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General relativistic celestial mechanics of binary systems. II. The post- Newtonian timing formula. (English) Zbl 0617.70010

[For part I see ibid. 43, 107-132 (1985; Zbl 0585.70010).]
Starting from a previously obtained ”quasi-Newtonian” solution of the equations of motion of a binary system at the first post-newtonian approximation of general relativity, we derive a new ”timing formula” giving the arrival times at the barycenter of the solar system of electromagnetic signals emitted by one member of a binary system. Our timing formula is simpler and more complete than presently existing timing formulas. We propose to use it as a timing model to be fitted to the arrival times of pulses from binary pulsars. Specifically we show that the use of this timing model in the analysis of the timing measurements of the Hulse-Taylor pulsar could determine more parameters than is presently done. This should lead to additional tests of the simplest model of this binary system and to the first test of relativistic theories of gravity independent of any hypothesis of ”cleanness” of the system.

MSC:

70F15 Celestial mechanics
83C25 Approximation procedures, weak fields in general relativity and gravitational theory
70H40 Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics
85A05 Galactic and stellar dynamics

Citations:

Zbl 0585.70010
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References:

[1] B.M. Barker and R.F. O’Connel , Phys. Rev. , t. D 12 , 1975 , p. 329 .
[2] L. Baroni , G. Callegari , C. Gualdi and P. Fortini . Lett. Nuov. Cim. , t. 27 , 1980 , p. 509 .
[3] R. Blandford and S.A. Teukolsky , Astrophys. J. , t. 205 , 1976 , p. 580 .
[4] V. Boriakoff , D.C. Ferguson , M.P. Haugan , Y. Terzian and S.A. Teukolsky , Astrophys. J. , t. 261 , 1982 , p. L97 .
[5] T. Damour , In Gravitational Radiation , N. Deruelle and T. Piran eds, North-Holland , Amsterdam , 1983 , p. 59 . · Zbl 0956.83522
[6] T. Damour , Phys. Rev. Lett. , t. 51 , 1983 , p. 1019 .
[7] T. Damour , In Proceedings of Journées Relativistes 1983 , S. Benenti, M. Ferraris and M. Francaviglia eds, Pitagora Editrice , Bologna , 1985 , p. 89 .
[8] T. Damour , To be submitted for publication, 1985 .
[9] T. Damour and N. Deruelle , Ann. Inst. H. Poincaré (Physique Theorique) , t. 43 , 1985 , p. 107 (quoted in the text as paper I). Numdam | MR 813140 | Zbl 0585.70010 · Zbl 0585.70010
[10] T. Damour and R. Ruffini , C. R. Acad. Sci. Paris , t. 279 , série A , 1974 , p. 971 .
[11] R. Epstein , Astrophys. J. , t. 216 , 1977 , p. 92 and errata. Astrophys. J. , t. 231 , 1979 , p. 644 .
[12] M.P. Haugan , Astrophys. J. , t. 296 , 1985 , p. 1 .
[13] R.A. Hulse and J.H. Taylor , Astrophys. J. , t. 195 , 1975 , p. L51 .
[14] M. Portilla and R. Lapiedra , in Actas de los E.R.E. 1983 , L. Mas ed., I. C. E ., Mallorca , 1984 , p. 267 .
[15] L.L. Smarr and R. Blandford , Astrophys. J. , t. 207 , 1976 , p. 574 .
[16] J.H. Taylor , L.A. Fowler and P.M. Mcculloch , Nature , t. 277 , 1979 , p. 437 .
[17] J.H. Taylor and J.M. Weisberg , Astrophys. J. , t. 253 , 1982 , p. 908 .
[18] F. Tisserand , Traité de Mécanique Céleste , tome I , Gauthier-Villars , Paris , 1960 . · Zbl 0093.23503
[19] J.M. Weisberg and J.H. Taylor , Phys. Rev. Lett. , t. 52 , 1984 , p. 1348 .
[20] C.M. Will , Theory and experiment in gravitational physics , Cambridge U. Press , Cambridge , 1981 . MR 778909
[21] C.M. Will , Phys. Rep. , t. 113 , 1984 , p. 345 . MR 773032
[22] C.M. Will , Ann. of Phys. ( N. Y .), t. 155 , 1984 , p. 133 . MR 751655
[23] M.P. Haugan , Report given at the Fourth Marcel Grossmann Meeting , Rome , Italy, 17 - 21 June 1985 .
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