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General Relativistic Orbital Effects in Compact Binary Stars (Solution by the Method of Celestial Mechanics)
School of Physics, Northeast Normal University, Changchun, China
- 1 School of Physics, Northeast Normal University, Changchun, China
World Journal of Mechanics·Volume 07 (2017)·Pages 360–369·Published 30 November 2017·DOI10.4236/wjm.2017.712027
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Abstract
Perturbation methods are employed to calculate time variation in the orbital elements of a compact binary system. It turns out that the semi-major axis and eccentricity exhibit only periodic variations. The longitude of periastron and mean longitude of epoch exhibit both secular and periodic variation. In addition, the relativistic effects on the time of periastron passage of binary stars are also given. Four compact binary systems (PSRJ0737-3039, PSR1913+16, PSR1543+12 and M33X-7) are considered. Numerical results for both secular and periodic effects are presented, and the possibility of observing them is discussed.
KeywordsGeneral Relativistic Orbital EffectCompact Binary Stars
- Brumberg, V.A. (1972) Relativistic Celestial Mechanics. Nauk, Moscow. (In Russian)
- Brumberg, V.A. (1985) Essential Relativistic Celestial Mechanics. Adam Hilger, Bristol.
- Rubincam, D.P. (1977) General Relativity and Satellite Orbit: The Motion of a Test Particle in the Schwarzchild Metric. Celestial Mechanics and Dynamical Astronomy, 15, 21-33. https://doi.org/10.1007/BF01229045
- Soffel, M.H., Ruder, H. and Schneider, M. (1987) The Two-Body Problem in the (Truncated) PPN Theory. Celestial Mechanics and Dynamical Astronomy, 40, 77-85. https://doi.org/10.1007/BF01232326
- Soffel, M.H. (1989) Relativity in Celestial Mechanics, Astronomy and Geodesy. Springer, Heidelberg. https://doi.org/10.1007/978-3-642-73406-9
- Iorio, L. (2005) On the Possibility of Measuring the Solar Oblateness and Some Relativistic Effects from Planetary Ranging. A & A, 433, 385-393.
- Will, C.M. (1981) Theory of Experiment in Gravitational Physics. Cambridge University Press, London, New York, New Rochelle, Melbourne, Sydney.
- Will. C.M. (2006) The Confrontation between General Relativity and Experiment. Living Reviews in Relativity, 9, 5-100. https://doi.org/10.12942/lrr-2006-3
- Damour. T. and Deruelle, N. (1985) General Relativistic Celestial Mechanics 1. The Post-Newtonian Motion. Annales de l’Institut Henri Poincaré, 43, 107-132.
- Damour, T. and Deruelle, N. (1986) General Relativistic Celestial Mechanics 11. The Post-Newtonian Timing Formulas. Annales de l’Institut Henri Poincaré, 44, 263-292.
- Schāefer, G. and Wex, N. (1993) Second Post-Newtonian Motion of Compact Binaries. Physics Letters A, 174, 196-205. https://doi.org/10.1016/0375-9601(93)90758-R
- Wex, N. (1995) The Second Post-Newtonian Motion of Compact Binary-Star Systems with Spin. Classical and Quantum Gravity, 12, 983. https://doi.org/10.1088/0264-9381/12/4/009
- Calura, M., et al. (1997) Post-Newtonian Lagrangian Planetary Equation. Physical Review D, 56, 4782-4788. https://doi.org/10.1103/PhysRevD.56.4782
- Iorio, L. (2007) The Post-Newtonian Mean Anomaly Advance as Further Post-Keplerian Parameter in Pulsar Binary Systems. Astrophys & Space Scince, 312, 331-335.
- Burgay, M., et al. (2003) An Increased Estimate of the Merger Rate of Double Neutron Stars from Observation of a Highly Relativistic System. Nature, 426, 531-533. https://doi.org/10.1038/nature02124