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.

The Pluto-Charon system has come into sharper focus following the flyby of New Horizons. We use N-body simulations to probe the unique dynamical history of this binary dwarf planet system. We follow the evolution of the debris disc that might have formed during the Charon-forming giant impact. First, we note that in situ formation of the four circumbinary moons is extremely difficult if Charon undergoes eccentric tidal evolution. We track collisions of disc debris with Charon, estimating that hundreds to hundreds of thousands of visible craters might arise from 0.3-5 km radius bodies. New Horizons data suggesting a dearth of these small craters may place constraints on the disc properties. While tidal heating will erase some of the cratering history, both tidal and radiogenic heating may also make it possible to differentiate disc debris craters from Kuiper belt object craters. We also track the debris ejected from the Pluto-Charon system into the Solar system; while most of this debris is ultimately lost from the Solar system, a few tens of 10-30 km radius bodies could survive as a Pluto-Charon collisional family. Most are plutinos in the 3: 2 resonance with Neptune, while a small number populate nearby resonances. We show that migration of the giant planets early in the Solar system's history would not destroy this collisional family. Finally, we suggest that identification of such a family would likely need to be based on composition as they show minimal clustering in relevant orbital parameters.

abstract: The Kuiper Belt Object Haumea is one of the most fascinating objects in the solar system. Spectral reflectance observations reveal a surface of almost pure water ice, yet it has a mass of 4.006 × 1021 kg, measured from orbits of its moons, along with an inferred mean radius of 715 km, and these imply a mean density of around 2600 kg m−3. Thus the surface ice must be a veneer over a rocky core. This model is supported by observations of Haumea's light curve, which shows large photometric variations over an anomalously rapid 3.9154-hour rotational period. Haumea's surface composition is uniform, therefore the light curve must be due to a varying area presented to the observer, implying that Haumea has an oblong, ellipsoidal shape. If Haumea's rotation axis is normal to our line of sight, and Haumea reflects with a lunar-like scattering function, then its axis ratios are p = b/a = 0.80 (in the equatorial cross section) and q = c/a = 0.52 (in the polar cross section). In this work, I assume that Haumea is in hydrostatic equilibrium, and I model it as a two-phase ellipsoid with an ice mantle and a rocky core. I model the core assuming it has a given density in the range between 2700–3300 kg m−3 with axis ratios that are free to vary. The metric which my code uses calculates the angle between the gravity vector and the surface normal, then averages this over both the outer surface and the core-mantle boundary. When this fit angle is minimized, it allows an interpretation of the size and shape of the core, as well as the thickness of the ice mantle. Results of my calculations show that Haumea's most likely core density is 2700–2800 kg m−3, with ice thicknesses anywhere from 12–32 km over the poles and as thin as 4–18 km over the equator. / Dissertation/Thesis / Masters Thesis Astrophysics 2015

abstract: In this thesis I model the thermal and structural evolution of Kuiper Belt Objects (KBOs) and explore their ability to retain undifferentiated crusts of rock and ice over geologic timescales. Previous calculations by Desch et al. (2009) predicted that initially homogenous KBOs comparable in size to Charon (R ~ 600 km) have surfaces too cold to permit the separation of rock and ice, and should always retain thick (~ 85 km) crusts, despite the partial differentiation of rock and ice inside the body. The retention of a thermally insulating, undifferentiated crust is favorable to the maintenance of subsurface liquid and potentially cryovolcanism on the KBO surface. A potential objection to these models is that the dense crust of rock and ice overlying an ice mantle represents a gravitationally unstable configuration that should overturn by Rayleigh-Taylor (RT) instabilities. I have calculated the growth rate of RT instabilities at the ice-crust interface, including the effect of rock on the viscosity. I have identified a critical ice viscosity for the instability to grow significantly over the age of the solar system. I have calculated the viscosity as a function of temperature for conditions relevant to marginal instability. I find that RT instabilities on a Charon-sized KBO require temperatures T > 143 K. Including this effect in thermal evolution models of KBOs, I find that the undifferentiated crust on KBOs is thinner than previously calculated, only ~ 50 km. While thinner, this crustal thickness is still significant, representing ~ 25% of the KBO mass, and helps to maintain subsurface liquid throughout most of the KBO's history. / Dissertation/Thesis / M.S. Astrophysics 2013

