Extragalactic Celestial Mechanics: The Equation of Evolution

  • D. Galletto
  • B. Barberis
Conference paper
Part of the Astrophysics and Space Science Library book series (ASSL, volume 127)


In the context of extragalaotic celestial mechanics the equation of evolution of the universe is deduced with reference both to the isotropic and the anisotropic case, without resorting to the Newtonian theory of gravitation. With regards to the constant which comes out in this deduction, astronomical observation suggests that it can be rightly identified with the gravitational constant. Some consequences of the equation of evolution are deduced. The results obtained are preceded by a historical and critical analysis relative to the attempts which have been made up to now in order to develop a theory of the universe in the Newtonian context.


Gravitational Constant Isotropic Case Astronomical Observation Cosmological Term Anisotropic Case 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    BARBERIS B., GALLETTO D., ‘Modelli d’ universo del tipo Bianchi I e propagazione della luce’, in: Atti del “6º Convegno Nazionale di Relatività Generale e Fisica della Gravitazione” (Firenze, 10–13 ottobre 1984) (in print),Google Scholar
  2. [2]
    BONDI H., Cosmology, 2nd ed., Cambridge Univ. Press, 1960.Google Scholar
  3. [3]
    DAVIDSON W.,EVANS A.B., ‘A Fresh Look at the Cosmological Singularity’, Nature Phys. Sci., 232 (1971), pp. 29–31.ADSGoogle Scholar
  4. [4]
    DAVIDSON W., EVANS A.B., ‘Newtonian Universes Expanding or Con-tracting with Shear and Rotation’, Internat. J. Theoret. Phys., 7 (1973), PP. 353–378.ADSCrossRefGoogle Scholar
  5. [5]
    DAVIDSON W., EVANS A.B., ‘Newtonian Universes with Shear’, Comm. Roy. Soc. Edinburgh, 10 (1977), pp. 123–145.MathSciNetADSGoogle Scholar
  6. [6]
    GALLETTO D., ‘Sui fondamenti della meccanica classica, della teo-ria newtoniana della gravitazione e della cosmologia newtoniana’, in: Atti del “3º Convegno Nazionale di Relatività Generale e Fi-sica della Gravitazione” (Torino, 18–21 settembre 1978), Accademia delle Scienze, Torino, 1981; pp. 111–157.Google Scholar
  7. [7]
    GALLETTO D., ‘Des principes de la mécanique classique aux théories de la gravitation de Newton et Einstein’, in: Atti del Convegno Internazionale “Aspetti matematici della teoria della relatività” (Roma, 5–6 giugno 1980), Accademia Nazionale dei Lincei, Roma, 1984; pp. 59–83.Google Scholar
  8. [8]
    GALLETTO D., BARBERIS B., ‘Sur les modèles newtoniens d’univers anisotropes et homogènes’, in: Benenti S., Ferraris M., Franca-viglia M. (eds.), Proceedings of “Journées Relativistes 1983” (Torino, May 5–8, 1983), Pitagora, Bologna, 1985; pp. 337–372.Google Scholar
  9. [9]
    GALLETTO D., BARBERIS B., ‘On the Deduction of the Equation of Evolution in Newtonian Cosmology’, Atti Accad. Sci. Torino, 118 (1984), pp. 85–96.MathSciNetGoogle Scholar
  10. [10]
    GALLETTO D., BARBERIS B., ‘Sulla legge di gravitazione univer-sale.I’, Atti Accad. Naz. Lincei Rend., Ser.VIII, 76 (1984), pp. 359–366.Google Scholar
  11. [11]
    GALLETTO D., BARBERIS B., ‘Extragalactic Celestial Mechanics: an Introduction’, in: Szebehely V.G. (ed.), Stability of the Solar System and its Minor Natural and Artificial Bodies, Proceedings of “The NATO Advanced Study Institute” (Cortina d’Ampezzo, August 6–18, 1984), Reidel, Dordrecht, 1985; pp. 333–347.Google Scholar
  12. [12]
    GALLETTO D., BARBERIS B., ‘Sui modelli newtoniani e relativistici d’universo omogenei e anisotropi: caso dei modelli del tipo Bianchi I’, in: Boll. Un. Mat. Ital., Ser. VI, Suppl. Vol.IV-A, N.1 (1985), pp. 177–210.Google Scholar
  13. [13]
    GALLETTO D., ‘Modelli d’universo e propagazione della luce’, in: Atti del “6o Convegno Nazionale di Relatività Generale e Fisica della Gravitazione” (Firenze, 10–13 ottobre 1984) (in print).Google Scholar
  14. [14]
