Thèse de doctorat : Astronomie : Paris, Faculté des sciences : 1857. Thèse de doctorat : Géométrie : Paris, Faculté des sciences : 1857. / Titre provenant de l'écran-titre.

For centuries, an orderly view of planetary system architectures dominated the discourse on planetary systems. However, there is growing evidence that many planetary systems underwent a period of upheaval, during which giant planets "migrated" from where they formed. This thesis addresses a question key to understanding how planetary systems evolve: is planetary migration typically a smooth, disk-driven process or a violent process involving strong multi-body gravitational interactions? First, we analyze evidence from the dynamical structure of debris disks dynamically sculpted during planets' migration. Based on the orbital properties our own solar system's Kuiper belt, we deduce that Neptune likely underwent both planet-planet scattering and smooth migration caused by interactions with leftover planetesimals. In another planetary system, Beta Pictoris, we find that the giant planet discovered there must be responsible for the observed warp of the system's debris belt, reconciling observations that suggested otherwise. Second, we develop two new approaches for characterizing planetary orbits: one for distinguishing the signal of a planet's orbit from aliases, spurious signals caused by gaps in the time sampling of the data, and another to measure the eccentricity of a planet's orbit from transit photometry, "the photoeccentric effect." We use the photoeccentric effect to determine whether any of the giant planets discovered by the Kepler Mission are currently undergoing planetary migration on highly elliptical orbits. We find a lack of such "super-eccentric" Jupiters, allowing us to place an upper limit on the fraction of hot Jupiters created by the stellar binary Kozai mechanism. Finally, we find new correlations between the orbital properties of planets and the metallicity of their host stars. Planets orbiting metal-rich stars show signatures of strong planet-planet gravitational interactions, while those orbiting metal-poor stars do not. Taken together, the results of thesis suggest that suggest that both disk migration and planet-planet interactions likely play a role in setting the architectures of planetary systems. / Astronomy

In a multi-planet system, gravitational interactions cause orbital eccentricity variations. For non-resonant systems, classical secular theory reveals that the eccentricities are vector sums of contributions from several eigenmodes. Examination of the eigenvectors often reveals subsets of planets that interact especially strongly as dynamical groups. Perturbations from other sources, such as tides, are shared among the planets through the secular interactions. If one planet's eccentricity is tidally damped, all the eigenmodes damp so as to leave a signature on their amplitudes. Therefore, if one desires to include some a priori tidal damping in an orbital fit, solutions should not assume the current eccentricity of that planet to be low, but rather for the eigenmodes that damp quickly to have low amplitude. The tidally perturbed planet may retain a substantial eccentricity, because some eigenmodes will be longer-lived. The secular eigenmodes, including relative damping rates, have been calculated for all 72 non-resonant extra-solar systems with adequate data. Tides also affect evolution of planets' semi-major axes, which is coupled with eccentricity evolution. A planet that, alone, would be quickly circularized so as to not experience much semi-major axis migration, could rapidly be forced into the star in the presence of an outer planet. Also, though such an inner planet may now be gone, the eccentricity of the outer planet could have been damped due to tides that acted on the inner planet. Any inferences about the primordial orbits of observed planets must consider these effects. For systems where the inner planet has not yet reached the star, the planets' eccentricities can be constrained for any particular assumed tidal dissipation factor Q', e.g. for the KOI-543 system, if the inner planet is rocky, the eccentricities must be<0.001. The habitable zone around low-mass stars is close to the star, precisely where tides are important. Low-mass stars are very long lived, and can be very old currently. A habitable planet likely needs tectonics for cycles that regulate the atmosphere, but a planet's internal heat will decay over long timescales. However, an outer planet could maintain the inner planet's eccentricity, allowing tidal heating to maintain long-term habitability. Secular interactions, coupled with tidal effects, may be critical for planetary habitability.

Ultra-wide Trans-Neptunian Binaries (TNBs) are extremely sensitive to perturbation, and therefore make excellent probes of the past and present dynamical environment of the outer Solar System. Using data gathered from a host of facilities we have determined the mutual orbits for a sample of seven wide TNBs whose periods exceed one year. This characterized sample provides us with new information about the probable formation scenarios of TNBs, and has significant implications for the early dynamical and collisional history of the Kuiper Belt. We show that these wide binaries have short collisional lifetimes, and use them to produce a new estimate of the number of small (~1 km) objects in the Kuiper Belt. Additionally, these systems are susceptible to tidal disruption, and we show that it is unlikely that they were ever subjected to a period of close encounters with the giant planets. We find that the current properties of these ultra-wide Trans-Neptunian Binaries suggest that planetesimal growth in the Cold Classical Kuiper Belt did not occur through slow hierarchical accretion, but rather through rapid gravitational collapse. / Graduate

