order of magnitude and their distances are arbitrary. Estimates for the minimum perimeter of the triangle formed by the bodies and for the rate of the expansion of the system are obtained from Sundman's modified general inequality when the total energy of the system is negative. These estimates are used to propose and to describe an escape mechanism based on genuine three-body dynamics and to offer a method to control the accuracy of numerical integrations of the problem of three bodies. The requirements for these two applications are contradictory since an escape is the consequence of a close triple approach which phenomenon is detrimental to the accuracy of the computations. Consequently, the numerical study of escape from a triple system must treat triple close approaches with high reliability.
Similar content being viewed by others
References
Agekian, T. A. and Anosova, Zh. P.: 1967,Astron. Zh. 44, 1261.
Birkhoff, G. D.: 1927,Dynamical Systems, American Math. Soc., Providence, R. I.
Chazy, J.: 1929,J. Math. Pure Appl. 8, 353.
Siegel, C. L. and Moser, J. K.: 1971,Lectures on Celestial Mechanics, Springer, New York, N.Y.
Sundman, K.: 1912,Acta Math. 36, 105.
Szebehely, V.: 1972,Proc. Nat. Acad. Sci. U.S.A. 69, 1077.
Szebehely, V. and Peters, F.: 1967,Astron. J. 72, 876.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Szebehely, V. Triple close approaches in the problem of three bodies. Celestial Mechanics 8, 163–167 (1973). https://doi.org/10.1007/BF01231409
Issue Date:
DOI: https://doi.org/10.1007/BF01231409