Mean motion resonances (MMRs) play an important role in the formation and evolution of planetary systems and have significantly influenced the orbital properties and distribution of planets and minor planets in the solar system and in. exoplanetary systems. Most previous theoretical analyses have focused on the low- to moderate-eccentricity regime, but with new discoveries of high-eccentricity resonant minor planets and even exoplanets, there is increasing motivation to examine MMRs in the high-eccentricity regime. Here we report on a study of the high-eccentricity regime of MMRs in the circular planar restricted three-body problem. Numerical analyses of the 2: 1 and the 3: 2 interior resonances are carried out for a wide range of planet-to-star mass ratio mu, and for a wide range of eccentricity of the test particle. The surface-of-section technique is used to study the phase space structure near resonances. We find that new stable libration zones appear at higher eccentricity at libration centers that are. shifted from those at low eccentricities. We provide physically intuitive explanations for these transitions in phase space, and we present novel results on the mass and eccentricity dependence of the resonance widths. Our results show that MMRs have sizable libration zones at high eccentricities, comparable to those at lower eccentricities.

Gegenstand dieser Dissertation ist eine umfassende Analyse der Stabilität von Asteroidenbahnen im Edgeworth-Kuiper-Gürtel am Beispiel der 3:5-, 4:7- und der 1:2-Bahnresonanz mit Neptun. Einen weiteren Schwerpunkt der Arbeit bildet die Untersuchung der numerischen Berechenbarkeit der Lyapunov-Zeit von Asteroidenbahnen. Ausgehend von einer allgemeinen Beschreibung der bei numerischen Berechnungen auftretenden Rundungs- und Diskretisierungsfehler wird deren Wachstum bei numerischen Integrationen ermittelt. Diese, teilweise maschinenabhängigen, Fehler beeinflussen die berechnete Trajektorie des Asteroiden ebenso wie die daraus abgeleitete Lyapunov-Zeit. Durch Beispielrechnungen mit unterschiedlichen Rechnerarchitekturen und Integrationsmethoden wird der Einfluss auf die erhaltenen Lyapunov-Zeiten eingehend untersucht. Als Maß zur Beschreibung dieser Abhängigkeit wird ein Berechenbarkeitsindex $\kappa$ definiert. Weiterhin wird gezeigt, dass die allgemeine Struktur des Phasenraumes robust gegenüber diesen Änderungen ist. Unter Nutzung dieser Erkenntnis werden anschließend ausgewählte Bahnresonanzen im Edgeworth-Kuiper-Gürtel untersucht. Grundlegende Charakteristika, wie die Resonanzbreiten, werden dabei aus einfachen Modellen abgeleitet. Eine möglichst realitätsnahe Beschreibung der Stabilität wird durch numerische Integration einer Vielzahl von Testkörpern zusammen mit den Planeten Jupiter bis Neptun erreicht. Die erhaltenen Ergebnisse werden dabei mit der beobachteten Verteilung der Asteroiden im Edgeworth-Kuiper-Gürtel verglichen. ---- Hinweis: Beim Betrachten der pdf-Version dieses Dokumentes mit dem Acrobat Reader mit einer Version kleiner 8.0 kann es unter Windows zu Problemen in der Darstellung der Abbildungen auf den Seiten 46, 72, 74, 79 und 86 kommen. Um die Datenpunkte zu sehen ist eine Vergrößerung von mehr als 800% notwendig. Alternativ kann in den Grundeinstellungen der Haken für das Glätten von Vektorgraphiken entfernt werden. / This dissertation presents a comprehensive description of the stability of asteroid orbits in the Edgeworth-Kuiper belt taking the 3:5, 4:7 and 1:2 mean motion resonance with Neptune as example. Further emphasis is given to the numerical computability of the Lyapunov time of asteroids. Starting with a general description of rounding and approximation errors in numerical computations, the growth of these errors within numerical integrations is estimated. These, partly machine-dependent errors influence the calculated trajectory of the asteroid as well as the derived Lyapunov time. Different hardware architectures and integration methods were used to investigate the influence on the computed Lyapunov time. As a measure of this dependence a computability index $\kappa$ is defined. Furthermore it is shown, that the general structure of phase space is robust against these changes. Subsequently, several selected mean motion resonances in the Edgeworth-Kuiper belt are investigated using these findings. Basic properties, like the resonance width, are deduced from simple models. To get a realistic description of the stability, a huge number of test particles was numerically integrated together with the planets Jupiter to Neptune. The obtained results are compared to the observed distribution of asteroids in the Edgeworth-Kuiper belt. ---- Additional information: If the pdf-file of this document is viewed using Acrobat Reader with a version less 8.0 under Windows the figures on page 46, 72, 74, 79 and 86 are shown incomplete. To see the data points a zoom factor larger than 800% is necessary. Alternatively the smoothing of vector graphics should be disabled in the settings of the reader.

