Theses and Dissertations from UMD
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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM
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Item The Tilts and Spins of Planets and Moons(2020) Rogoszinski, Zeeve; Hamilton, Douglas P; Astronomy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The planets' spin states, specifically their tilts and spins, can provide useful constraints to planetary formation as they evolve and interact with their surroundings. In this thesis, we explore the spin dynamics required to reproduce Uranus's and Neptune's spin states through collisions, gas accretion, and secular spin-orbit resonances, and discuss the role these processes play in the greater context of solar system formation. Gas accretion is the likely source for their similar spin periods, yet a simple 2D accretion model with gas flowing to the planet's equator yields planets spinning at near break-up speeds. We confirm this using numerical simulations, further supporting the idea that a combination of magnetic effects and polar accretion are responsible for the gas planets' slower spin periods. Gas accretion should also drive obliquities to 0°, but both Uranus and Neptune are tilted to 98° and 30° respectively. The leading hypothesis for their large obliquities is giant collisions, where for Uranus an Earth mass impactor struck the planet's North pole, while Neptune was struck by an impactor closer to the mass of Mars. Generating two nearly identically sized planets with widely different tilts yet very similar spins is, however, a low probability event, as the planets would likely remain near their initial spin states. We compare different collisional models for tilted, untilted, spinning, and non-spinning planets, and find that two 0.5 M_{\oplus} impacts produce better likelihoods than a single M_{\oplus} strike. We can noticeably improve these statistics if the planet was already tilted beyond 40° by a spin-orbit resonance, and an initial tilt of 70° can increase the likelihood by an order of magnitude, compared to a pure collision scenario, while also halving the mass of the required subsequent impactor. Tilting a planet without altering its spin period or inner satellite system is possible with a secular spin-orbit resonance, a coupling between spin and orbit precession frequencies, yet neither Uranus's nor Neptune's spin axes are precessing fast enough to match any present-day orbital precession rates. Here, we seek conditions in the past that could have augmented the ice giant's spin precession rates enough to excite their obliquities. First, we explore the possibility of Uranus forming closer to the Sun, as solar tides near 7 au can increase spin precession rates enough to match another planet's orbital precession rate located beyond Saturn. We show using numerical simulations that Uranus can be tilted to 90° on 100 Myr timescales, but leaving Uranus between Jupiter and Saturn for that long is unstable. While resonance kicks can tilt the planet to ~ 40° on 10 Myr timescales, conditions need to be ideal. Another way to increase the ice giants' spin precession rates is if they harbored circumplanetary disks 3-10 times the mass of their satellite systems. We find that the presence of a massive disk moves the Laplace radius significantly outwards from its classical value, resulting in more of the disk contributing to the planet's pole precession. In this case, the planets would resonate with their own orbits during the lifetime of the disk (~1 Myr), and Uranus can potentially be tilted to as high as 70°. Neptune, by contrast, can be tilted all the way to 30°, eliminating the need for collisions altogether. Lastly, in the spirit of collisions and spin dynamics, we explore a collisional origin to the spin rates of the irregular satellites around Saturn, and show the conditions required to also vary the satellites' orbits. Irregular satellites are located far away from the planet on highly eccentric and inclined orbits, and recently reported Cassini observations show that the satellites that orbit retrograde spin on average faster than satellites that orbit prograde to Saturn's spin. Generating the spin rates of both prograde and retrograde populations, sans Phoebe, through collisions requires an initial population of 10^4 - 10^5 particles more massive than 10^9 kg, and have more than half of them orbit in the retrograde direction. Spinning up Phoebe to its current spin rate requires imparting about 10% of its mass with giant collisions, which is enough to significantly alter its orbital parameters. As such, Phoebe may have scattered the inner prograde irregular satellites to more eccentric orbits, but this signature may also be a result of observation bias.Item Resonances in Ring, Satellite, and Planetary Systems(2020) Rimlinger, Thomas; Hamilton, Douglas P; Astronomy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this thesis, we study the origin and evolution of planets, rings, and moons in the context of orbital dynamics. In particular, we investigate the Kepler 36 exoplanet system, which features two known planets whose semimajor axes differ by 0.01 AU but whose densities differ by nearly a factor of 10, in contrast to predictions from standard Solar System evolution theory. We use resonance and perturbation theory to show that these planets could have migrated to their current positions through a swarm of smaller bodies that knocked them progressively closer together.We then develop a set of orbital