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Fuzzy Boundary Jupiter Moon Tour Trajectories Using the Bifurcation Method
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bello, Miguel Angel Olmos González, José Alejandro Sánchez, Mariano Janin, Guy |
| Copyright Year | 2004 |
| Abstract | The consideration of transfers to the Fuzzy Boundary region represents one of the more advanced concepts when trying to reduce the propellant requirements to obtain an interplanetary goal. DEIMOS Space, under ESA contract, has developed a tool to generate such transfers to inner planets, giant planets and natural moons of giant planets. The method is based on the Systematic Scan Search of Bifurcations, with a threestep approach consisting on: selection of strategy, generation of initial solutions and numerical optimisation. The generation of the initial solution by systematic search of bifurcations is accomplished by splitting the trajectory into smaller arcs. The initial guess of the trajectories must be obtained always by backwards propagation from the final targeting conditions. Forward propagation is used from the initial conditions to match the backwards propagation previously derived. Different values of the orbit eccentricity are used when propagating (typically ranging between 0.9 and 1.1, close to the parabolic orbit). This leads to three different types of trajectory: close orbits below the Fuzzy region, escape trajectories and trajectories reaching maximum and minimum distances within the Fuzzy region. The actual change of nature in the resulting orbit corresponds to a bifurcation. Matching of forwards and backwards propagation will take place within the Fuzzy region, using in general a manoeuvre or a low-thrust arc. Finally, an optimisation process is started to obtain a full continuous numerically integrated trajectory, with minimum required propellant consumption. One of the key advantages of this new method is the large number of solutions found, thanks to its systematic scan approach. In particular, it has been applied to systematically explore trajectories between the different moons of a giant planet by using the Fuzzy Regions of those moons. A Tour of the Jupiter Galilean Moons has been created, allowing a spacecraft to visit a sequence of moons with a reduced fuel consumption when compared to classical solutions. A direct application of the method is the USA JIMO mission or ESA’s proposed Europa mission. 1. DESCRIPTION OF THE METHOD The numerical algorithm proposed to solve the problem is based on a three-step strategy. 1.1 Selection of WSB transfer strategy For each particular problem, a sequence of events is defined according to previous theoretical analyses of the problem. This sequence of events completely defines the selected WSB strategy, including the potential use of gravity assists or low thrust arcs. 1.2 Generation of initial solutions Once the WSB transfer strategy is selected, simplified methods are used to generate a database of, in general, non-optimal transfer trajectories. The whole trajectory is divided in various arcs, and initial solutions are piecewise computed. This is the most critical phase of the method. For classical interplanetary trajectories, patched conics are used to generate the initial guess of the final solution. However, the very complex dynamics of the weak stability boundaries makes impossible the use of simple analytical calculations. This is a very critical phase, as the final refinement of the trajectory must converge to the local minimum closest to the provided initial guess of the trajectory. A Systematic Scan Search of Bifurcations provides a very robust way to generate optimum transfers. This method is based on the division of the whole trajectory into smaller arcs and the individual generation of initial solutions for all of them. Normal arcs out the WSB regions are generated by Keplerian approximation or Lambert solver modules. Trajectories within the WSB regions are generated using a numerical integrator and single or multiple shooting methods. The key factors of the method are: The initial guess of the WSB trajectories must be obtained always by backwards propagation from the final targeting conditions. The trajectory must be propagated forwards from the initial conditions (i.e. interplanetary trajectory) to match the backwards propagation previously derived. Matching of forwards and backwards propagation will take place within the WSB region, in general. If a manoeuvre or a low-thrust arc is allowed at the WSB region, a high flexibility in finding the final solution is obtained. However, the final optimisation process tends to remove this manoeuvre whenever possible. In order to illustrate how the bifurcations are practically obtained, let assume a transfer from an interplanetary trajectory to a final orbit around a given planet via WSB of the planet-Sun system. The generation of the initial solution by systematic search of bifurcations is accomplished by splitting the trajectory up into two arcs; one arc from the WSB region to the final injection conditions, which is obtained by backwards propagation since a large information on the final state is given and another arc from the arrival hyperbola up to the WSB region, which is obtained by forwards propagation. The bifurcations are linked to the final target orbit (pericentre and apocentre radii, inclination, right ascension of the ascending node and argument of pericentre) and the orbit injection date. They are found by performing backwards propagation from the final orbit injection point (pericentre) for different values of the arrival orbit eccentricity (typically ranging between 0.9 and 1.1, close to the parabolic orbit). For increasing values of the arrival orbit eccentricity, the backwards propagation leads to three different types of trajectory (Fig. 1): Type 1: the trajectory remains below the WSB region. Type 2: the trajectory reaches maximum and minimum distances within the WSB region. Although this region is somehow not very well defined “a priori”, typical values lie between 0.75 and 1.5 times the distance of the lagrangian L1 (or L2) point. Type 3: the trajectory escapes from the planet influence |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://issfd.org/ISSFD_2004/papers/P1079.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
