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Discrete Newtonian gravitation and the three-body problem

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Abstract

Newtonian gravitation is studied from a discrete point of view, in that the dynamical equation is an energy-conserving difference equation. Application is made to planetary-type, nondegenerate three-body problems and several computer examples of perturbed orbits are given.

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References

  1. B. J. Alder, Studies in molecular dynamics III: A mixture of hard spheres,J. Chem. Phys. 40, 2724 (1964).

    Google Scholar 

  2. G. Birkhoff and R. E. Langer (eds.),Orbit Theory (Proc. of a Symp. in Applied Math., IX), (Amer. Math. Soc., Providence, Rhode Island, 1959).

    Google Scholar 

  3. W. J. Eckert, D. Brouwer, and G. M. Clemence, Coordinates of the five outer planets, 1653–2060,Astr. Papers Am. Ephem. 12 (1951).

  4. J. Gillespie and J. Nuttall (eds.),Three-Particle Scattering in Quantum Mechanics (Benjamin, New York, 1968).

    Google Scholar 

  5. D. Greenspan, Numerical studies of the 3-body problem,SIAM J. Appl. Math. 20, 67 (1971).

    Google Scholar 

  6. J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird,Molecular Theory of Gases and Liquids (Wiley, New York, 1954).

    Google Scholar 

  7. E. Leimanis, Some recent advances in the dynamics of rigid bodies and celestial mechanics, inSurvey in Applied Math., II (Wiley, New York, 1958).

    Google Scholar 

  8. W. R. Longley, A class of periodic orbits of an infinitesimal body subject to the attraction ofn finite bodies,Trans. Am. Math. Soc. 8, 159 (1907).

    Google Scholar 

  9. R. H. Miller and N. Alton, Three dimensionaln-body calculations, ICR Quart. Rpt. #18, Univ. Chicago, 1968.

  10. L. M. Rauch and W. C. Riddell, Iteration solutions of the analyticaln-body problem,SIAM J. Appl. Math. 8, 568 (1960).

    Google Scholar 

  11. A. B. Schubert, Fortran program for the three-body problem, Appendix, Tech. Rpt. #133, Department of Computer Science, Univ. of Wisconsin, 1971.

  12. E. Stromgren, Connaissance actuelle des orbites dans le problème des trois corps,Bull. Astr. (2),9, 87 (1935).

    Google Scholar 

  13. J. E. Welch, F. H. Harlow, J. P. Shannon, and B. J. Daly, The MAC method, Tech. Rpt. #3425, Los Alamos Sci. Lab., Los Alamos, New Mexico, 1966.

    Google Scholar 

  14. A. Wintner,The analytical Foundations of Celestial Mechanics (Princeton Univ. Press, Princeton, New Jersey, 1947).

    Google Scholar 

  15. J. Zumkley, Ein numerisch gerechneter Specialfall des allgemeinen Dreikörperproblems in vereinfachter Behandlung,Astr. Nachr. 272, 66 (1941).

    Google Scholar 

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Greenspan, D. Discrete Newtonian gravitation and the three-body problem. Found Phys 4, 299–310 (1974). https://doi.org/10.1007/BF00712693

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