Earth frozen orbits

Abstract

A frozen orbit is an orbit chosen such that the effect of perturbations on (a combination of) the mean orbital elements is minimized. The concept first appeared in literature in 1978, and was applied that same year to the Seasat mission. This altimetry mission featured strict requirements on the accuracy of the altitude of the satellite above the sea surface. By designing an orbit for which the mean eccentricity and mean argument of periapsis remain static, the satellite’s altitude will theoretically be constant, depending only on location of the sub-satellite point. Classically, the theory behind frozen orbits is only based on the J2- and J3-term of the spherical har- monics gravity field model and clever manipulation of the Lagrange planetary equations. Through considerable analytical effort, it is possible to include all other zonal gravity field terms into the equation, but this approach is limited to perturbations that can be cast into the form of a disturbing potential. The aim of this thesis is to find a numerical method that overcomes this limit and to use that method to investigate the effects of including third-body gravity, atmospheric drag and solar radiation pressure on the mean orbital elements. To do this, the frozen orbit problem is formulated as an optimization problem. Use is made of Differential Evolution (DE) and grid searching to simulate many trajectories and to find a set of injection parameters that results in a minimal variation in the mean eccentricity and mean argument of periapsis. The mean elements are reconstructed from the osculating elements by making use of the Eckstein-Ustinov theory and subsequent numerical averaging. In combination with Precise Orbit Determination (POD) data, this reconstruction is used to investigate the variations in the mean orbital elements of ERS-2 and TOPEX/Poseidon. Subsequently, the numerical method is applied to various orbital dynamics models. When applied to zonal gravity fields, the new method is found to be in good agreement with analytical solutions. The influence of other perturbations on solutions found in zonal models is examined, and it is found that taking these perturbations into account during the optimization process does not lead to significant improvements with respect to the simple zonal case, nor does it lead to significant changes in the found injection conditions. For the assumed satellite characteristics, radiation pressure is found to be the most influential perturbation, causing fluctuations in the mean eccentricity of ±3%.