elements designed to be used for a body orbiting an oblate host such as Saturn. Our corrections properly vanish in the limit that the oblateness terms go to 0, in contrast to the so-called “epicyclic elements,” which do not correctly reduce to their osculating counterparts. We compare the accuracy of our elements to the epicyclic elements as well as a simple numerical fit. We also provide an explicit inverse function for our elements that transforms them back to state vectors. Next, we study the confinement of narrow, eccentric rings. Dozens of these odd structures are known to orbit the three outer planets as well as several small bodies, but simple theory predicts they should spread on timescales as short as tens of years. The standard confinement theory suggests that these rings can be “shepherded” by nearby satellites, but most narrow rings lack such nearby satellites. We argue that by circularizing, eccentric rings can lengthen their spreading timescales by a factor of 100,000. We support our theory with simulations of narrow eccentric ringlets and find that we can self-confine the Titan ringlet at Saturn. Finally, we consider the formation and evolution of Saturn’s largest moon, Titan. No self-consistent theory exists that can explain all of its unusual features, including its enormous mass, “lonely” location within Saturn’s satellite system, and relatively high orbital eccentricity and inclination. We argue that Titan could have formed from a dynamical instability within a resonant chain of moons similar to the modern-day Galilean chain of Io, Europa, and Ganymede at Jupiter. We sim- ulate this process for a wide variety of tidal migration and eccentricity damping strengths along with over a hundred unique possible mass distributions and find that instabilities are rare but possible.Item Application of X-ray Pulsar Navigation: A Characterization of the Earth Orbit Trade Space(2015) Yu, Wayne; Healy, Liam; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The potential for pulsars as a navigation source has been studied since their discovery in 1967. X-ray pulsar navigation (XNAV) is a celestial navigation system that uses the consistent timing nature of X-ray photons from milli-second pulsars (MSP) to perform space navigation. Much of the challenge of XNAV comes from the faint signal, availability, and distant nature of pulsars. This thesis is the study of pulsar XNAV measurements for extended Kalman filter (EKF) tracking performance within a wide trade space of bounded Earth orbits, using a simulation of existing X-ray detector space hardware. An example of an X-ray detector for XNAV is the NASA Station Explorer for X-ray Timing and Navigation (SEXTANT) mission, a technology demonstration of XNAV set to perform on the International Space Station (ISS) in 2016. The study shows that the closed Earth orbit for XNAV performance is reliant on the orbit semi-major axis and eccentricity as well as orbit inclination. These parameters are the primary drivers of pulsar measurement availability and significantly influence the natural spacecraft orbit dynamics. Sensitivity to initial orbit determination error growth due to the scarcity of XNAV measurements within an orbital period require appropriate timing of initial XNAV measurements. The orbit angles of argument of perigee and right ascension of the ascending node, alongside the other orbit parameters, complete the initial cadence of XNAV measurements. The performance of initial XNAV measurements then propagates throughout the experimental period.Item Cometary Escape in the Restricted Circular Planar Three Body Problem(2011) Galante, Joseph Robert; Kaloshin, Vadim Yu; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The classical principle of least action says that orbits of mechanical systems extremize action; an important subclass are those orbits that minimize action. This principle is utilized along with Aubry-Mather theory to construct regions of instability for a certain three body problem, given by a Hamiltonian system of two degrees of freedom. In principle, these methods can be applied to construct instability regions for a variety of Hamiltonian systems with $2$ degrees of freedom. The Hamiltonian model considered in this thesis describes the dynamics of a Sun-Jupiter-Comet system and under some simplifying assumptions, the existence of instabilities for the orbit of the comet is shown. In particular it is shown that a comet which starts close to an orbit in the shape of an ellipse of eccentricity $e=0.66$ can increase in eccentricity to beyond $e=1$. Furthermore, there exist ejection orbits for the comet. Such orbits are initially well within the range of our solar system. This might give an indication of why most objects rotating around the Sun in our solar system have relatively low eccentricity. Several new theoretical tools are introduced in this thesis as well. The most notable is a checkable sufficient condition to verify that an exact area preserving map is an exact area preserving twist map in a certain coordinate system. This coordinate system is constructed by ``spreading the cumulative twist'' which arises from the long term dynamics of system. Many of the results of the thesis are `computer assisted' and utilize recent advances in rigorous numerical integration. It is through the application of these advances in computing that it has become possible to state deep results for realistic solar systems. This has been the dream of many since humans first observed the stars so long ago.