Titlebook: General Relativistic and Post-Newtonian Dynamics for Near-Earth Objects and Solar System Bodies; Joseph O’Leary Book 2021 The Editor(s) (i

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Post-Newtonian Satellite Orbits2; Misner et?al. 1973; Weinberg 1972) of the field equations of gravity. The first direct observation of gravitational waves was due to the coalescence of a binary black hole system (Abbott et?al. 2016), which was detected by the advanced laser interferometer gravitational-wave observatory collabora

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Post-Newtonian Two-Centre Problem. A class of dynamical systems which are integrable are those which are separable (Whittaker 1988). A further class of integrable systems discovered by Liouville (see ó?Mathúna 2008 for a detailed historical account) are the particular systems with kinetic and potential energies prescribed according

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General Relativistic Orbit Determination numerical integration of Newton’s second law of motion, combined with linearly superimposed perturbative forces. Specifically, this corresponds to the perturbed three-dimensional acceleration of the spatial coordinates for a given body with respect to the absolute coordinate time of Newtonian mecha

Omniscient

Spherically Symmetric General Relativityntains two arbitrary constants of integration. Using the weak-field limit of general relativity, we identify one constant with the classical Newtonian gravitational potential, and the additional constant allows for a generalisation of the Eddington–Finkelstein transformation and the Kruskal–Szekeres coordinates.

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Post-Newtonian Satellite Orbitse of a binary black hole system (Abbott et?al. 2016), which was detected by the advanced laser interferometer gravitational-wave observatory collaboration (Abbott et?al. 2009; Harry and Collaboration 2010).

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Post-Newtonian Two-Centre Problem to Eqs. (.). Liouville-integrable systems exploit the Hamiltonian in the Euler–Lagrange equations of motion and the solution is expressible in terms of first integrals or equivalent integral equations.