Tests of General Relativity are often done in the Solar System by using tracking data from interplanetary space missions, to measure the perturbation on the orbits of the planets that is predicted by General Relativity. The next best opportunity for such a test is the BepiColombo
...
Tests of General Relativity are often done in the Solar System by using tracking data from interplanetary space missions, to measure the perturbation on the orbits of the planets that is predicted by General Relativity. The next best opportunity for such a test is the BepiColombo spacecraft by the European Space Agency, which will arrive at Mercury in late 2025. However, a very similar perturbation is also produced by the gravitational oblateness of the Sun through the zonal coefficient J2. The exact value of this coefficient has been hard to determine despite centuries of observations of the solar shape, and besides the accuracy of the tracking data it is the main source of uncertainty for the tests of gravitational theory. Recent publications in heliophysics suggest that higher order effects might also be of relevant influence too, such as coefficient J2 being dynamic along the solar cycle, or the fourth zonal coefficient J4. This thesis project attempts to bring together two fields of research: the field that tries to test General Relativity (GR) in the Solar System, and the field of heliophysics that tries to unravel the structure of the Sun. The orbit of Mercury, as well as the observations of BepiColombo and it predecessor MESSENGER, are simulated in a virtual reality where settings of the solar shape are varied. Relevant parameters to tests of gravity are then estimated using a least-squares algorithm and their error is analysed. It is found that the amplitude of a periodic component of the solar oblateness can be found with an uncertainty of 0.02% of the value of J2. It is also found that if a periodic component exists with an amplitude higher than 1%, it can lead to errors in the experiments of GR to the point that results oppose the theory of General Relativity. Expected values for J4 from heliophysics currently do not influence the orbit of Mercury by a measurable amount. Based on this work, it is recommended to those in the field who test General Relativity using data from BepiColombo, to take this effect into consideration to prevent getting results in their experiments that can lead physicists in the wrong direction concerning the development of gravitational theory.
