Fundamental physics measurements with Galileo FOC satellites and the Galileo for science project. II. A box wing for modeling direct solar radiation pressure and preliminaries orbit determinations

This paper concerns the development of a first simplified model to take into account the perturbations produced by the nongravitational forces acting on the satellites of the Galileo FOC constellation and the corresponding first orbital determinations within the G4S_2.0 project. G4S_2.0 has a series of objectives in verifying the gravitational interaction in the weak field limit of the theory of general relativity, exploiting in particular the eccentricity of the orbits of some Galileo FOC satellites and the precise measurements that can be derived from the atomic clocks on board these satellites. The study focused on the model for the acceleration produced by direct solar radiation pressure on the satellites. This is the largest of all nongravitational perturbations. It is therefore necessary to build a sufficiently accurate model for it before being able to seriously consider smaller perturbation effects, such as those related to terrestrial radiation and thermal thrust effects. The work presents new aspects in the literature of navigation satellites. One of these is the determination of the effects in the Keplerian elements produced by the direct solar acceleration obtained from a box -wing model of the satellite. A second aspect is the comparison of these predictions in the orbital elements with the corresponding orbital residuals achieved from an orbit determination of the satellite. The study therefore highlights even more the importance of being able to improve the model of the perturbation originating from solar radiation in the field of global navigation satellite systems. This is very important if one wants to extract gravitational measurements from the orbit and clock -bias measurements of these satellites to verify the predictions of general relativity and compare them with those of alternative theories of gravitation.