Trajectory mission design and navigation for a space weather forecast

This thesis research will be based on the trajectory mission design and navigation design for prospective future missions to the Triangular Lagrange Points L5 and L4 in the Sun-Earth and Earth-Moon systems. The research proposed here will be divided into four parts. ? The first problem will be devoted to studying the circular restricted three-body problem (CRTBP) in the Sun-Earth system. With this model, we will generate potential optimized orbit solutions in the planar CRTBP and also in three-dimensional orbits in order to study the Sun above the ecliptic plane. Orbit determination analysis will also be examined using different orbit determination methods. Finally, we will analyze the stability of the trajectories and their stationkeeping requirements. ? The second part of this thesis will deal with the bicircular problem (BCP) in the Earth-Moon system. As in the work on the CRTBP, we will understand and analyze the stability of the different types of periodic orbits (quasi-periodic orbits) obtained under the influence of the Moon and the Sun. ? The third part will describe the elliptic restricted three-body problem (ERTBP) in the Sun-Earth system. As in the work on the CRTBP, we will analyze the stability of the different types of periodic orbits (quasi-periodic orbits) obtained due to the effects of the eccentricity of the Earth around the Sun. We will partially analyze the BCP and ERTBP but the main focus of the research will be based on the CRTBP and the JPL Ephemeris Model. ? The last problem is the new JPL Ephemeris Model, DE421. With this ephemeris model, we will determine how accurate the models CRTBP, BCP and ERTBP are in comparison with the real one. By studying the real model, we will have a more thorough insight into why some of the orbits obtained in both the CRTBP and ERTBP lose their symmetry when adding the influence of higher order perturbations into the dynamical model. ? Besides finding periodic and quasi-periodic orbits for different models, part of this trajectory mission design will be dedicated to the optimization of the trajectory, utilizing a differential corrector. Finally, we will close this section by developing some semi-analytical work based on different techniques, such as the Lie Series expansions. We will use these methods to have better approximations of the nonlinear problem in the neighborhood of the triangular points and to obtain a more accurate analysis of the stability of these orbits. ? Along with the trajectory mission design, part of this thesis work will be oriented towards the orbit determination analysis from the beginning of the mission at a predefined parking orbit around Earth to the end of the mission at the Libration Orbit (Trojan Orbit) around the triangular points. Orbit determination will be needed to provide a more accurate estimation of the trajectory of the spacecraft at different stages: launch, mid-course and arrival. ? We know that after the launch phase, the spacecraft will be sensitive to large errors that make the spacecraft deviate from the nominal trajectory. The main goal will be to determine the state of the spacecraft as accurately as possible. We know that the state of the spacecraft is determined from the measurements, such as range or Doppler data. Given these launch errors, we will have to perform correction maneuvers to adjust the perturbed trajectory to go back to the nominal trajectory or an alternate trajectory that satisfies the mission requirements. Can we achieve this with a single correction maneuver? The answer is "No" for several reasons. First, the dynamical model is not perfect, even for our most realistic models. Secondly, the measurements have uncertainties. Thirdly, the spacecraft trajectory can only be estimated. Finally, each trajectory correction maneuver also has its own sources of execution errors.