The Newtonian and Relativistic Theory of Orbits and the Emission of Gravitational Waves
108 The Open Astronomy Journal, 2011, 4, (Suppl 1-M7) 108-150 Open Access The Newtonian and Relativistic Theory of Orbits and the Emission of Gravitational Waves Mariafelicia De Laurentis1,2,* 1Dipartimento di Scienze Fisiche, Universitá di Napoli " Federico II",Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126, Napoli, Italy 2INFN Sez. di Napoli, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126, Napoli, Italy Abstract: This review paper is devoted to the theory of orbits. We start with the discussion of the Newtonian problem of motion then we consider the relativistic problem of motion, in particular the post-Newtonian (PN) approximation and the further gravitomagnetic corrections. Finally by a classification of orbits in accordance with the conditions of motion, we calculate the gravitational waves luminosity for different types of stellar encounters and orbits. Keywords: Theroy of orbits, gravitational waves, post-newtonian (PN) approximation, LISA, transverse traceless, Elliptical orbits. 1. INTRODUCTION of General Relativity (GR). Indeed, the PN approximation method, developed by Einstein himself [1], Droste and de Dynamics of standard and compact astrophysical bodies could be aimed to unravelling the information contained in Sitter [2, 3] within one year after the publication of GR, led the gravitational wave (GW) signals. Several situations are to the predictions of i) the relativistic advance of perihelion of planets, ii) the gravitational redshift, iii) the deflection possible such as GWs emitted by coalescing compact binaries–systems of neutron stars (NS), black holes (BH) of light, iv) the relativistic precession of the Moon orbit, that driven into coalescence by emission of gravitational are the so–called "classical" tests of GR.
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