    GALLETTO D., BARBERIS B., ‘On the Gravitational Paradox’ (to appear).Google Scholar
  15. [15]
    GALLETTO D., ‘Cosmologia newtoniana e legge di gravitazione uni-versale’ (to appear).Google Scholar
  16. [16]
    GÖDEL K., ‘An Example of a New Type of Cosmological Solutions of Einstein’s Field Equations of Gravitation’, Rev. Modern Phys., 21 (1949), pp. 447–450.ADSzbMATHCrossRefGoogle Scholar
  17. [17]
    HECKMANN O., SCHÜCKING E., ‘Bemerkungen zur Newtonschen Kosmolo-gie. I’, Z. Astrophys., 38 (1955), pp. 95–109.MathSciNetADSGoogle Scholar
  18. [18]
    HECKMANN O., SCHÜCKING E., ‘Bemerkungen zur Newtonschen Kosmolo-gie. II’, Z. Astrophys., 40 (1956), pp. 81–92.MathSciNetADSGoogle Scholar
  19. [19]
    HECKMANN O., SCHÜCKING E., ‘Ein Weltmodell der Newtonschen Kosmo-logie mit Expansion und Rotation’, Helv. Phys. Acta, Suppl. IV (1956), pp. 114–115.Google Scholar
  20. [20]
    HECKMANN O., SCHÜCKING E., ‘Newtonsche und Einsteinsche Kosmolo-gie’, in: Flugge S. (ed.), Handbuch der Physik, 53, Springer-Verlag, Berlin, 1959; pp. 489–519,Google Scholar
  21. [21]
    HECKMANN O., ‘On the Possible Influence of a General Rotation on the Expansion of the Universe’, Astronom. J., 66 (1961), pp. 599–603.MathSciNetADSCrossRefGoogle Scholar
  22. [22]
    LAYZER D., ‘On the Significance of Newtonian Cosmology’, Astron. J., 59 (1954), pp. 268–270.MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    MAVRIDÈS S., L’Univers relativiste, Masson, Paris, 1973.Google Scholar
  24. [24]
    McCREA W.H., MILNE E.A., ‘Newtonian Universes and the Curvature of Space’, Quart. J. Math. (Oxford Ser.), 5 (1934), pp. 73–80.CrossRefGoogle Scholar
  25. [25]
    MILNE E.A., ‘A Newtonian Expanding Universe’, Quart. J. Math. (Oxford Ser.), 5 (1934), pp. 64–72.Google Scholar
  26. [26]
    NARLIKAR J.V., ‘Newtonian Universes with Shear and Rotation’, Mon. Not. Roy. Astronom. Soc, 126 (1963), pp. 203–208.MathSciNetADSzbMATHGoogle Scholar
  27. [27]
    NARLIKAR J.V., ‘On Newtonian Universes’, Mon. Not. Roy. Astronom. Soc, 131 (1966), pp. 501–502.ADSGoogle Scholar
  28. [28]
    NARLIKAR J.V., Lectures on General Relativity and Cosmology, Mac-Millan Press, London, 1979.Google Scholar
  29. [29]
    RAYCHAUDHURI A.K., ‘Relativistic and Newtonian Cosmology’, Z. Astrophysik, 43 (1957), pp. 161–164.ADSGoogle Scholar
  30. [30]
    RAYCHAUDHURI A.K., Theoretical Cosmology, Clarendon Press, Oxford, 1979.zbMATHGoogle Scholar
  31. [31]
    REES M.J., ‘Is the Universe Flat?’, J. Astrophys. Astr., 5 (1984), PP. 331–348.ADSCrossRefGoogle Scholar
  32. [32]
    SHIKIN I.S., ‘Homogeneous Anisotropic Models with Shear in Newto-nian Cosmology’, Z. Eksper. Teoret. Fiz., 59 (1970), pp. 182–194 [English transl. in: Soviet Physics JETP, 32 (1971), pp. 101–107].Google Scholar
  33. [33]
    SHIKIN I.S., ‘Analogs of Anisotropic Homogeneous Models of General Relativity in Newtonian Cosmology’, Z. Eksper. Teoret.Fiz., 61 (1971), pp. 445–453 [English transl. in: Soviet Physics JETP, 34 (1972), pp. 236–240].Google Scholar
  34. [34]
    WEINBERG S., Gravitation and Cosmology: Principles and Applica-tions of the General Theory of Relativity, Wiley, New York, 1972.Google Scholar
  35. [35]
    ZEL’DOVICH Ya.B., ‘Newtonian and Einsteinian Motion of Homogeneous Matter’, Astronom. Z., 41 (1964), pp. 873–883 [English transl. in: Soviet Astronom.-AJ, 8 (1965), pp. 700–707].Google Scholar
  36. [36]
    ZEL’DOVICH Ya.B., ‘On Anisotropic Motion of Homogeneous Matter’, Mon. Not. Roy. Astronom. Soc, 129 (1965), pp. 19–20.ADSGoogle Scholar
  37. [37]
    ZEL’DOVICH Ya.B., N0VIK0V I.D., The Structure and Evolution of the Universe (Relativistic Astrophysics, vol.2), Univ. Chicago Press, 1983.Google Scholar

Copyright information

© D. Reidel Publishing Company 1986

Authors and Affiliations

  • D. Galletto
    • 1
  • B. Barberis
    • 1
  1. 1.Istituto di Fisica Matematica “J.-Louis Lagrange”TorinoItaly

Personalised recommendations