Multiple gravity assist (MGA) spacecraft trajectories can be difficult to find, an intractable problem to solve completely. However, these trajectories have enormous benefits for missions to challenging destinations such as outer planets and primitive bodies. Techniques are presented to aid in solving this problem with a global search tool and additional investigation into one particular proximity operations option is discussed. Explore is a global grid-search MGA trajectory pathsolving tool. An efficient sequential tree search eliminates v∞ discontinuities and prunes trajectories. Performance indices may be applied to further prune the search, with multiple objectives handled by allowing these indices to change between trajectory segments and by pruning with a Pareto-optimality ranking. The MGA search is extended to include deep space maneuvers (DSM), v∞ leveraging transfers (VILT) and low-thrust (LT) transfers. In addition, rendezvous or nπ sequences can patch the transfers together, enabling automatic augmentation of the MGA sequence. Details of VILT segments and nπ sequences are presented: A boundaryvalue problem (BVP) VILT formulation using a one-dimensional root-solve enables inclusion of an efficient class of maneuvers with runtime comparable to solving ballistic transfers. Importantly, the BVP VILT also allows the calculation of velocity-aligned apsidal maneuvers (VAM), including inter-body transfers and orbit insertion maneuvers. A method for automated inclusion of nπ transfers such as resonant returns and back-flip trajectories is introduced: a BVP is posed on the v∞ sphere and solved with one or more nπ transfers – which may additionally fulfill specified science objectives. The nπ sequence BVP is implemented within the broader search, combining nπ and other transfers in the same trajectory. To aid proximity operations around small bodies, analytical methods are used to investigate stability regions in the presence of significant solar radiation pressure (SRP) and body oblateness perturbations. The interactions of these perturbations allow for heliotropic orbits, a stable family of low-altitude orbits investigated in detail. A novel constrained double-averaging technique analytically determines inclined heliotropic orbits. This type of knowledge is uniquely valuable for small body missions where SRP and irregular body shape are very important and where target selection is often a part of the mission design.

Cette thèse, composée de deux parties, porte sur l’étude d’instabilités au sein d’un milieugranulaire.La première partie de cette thèse est consacrée à l’instabilité de tôle ondulée, c’est-àdirel’apparition d’un motif de rides sur une piste soumise au passage répété de véhicules.Nos travaux expérimentaux ainsi que des simulations numériques de dynamique moléculairenous ont permis de progresser dans la compréhension de ce phénomène. Pour uneroue rigide tirée à vitesse constante, nous avons étudié quantitativement l’impact de lacohésion du milieu granulaire sur les caractéristiques de l’instabilité : vitesse critique, longueurd’onde et taux de croissance. Nous avons enfin entrepris des études préliminairessur un fluide à seuil simple : un microgel de carbopol.Dans la seconde partie, nous étudions la ségrégation granulaire au sein des astéroïdeslâches. Plusieurs indices montrent qu’un grand nombre d’entre eux sont des empilementsde grains, sans cohésion interne et liés par la gravité. Leur répartition n’est pas homogène,avec des zones lisses recouvertes de fines poussières et d’autres où s’accumulent les grosblocs. Nous avons simulé numériquement un empilement granulaire et nous l’avons soumisà des secousses répétées : nous avons réussi à reproduire la ségrégation. Nous avonsétudié l’influence des paramètres physiques et numériques sur le niveau de ségrégation etla dynamique du phénomène. Nous nous sommes aussi intéressés aux phénomènes physiquespouvant causer la ségrégation : convection granulaire, tamisage cinétique, pressionde déplétion, etc. Enfin, nous avons mis en évidence une instabilité azimutale qui peutexpliquer les observations faites pendant les missions spatiales. / This thesis, consisting of two parts, is focusing on instabilities into a granular assembly.The first part deals with washboard road instability, which is the growth of a ripplepattern on a track subjected to repeated passages of vehicles. Our experimental work aswell as soft spheres numerical simulations provide us a better understanding of this phenomenon.In the case of a rigid wheel dragged at constant velocity, we quantitatively studiedthe impact of the cohesion into the granular media on the main features of the instability :critical velocity, wavelength and growth rates. Finally, we have begun preliminary studieson a yield stress fluid, namely a carbopol microgel.The second part is devoted to the granular segregation in asteroids. Several keys showthat a significant part of them are rubble-piles, without internal cohesion and held togetherby their weak self-gravity. The distribution of grains is heterogeneous : while some regionsconsist in fine sand or powder, large boulders seem to accumulate in other parts. Wenumerically simulated a granular pile and subjected it to repeated quakes : we managedto reproduce segregation. We studied the influence of physical and numerical parameterson the segregation level and the dynamics of the phenomenon. We also investigate variouscauses of the segregation : granular convection, kinetic sieving, depletion pressure, etc.Finally, we highlighted an azimuthal segregation which can explain observations duringspatial missions.