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

Admonish

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

progestin

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.