Thesis project, named "Determination of the Orbital Elements for One Body under Parametrized Post Newtonian Metric", submitted for the degree of Bachelor of Physics at Universidad Nacional de Colombia.
The main objective of this work is to determine the orbit followed by a test particle without rotation, around a gravitationally weak body rotating slowly. The system is approached by means of the Post-Newtonian Parameterized (PPN) metric to first order, written in terms of three potentials; the metric is constructed following the standard Post-Newtonian gauge. The Newtonian potential is written including the quadrupole moment and the other two potentials are determined by considering the slow rotation and axial symmetry of the central body. The orbit is completely and univocally characterized by the six orbital elements given by the disturbing force, the latter calculated with the proposed metric. Four types of forces are obtained, i.e., due to the quadrupole Newtonian and relativistic momentum, Schwarzschild type and due to the rotation of the central body. The results are applied to the system Earth + Artificial Satellites, for the Geostationary Orbit and the Molniya type, showing graphs for each orbital element and managing to reproduce adequately what is shown in the literature. A small analysis of the order of magnitude of the mentioned perturbations is made.
In this repository is upload, in the Code folder, the Mathematica Notebook used to develop some of the algebraic steps that lead to the final results, as well as the Jupyter Notebook created to plot the results. In the Tesis folder is located the latex files of the final document.
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