Abstract
A classification of the possible types of the relative orbits of realistic binary stars in the post-Newtonian approximation of general relativity is presented. Definitions of the relativistic conic sections and their elements are proposed, generalizing the corresponding ones of classical celestial mechanics. The results are compared and contrasted with the classical ones and some new predictions of purely post-Newtonian origin and nature are presented.
Similar content being viewed by others
References
Spyrou, N. (1981).Gen. Rel. Grav.,13, 473 (Paper I).
Spyrou, N. (1981).Gen. Rel. Grav.,13, 487.
Spyrou, N. (1978).Gen. Rel. Grav.,9, 519.
Caporali, A. (1979). Ph.D. thesis, University of Munich, Preprint No. MPI-PAE/Astro 219, February 1980, Munich, West Germany.
Caporali, A., and Spyrou, N. (1981).Gen. Rel. Grav.,13, 689.
Spyrou, N. (1977).Gen. Rel. Grav.,8, 491.
Spyrou, N. (1983). Possible contraction of the members of the binary pulsar PSR 1913+16 and its astrophysical consequences, inProceedings of the IAU Symposium No. 104: Early Evolution of the Universe and Its Present Structure, August 1982, Crete-Greece, G. Abell and G. Chincarini, eds., (in press).
Chandrasekhar, S. (1965).Astrophys. J.,142, 1488.
Ehlers, J., Rosenblum, A., Goldberg, J. N. Havas, P. (1976).Astrophys. J. (Lett.),208, L77.
Fock, V. (1966).The Theory of Space, Time and Gravitation, 2nd ed., Pergamon Press, New York.
Anderson, J. L., and DeCanio, T. C. (1975).Gen. Rel. Grav.,6, 197.
Chandrasekhar, S., and Esposito, P. (1970).Astrophys. J.,160, 153.
Ehlers, J. (1977). Weak-field approximations and equations of motion in general relativity, inProceedings of the International School of General Relativistic Effects in Physics and Astrophysics: Experiments and Theory, Erice-Trapani-Sicily, ed. Ehlers, J., Preprint No. MPI-PAE/astro,138, 45, Munich.
Ehlers, J. (1980). Isolated systems in general relativity inProceedings of the Ninth Texas Symposium on Relativistic Astrophysics, December 1978, Munich, West Germany, ed. J. Ehlers, J. J. Perry, and M. Walker, Annals of the New York Academy of Sciences,336, 279, New York.
Kerlick, G. D. (1979).Gen. Rel. Grav.,12, 467.
Kerlick, G. D. (1979).Gen. Rel. Grav.,12, 521.
Caporali, A. (1981).Nuovo Cimento,61B, 181.
Caporali, A. (1981).Nuovo Cimento,61B, 205.
Caporali, A. (1981).Nuovo Cimento,61B, 213.
Burke, W. L. (1971).J. Math. Phys.,12, 401.
D'Eath, P. D. (1975).Phys. Rev. D.,11, 1387.
D'Eath, P. D. (1975).Phys. Rev. D.,12, 2183.
Kates, R. E. (1980).Phys. Rev. D.,22, 1853.
Kates, R. E. (1980).Phys. Rev. D.,22, 1879.
Kates, R. E. (1980).Phys. Rev. D.,22, 1871.
Einstein, A., Infeld, L., and Hoffman, B. (1938).Ann. Math.,39, 65.
Spyrou, N. (1977).Gen. Rel. Grav.,8, 463.
Caporali, A. (1980). Torques on a nearly rigid body in a relativistic gravitational field, Marshall Space Flight Center (NASA) preprint, Alabama.
Contopoulos, G., and Spyrou, N. (1976).Astrophys. J.,205, 592.
Spyrou, N. (1979).Gen. Rel. Grav.,10, 581.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Spyrou, N. Relativistic conic sections. Gen Relat Gravit 15, 363–374 (1983). https://doi.org/10.1007/BF00759165
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00759165