A key challenge in low-thrust trajectory design is generating preliminary solutions that simultaneously detail the evolution of the spacecraft position and velocity vectors, as well as the thrust history. To address this difficulty, a dynamical model that incorporates a low-thrust force into the circular restricted 3-body problem (CR3BP), i.e., the CR3BP+LT, is constructed and analyzed. Control strategies that deliver specific energy changes (including zero energy change to deliver a conservative system) are derived and investigated, and dynamical structures within the CR3BP+LT are explored as candidate solutions to seed initial low-thrust trajectory designs. Furthermore, insights from dynamical systems theory are leveraged to inform the design process. In the combined model, the addition of a low-thrust force modifies the locations and stability of the equilibrium solutions, resulting in flow configurations that differ from the natural behavior in the CR3BP. The application of simplifying assumptions yields a conservative, autonomous system with properties that supply useful insights. For instance, "forbidden regions" at fixed energy levels bound low-thrust motion, and analytical equations are available to guide the navigation through energy space. Linearized dynamics about the equilibria supply hyperbolic and center manifold structures, similar to the ballistic CR3BP. Low-thrust periodic orbits in the vicinity of the equilibrium solutions also admit hyperbolic and center manifolds, providing an even greater number of dynamical structures to be employed in preliminary trajectory designs. Several applications of the structures and insights derived from the CR3BP+LT are presented, including several strategies for transit and capture near the smaller CR3BP primary body. Finally, an interactive trajectory design framework is presented to explore and utilize the structures and insights delivered by this investigation.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20898号 / 理博第4350号 / 新制||理||1624(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 田中 貴浩, 准教授 樽家 篤史, 教授 川合 光 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

Three methods for solving the orbital intercept problem in the presence of an oblate earth are presented. Both iterative and direct approaches for solving the problem were compared in the bases of computational time and relative accuracy of the results. The two iterative methods were found to agree to eight significant figures for all elliptic intercept orbits studied. The results obtained from the direct approach were found to agree with the iterative methods's results to eight significant figures for low intercept eccentricities ( e < 0.2), and to five significant figures for high intercept orbit eccentricities (e = 0.9). However, the direct method was found to be twice as fast, computationally, as either of the two iterative methods. The iterative methods each take essentially the same amount of computational time. Neither type of routine yields accurate results for half-revolution intercept and hyperbolic intercept orbits. The method for developing these procedures, the computer code implementing the methods, and selected results are included. / M.S.

The four longest period Kuiper Belt objects have orbital periods close to integer ratios with each other. A hypothetical planet with an orbital period of similar to 17,117 years and a semimajor axis similar to 665 au would have N/1 and N/2 period ratios with these four objects. The orbital geometries and dynamics of resonant orbits constrain the orbital plane, the orbital eccentricity, and the mass of such a planet as well as its current location in its orbital path.

In the coming years, high-contrast imaging surveys are expected to reveal the characteristics of the population of wide-orbit, massive, exoplanets. To date, a handful of wide planetary mass companions are known, but only one such multi-planet system has been discovered: HR 8799. For low mass planetary systems, multi-planet interactions play an important role in setting system architecture. In this paper, we explore the stability of these high mass, multi-planet systems. While empirical relationships exist that predict how system stability scales with planet spacing at low masses, we show that extrapolating to super-Jupiter masses can lead to up to an order of magnitude overestimate of stability for massive, tightly packed systems. We show that at both low and high planet masses, overlapping mean-motion resonances trigger chaotic orbital evolution, which leads to system instability. We attribute some of the difference in behavior as a function of mass to the increasing importance of second order resonances at high planet-star mass ratios. We use our tailored high mass planet results to estimate the maximum number of planets that might reside in double component debris disk systems, whose gaps may indicate the presence of massive bodies.

High levels of dust have been detected in the immediate vicinity of many stars, both young and old. A promising scenario to explain the presence of this short-lived dust is that these analogues to the zodiacal cloud (or exozodis) are refilled in situ through cometary activity and sublimation. As the reservoir of comets is not expected to be replenished, the presence of these exozodis in old systems has yet to be adequately explained. It was recently suggested that mean-motion resonances with exterior planets on moderately eccentric (e(p) greater than or similar to 0.1) orbits could scatter planetesimals on to cometary orbits with delays of the order of several 100 Myr. Theoretically, this mechanism is also expected to sustain continuous production of active comets once it has started, potentially over Gyr time-scales. We aim here to investigate the ability of this mechanism to generate scattering on to cometary orbits compatible with the production of an exozodi on long time-scales. We combine analytical predictions and complementary numerical N-body simulations to study its characteristics. We show, using order of magnitude estimates, that via this mechanism, low-mass discs comparable to the Kuiper belt could sustain comet scattering at rates compatible with the presence of the exozodis which are detected around Solar-type stars, and on Gyr time-scales. We also find that the levels of dust detected around Vega could be sustained via our proposed mechanism if an eccentric Jupiter-like planet were present exterior to the system's cold debris disc.