Gegenstand dieser Dissertation ist eine umfassende Analyse der Stabilität von Asteroidenbahnen im Edgeworth-Kuiper-Gürtel am Beispiel der 3:5-, 4:7- und der 1:2-Bahnresonanz mit Neptun. Einen weiteren Schwerpunkt der Arbeit bildet die Untersuchung der numerischen Berechenbarkeit der Lyapunov-Zeit von Asteroidenbahnen. Ausgehend von einer allgemeinen Beschreibung der bei numerischen Berechnungen auftretenden Rundungs- und Diskretisierungsfehler wird deren Wachstum bei numerischen Integrationen ermittelt. Diese, teilweise maschinenabhängigen, Fehler beeinflussen die berechnete Trajektorie des Asteroiden ebenso wie die daraus abgeleitete Lyapunov-Zeit. Durch Beispielrechnungen mit unterschiedlichen Rechnerarchitekturen und Integrationsmethoden wird der Einfluss auf die erhaltenen Lyapunov-Zeiten eingehend untersucht. Als Maß zur Beschreibung dieser Abhängigkeit wird ein Berechenbarkeitsindex $\kappa$ definiert. Weiterhin wird gezeigt, dass die allgemeine Struktur des Phasenraumes robust gegenüber diesen Änderungen ist. Unter Nutzung dieser Erkenntnis werden anschließend ausgewählte Bahnresonanzen im Edgeworth-Kuiper-Gürtel untersucht. Grundlegende Charakteristika, wie die Resonanzbreiten, werden dabei aus einfachen Modellen abgeleitet. Eine möglichst realitätsnahe Beschreibung der Stabilität wird durch numerische Integration einer Vielzahl von Testkörpern zusammen mit den Planeten Jupiter bis Neptun erreicht. Die erhaltenen Ergebnisse werden dabei mit der beobachteten Verteilung der Asteroiden im Edgeworth-Kuiper-Gürtel verglichen. ---- Hinweis: Beim Betrachten der pdf-Version dieses Dokumentes mit dem Acrobat Reader mit einer Version kleiner 8.0 kann es unter Windows zu Problemen in der Darstellung der Abbildungen auf den Seiten 46, 72, 74, 79 und 86 kommen. Um die Datenpunkte zu sehen ist eine Vergrößerung von mehr als 800% notwendig. Alternativ kann in den Grundeinstellungen der Haken für das Glätten von Vektorgraphiken entfernt werden. / This dissertation presents a comprehensive description of the stability of asteroid orbits in the Edgeworth-Kuiper belt taking the 3:5, 4:7 and 1:2 mean motion resonance with Neptune as example. Further emphasis is given to the numerical computability of the Lyapunov time of asteroids. Starting with a general description of rounding and approximation errors in numerical computations, the growth of these errors within numerical integrations is estimated. These, partly machine-dependent errors influence the calculated trajectory of the asteroid as well as the derived Lyapunov time. Different hardware architectures and integration methods were used to investigate the influence on the computed Lyapunov time. As a measure of this dependence a computability index $\kappa$ is defined. Furthermore it is shown, that the general structure of phase space is robust against these changes. Subsequently, several selected mean motion resonances in the Edgeworth-Kuiper belt are investigated using these findings. Basic properties, like the resonance width, are deduced from simple models. To get a realistic description of the stability, a huge number of test particles was numerically integrated together with the planets Jupiter to Neptune. The obtained results are compared to the observed distribution of asteroids in the Edgeworth-Kuiper belt. ---- Additional information: If the pdf-file of this document is viewed using Acrobat Reader with a version less 8.0 under Windows the figures on page 46, 72, 74, 79 and 86 are shown incomplete. To see the data points a zoom factor larger than 800% is necessary. Alternatively the smoothing of vector graphics should be disabled in the settings of the reader.

