Study of the dynamics around celestial bodies using analytical and semi-analytical techniques - Cardoso dos Santos, Josué (2018)
Nowadays, despite the technological development experienced by science in general, a fact especially evident by the available powerful computer machines, the analytical and semi-analytical methods to study different space problems are still of great importance in the fields of astrodynamics and celestial mechanics. From the physical understanding of the motion of celestial bodies to the planing and designing of space missions, the use of mathematical models to deal with a very large number of contemporary problems plays a fundamental role in the progress of human knowledge. In this context, the present thesis presents the use of different mathematical techniques to deal with different various and current problems in astrodynamics and celestial mechanics. The studies developed throughout this work are applicable to both areas. The topics studied are the following ones: (1) The development of disturbing potentials using the double-averaging process, in order to be included in the Lagrange planetary which are numerically integrated to study features of orbits around Mercury and the Galilean moon Callisto; (2) The use of different perturbation integrals, techniques to identify and map different perturbations present in a planetary system, with focus on the analysis of systems of Giant planets with their massive moons; (3) The use of the concept of intermediary Hamiltonian and the use of a canonical transformation called elimination of the parallax, both to deal with binary systems in the context of the roto-orbital dynamics, this one as an approach of the fulltwo body problem; (4) An updated analysis of Gauss variational equations to study quasisatellite orbits around the Martian moon Phobos and with analytical predictions made after obtaining linear and averaged equations of motions. Therefore, this thesis intend not only to provide important analysis and results for each specific problem which it deals with along its pages, but also seeks to highlighting the merit and current relevance of different analytical and semi-analytical methods to be used in the fields of astrodynamics and celestial mechanics. Additionally, the author also hopes to offer an outcome of diverse interesting ideas and methods to be explored in future investigations in these research fields.