Joseph O’Leary, University of South Australia and SERC Limited; James M. Hill, University of South Australia
Keywords: general relativity, astronomy, orbital dynamics, energy integrals, post-newtonian approximation
Abstract:
The general theory of relativity is now widely accepted as providing the most accurate theory of gravity. However, the field equations of General Relativity (GR) constitute a system of ten non-linear, coupled partial differential equations. Hence, exact analytical solutions often embody high degrees of symmetry and physical constraints in order to reduce the complexity associated with such systems. In order to combat the difficulties associated with Einsteins highly non-linear theory of gravity, and facilitate the modelling of realistic astrophysical systems, approximation methods have been developed to determine n-body equations of motion and approximate solutions to the field equations of GR.
The post-Newtonian (PN) approximation for GR is widely adopted by geodesy and astronomy communities alike. Presently, the levels of accuracy required in geodetic techniques require that reference frames, planetary/satellite orbits be treated within the first-PN regime. In a recent note [1], we derived the energy associated with a near-Earth object in the first-PN approximation which is obtained by seeking a Jacobi-like integral associated with the relativistic equations of motion. The newly obtained energy integral is of exponential order and produces known results following a Taylor series approximation. In this paper, we investigate the conservation properties of both energy integrals by employing symplectic (strutcure-preserving) integration schemes.
[1] OLeary, J., Hill, J.M. & Bennett, J.C. Celest Mech Dyn Astr (2018) 130: 44.
Date of Conference: September 11-14, 2018
Track: Poster