Abstract
The distinctive feature of the relativistic restricted three-body problem within the c −5 order of accuracy (2\(\frac{1}{2}\) post-Newtonian approximation) is the presence of the gravitational radiation. To simplify the problem the motion of the massive binary components is assumed to be quasi-circular. In terms of time these orbits have linearly changing radii and quadratically changing phase angles. By substituting this motion into the Newtonian-like equations of motion one gets the quasi-Newtonian restricted quasi-circular three-body problem sufficient to take into account the main indirect perturbations caused by the binary radiation terms. Such problem admits the Lagrange-like quasi-libration solutions and rather simple quasi-circular orbits lying at large distance from the binary.
Similar content being viewed by others
References
Anderson, J. L. and Decanio, T. C.: 1975, 'Equations of hydrodynamics in general relativity in the slow-motion approximation', Gen. Rel. Grav. 6, 197-238.
Brumberg, V. A.: 1991, Essential Relativistic Celestial Mechanics, Hilger, Bristol.
Brumberg, V. A.: 1995, Analytical Techniques of Celestial Mechanics, Springer-Verlag, Heidelberg.
Damour, T.: 1983, 'Gravitational radiation and the motion of compact bodies', In: N. Deruelle and T. Piran (eds), Gravitational Radiation, North-Holland, Amsterdam, pp. 59-144.
Damour, T.: 1985, 'Un nouveau test de la relativité générale', In: S. Benenti, M. Ferraris and M. Francaviglia (eds), Proc. Journées Relativistes 1983, Pitagora Ed., Bologna, pp. 89-110.
Damour, T.: 1987, 'The problem of motion in newtonian and einsteinian gravity', In: S.W. Hawking and W. Israel (eds), 300 Years of Gravitation, Cambridge Univ. Press, Cambridge, pp. 128-198.
Kopejkin, S. M.: 1985, 'The equations of motion of extended bodies in general relativity with conservative corrections and radiation damping taken into account', Astron. Zh. 62, 889-904 (in Russian).
Kopejkin, S. M.: 1986, 'The Motion of Gravitating Bodies with Conservative and Radiation Relativistic Corrections Taken into Account', PhD Dissertation, Moscow State University (in Russian).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Brumberg, V.A. Special Solutions in a Simplified Restricted Three-Body Problem with Gravitational Radiation Taken into Account. Celestial Mechanics and Dynamical Astronomy 85, 269–291 (2003). https://doi.org/10.1023/A:1022568504789
Issue Date:
DOI: https://doi.org/10.1023/A:1022568504789