Nesta tese estudamos algumas regiões de aparente estabilidade no cinturão de asteróides e no cinturão de Kuiper, analisando a evoluçãao dinâmica dos objetos nessas regiões por intervalos de tempo muito longos, em geral, da ordem da idade do Sistema Solar. Centramos principalmente nossa atenção no estudo das populações de pequenos corpos ressonantes, analisando três exemplos diferentes: a ressonância 2/1 com Júpiter e seu entorno (falha de Hecuba), a ressonância 2/3 com Netuno (Plutinos), e a ressonância 1/1 com Júpiter (Troianos). Atacamos o problema com diferentes ferramentas numéricas e analíticas: integração numérica direta de modelos precisos, modelos estatísticos de caminhada aleatória, modelos semi-analíticos baseados no desenvolvimento assimétrico da função perturbadora, cálculo de expoentes de Lyapunov, análise de freqüências, determinação de elementos próprios e taxas de difusão, etc. Os resultados obtidos permitem elaborar conclusões sobre a possível origem e evolução dinâmica destas populações. / In this thesis, we study some regions of regular motion in the asteroid main belt and in the Kuiper belt. We analyze the dynamical evolution in these regions over time scales of the order of the age of the Solar System. We centered our study on the populations of resonant minor bodies, discussing three examples: the 2/1 mean motion resonance with Jupiter (Hecuba gap), the 2/3 resonance with Neptune (Plutinos), and the 1/1 resonance with Jupiter (Trojans). We attack the problem with several different tools, both analytic and numeric: integration of N-body models, random-walk statistical models, semi-analytical models based on the assymetric expansion of the disturbing function, calculation of the maximum Lyapunov exponent, frequancy analysis, estimates of the diffusion of proper elements, etc. The results allow to draw conclusions about the possible origin of these populations.

Nesta tese estudamos algumas regiões de aparente estabilidade no cinturão de asteróides e no cinturão de Kuiper, analisando a evoluçãao dinâmica dos objetos nessas regiões por intervalos de tempo muito longos, em geral, da ordem da idade do Sistema Solar. Centramos principalmente nossa atenção no estudo das populações de pequenos corpos ressonantes, analisando três exemplos diferentes: a ressonância 2/1 com Júpiter e seu entorno (falha de Hecuba), a ressonância 2/3 com Netuno (Plutinos), e a ressonância 1/1 com Júpiter (Troianos). Atacamos o problema com diferentes ferramentas numéricas e analíticas: integração numérica direta de modelos precisos, modelos estatísticos de caminhada aleatória, modelos semi-analíticos baseados no desenvolvimento assimétrico da função perturbadora, cálculo de expoentes de Lyapunov, análise de freqüências, determinação de elementos próprios e taxas de difusão, etc. Os resultados obtidos permitem elaborar conclusões sobre a possível origem e evolução dinâmica destas populações. / In this thesis, we study some regions of regular motion in the asteroid main belt and in the Kuiper belt. We analyze the dynamical evolution in these regions over time scales of the order of the age of the Solar System. We centered our study on the populations of resonant minor bodies, discussing three examples: the 2/1 mean motion resonance with Jupiter (Hecuba gap), the 2/3 resonance with Neptune (Plutinos), and the 1/1 resonance with Jupiter (Trojans). We attack the problem with several different tools, both analytic and numeric: integration of N-body models, random-walk statistical models, semi-analytical models based on the assymetric expansion of the disturbing function, calculation of the maximum Lyapunov exponent, frequancy analysis, estimates of the diffusion of proper elements, etc. The results allow to draw conclusions about the possible origin of these populations.

Planetary systems are not only composed of planets, but also of km-sized rocky and icy bodies that are confined within belts similar to the Asteroid and Kuiper belt in the Solar System. Mutual collisions within these belts grind down solids producing dust and giving rise to debris discs. Primitive asteroids and comets likely played a major role in the emergence of life on Earth through their delivery of volatiles early in the lifetime of our planet. Cometary impacts, therefore, could be a necessary condition for the emergence of life in exoplanets and the study of debris discs essential to determine the ubiquity of such phenomenon. Moreover, exocometary discs provide a unique window into the origins and outer regions of planetary systems as comets do within our Solar System. Initially, in Chapter 1 I present an overview of the study of exoplanetary systems, focusing on debris discs. I discuss the basics of planet formation, its connection with debris discs, and how these evolve and interact with planets. I also describe how we observe these discs and probe their volatile component that is locked inside exocomets, and some evidence supporting the idea of exocomets venturing into the inner regions of planetary systems. Then, in Chapters 2, 3, 4 and 5 I present new ALMA observations of the systems HD 181327, η Corvi, the multiplanet system 61 Vir and HD 107146, which host debris discs. In the first two, I highlight the derivation of the density structure of their discs and the detection of volatiles being released by exocomets; while in the third and fourth I compare the observations with simulations, which I use to set constraints on the underlying planetesimal distribution and mass and orbital distance of unseen planets. Finally, in Chapter 6 I present result obtained from N-body simulations to study the process of inward transport of comets by a multiplanetary system and how these can deliver material to inner planets and explain the frequently observed exozodiacal dust. To conclude, in Chapter 7 I summarise the results and conclusions of this dissertation and discuss ongoing and future work.