The purpose of this study is to develop an understanding of the observability of small-scale dynamical Solar System features in meteor orbit radar data, particularly with reference to mean motion resonance effects. Particular focus is placed on the presence of `resonant swarms' in meteoroid streams: the resonant swarm at the 7:2 Jovian mean-motion resonance is used as an example, as it best satisfies radar observability criterion. Furthermore, evidence for this structure exists in visual meteor data. The radar dataset used for this study is that of the Canadian Meteor Orbit Radar (CMOR) as this dataset contains the largest number of meteoroid stream particles. The aim here is to determine whether the Taurid resonant swarm is observable in datasets produced by radars such as CMOR, or what improvements in individual orbital uncertainties are necessary for positive detection to be possible. The observability of the Taurid swarm in radar data depends on the limitations of the radar data (in terms of the individual measurement uncertainties); and on the properties of the resonance itself. Both aspects are investigated in this thesis. A statistical study is first conducted to assess whether evidence for the swarm exists in a dataset containing CMOR Northern and Southern Taurids from the years 2002 to 2007. It is found that the level of variations present is consistent with that expected due to random fluctuations: there is no evidence for a statistically significant resonant feature at the location of the 7:2 Jovian resonance. Additionally, the observability of various sizes of resonant peak for different sizes of dataset and for different levels of measurement uncertainties is investigated by addition of a modelled resonant feature to the data, followed by replacement of individual meteors by Gaussian profiles to simulate the effect of orbital uncertainties. It is clear that the level of broadening resulting from the uncertainties of the CMOR data used will not allow the observation of a resonant peak of the expected size. Detection is expected to be more likely in a `swarm encounter year' (a year in which the geometry between the resonant swarm and Earth is favourable to detection). The velocity uncertainties of a meteor orbit radar (similar to CMOR) need to be improved by a factor of 5 to 10 (relative to the CMOR uncertainties) in order to detect a resonant swarm that is composed of ~30% to ~5% (respectively) of the total number of observed Taurids in a swarm encounter year. An improvement significantly greater than a factor of ~10 is unlikely to result in a significant improvement in the ability to detect the resonant swarm. It is expected that a factor of 10 improvement in radar measurement uncertainties is achievable with the current techniques of radar systems and signal processing. These statistical tests require knowledge of the resonant width of the 7:2 Jovian resonance in semi-major axis, as this provides the size of the resonant feature of interest. Such resonant or libration widths can be determined analytically for orbits with low eccentricities. As Taurid orbits have high eccentricities (e~0.83), a hierarchical N-body integrator is used to examine the dynamics in the region of the 7:2 resonance, and determine a resonant width of (0.047±0.005) AU. To verify this method the standard analytic equations and a semi-analytic method are compared (at low eccentricities) with the numerical resonant width values: the agreement is within 10% for eccentricities below 0.4. It is important to know what proportion of radar Taurids are expected to be resonant in a swarm year in order to evaluate the observability of the swarm in radar data. One important factor that may affect this is the mass distribution of particles in the swarm. This is investigated by ejecting particles in multiple directions from three model comets: the first with a mass and orbit in agreement with those of the current 2P/Encke; the second with 2P/Encke mass and an orbit matching that of the proposed proto-Encke object; and a third with the mass and orbit of proto-Encke. The resulting orbits are examined to determine what proportion will land within the 7:2 resonance, for a range of particle masses and densities. The instantaneous effect of radiation pressure on the orbits of ejected particles is also considered. However, it is difficult to determine accurate capture percentage values due to the uncertainty surrounding cometary ejection mechanisms. Nevertheless, it is found that capture of Taurids into the 7:2 resonance by all comets is possible. Using comparisons between the percentages of visual-sized and radar-sized particles captured, it is determined that in weak swarm years (in which only 20% of visual meteoroids detected are resonant) only 4% to 5% of observed visual Taurids are expected to be resonant. Such a swarm would be on the edge of observability. However, in stronger swarm years (such as 2005), the resonant proportion will exceed that required for detection with a reduction in CMOR measurement uncertainties of a factor of ten.

Context: Slivan (2002) determined spin state of ten asteroids in the Koronis family. Surprisingly, all four asteroids with prograde sense of rotation were shown to have spin axes nearly parallel in the inertial space. All asteroids with retrograde sense of rotation had large obliquities and rotation periods either short or long. It was shown that Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect can explain all these peculiar facts. In particular, it drives spin axes of the prograde rotators to be captured in a secular spin-orbital resonance known as Cassini state 2. Vokrouhlický et al. (2002) dubbed these configurations "Slivan states". Aims: A question arises whether Slivan states could exist also in other regions of the main asteroid belt, in particular its inner part, where observations are most easily obtained. Here, however, dynamical difficulties arise due to convergence of the proper frequency s and the planetary frequency s6. We investigate possibilities of a long-term stable capture in the Slivan state in the inner part of the main belt. Method: We used SWIFT integrator to determine orbital evolution of selected asteroids in the inner part of the main belt. In the case of 20 Massalia, we observed the asteroid in 2011, and used these new data to help better solve the rotation state using the...

L'ensemble des travaux menés au cours de cette thèse concerne l'étude de la résonance co-orbitale. Ce domaine de trajectoires particulières, où un astéroïde et une planète gravitent autour du Soleil avec la même période de révolution, possède une dynamique très riche liée aux célèbres configurations équilatérales de Lagrange, L4 et L5, ainsi qu'aux configurations alignées de Euler, L1, L2 et L3. Un exemple majeur dans le système solaire est donné par les astéroïdes « troyens » qui accompagnent Jupiter au voisinage des équilibres L4 et L5. Une deuxième configuration étonnante est donnée par les satellites Janus et Épiméthée qui gravitent autour de la planète Saturne ; suite à la forme décrite par la trajectoire d’un des satellites dans un repère tournant avec l’autre, la dynamique résultante est appelée « fer-à-cheval ». Un nouveau type de dynamique a été récemment misen évidence dans le contexte de la résonance coorbitale : les « quasi-satellites ». Il s’agit de configurations remarquables où, dans un repère tournant avec la planète, la trajectoire de l’astéroïde correspond à celle d’un satellite rétrograde. Des astéroïdes accompagnant les planètes Venus, Jupiter et la Terre ont notamment été observés dans ces configurations. La dynamique des quasi-satellites possède un grand intérêt, pas seulement parce qu’elle relie les différents domaines de la résonance co-orbitale (voir les travaux de Namouni, 1999) mais aussi parce qu’elle semble faire le pont entre les notions de satellisation et celles de trajectoires héliocentriques. Cependant, bien que le terme « quasi-satellite" soit devenu dominant dans la communauté de mécanique céleste, certains auteurs utilisent plutôt la terminologie « satellite rétrograde » révélant ainsi une ambiguïté sur la définition de ces trajectoires. Les récentes découvertes autour des exo-planètes ont motivé le développement de travaux concernant la résonance co-orbitale dans le problème des trois corps planétaire. Dans ce contexte Giuppone et al. (2010) ont mis en évidence (par une méthode numérique) les quasisatellites ainsi que des nouvelles familles de configurations remarquables : les orbites « anti-Lagrange ». La troisième partie de thèse présente alors une méthode analytique pour l'étude planétaire, permettant de révéler analytiquement les orbites anti-Lagrange ainsi qu'une esquisse d'étude des quasisatellites en adaptant à ce contexte plus général la méthode présentée dans la seconde partie. Pour ces raisons, la première partie de cette thèse a consisté à clarifier la définition de ces orbites en revisitant le cas circulaire-plan (trajectoires coplanaires avec la planète qui gravite sur une orbite circulaire) dans le cadre du problème moyen. Dans la deuxième partie de cette thèse, nous avons développé une méthode analytique apte à explorer le domaine des quasi-satellites dans le cadre du problème moyen. Nous avons réalisé cette exploration dans le cas circulaire-plan et proposé une extension aux cas excentrique-plan et circulaire-spatial. / This work of thesis focuses on the study of the coorbital resonance. This domain of particular trajectories, where an asteroid and a planet gravitate around the Sun with the same period possesses a very rich dynamics connected to the famous Lagrange’s equilateral configurations L4 and L5, as well as to the Eulerian’s configurations L1, L2 and L3. A major example in the solar system is given by the “Trojan” asteroids harboured by Jupiter in the neighborhood of L4 and L5. A second astonishing configuration is given by the system Saturn-Janus-Epimetheus; this peculiar dynamics is known as “horseshoe”. Recently, a new type of dynamics has been highlighted in the context of co-orbital resonance: the quasi-satellites. They correspond to remarkable configurations : in the rotating frame with the planet, the trajectory of the asteroid seems the one of a retrograde satellite. Some asteroids harboured by Venus, Jupiter and the Earth have been observed in this kind of configuration. The quasi-satellite dynamics possesses great interest not only because it connects the different domains of the co-orbital resonance (see works of Namouni, 1999), but also because it seems to bridge the gap between satellization and heliocentric trajectories. However, despite the term quasi-satellite has become dominant in the celestial mechanics community, some authors rather use the term “retrograde satellite”. This reveals an ambiguity on the definition of these trajectories. For these reasons, the first part of this thesis consisted in clarifying the definition of these orbits by revisiting the planar-circular case (planet on circular motion) in the framework of the averaged problem. In the second part of this thesis, we developed an analytic method to explore the quasi-satellite domain in the averaged problem. We realized this exploration in the planar-circular case and proposed an extension to the planar-eccentric and spatial-circular cases. The recent discoveries around the exo-planets motivated some works on the co-orbital resonance in the planetary Three-Body Problem. In this context, Giuppone et al. (2010) highlighted (numerically) the quasi-satellite as well as new families of remarkable configurations: the “anti-Lagrange”. Then the third part of this thesis presents an analytical method for the planetary problem that allows to reveal the anti-Lagrange orbits as well as a sketch of study of quasi-satellite trajectories.