Resonant and Secular Orbital Interations

In stable solar systems, planets remain in nearly elliptical orbits around their stars. Over longer timescales, however, their orbital shapes and sizes change due to mutual gravitational perturbations. Orbits of satellites around a planet vary for the same reason. Because of their interactions, the orbits of planets and satellites today are different from what they were earlier. In order to determine their original orbits, which are critical constraints on formation theories, it is crucial to understand how orbits evolve over the age of the Solar System. Depending on their timescale, we classify orbital interactions as either short-term (orbital resonances) or long-term (secular evolution). My work involves examples of both interaction types. Resonant history of the small Neptunian satellites In satellite systems, tidal migration brings satellite orbits in and out of resonances. During a resonance passage, satellite orbits change dramatically in a very short period of time. We investigate the resonant history of the six small Neptunian moons. In this unique system, the exotic orbit of the large captured Triton (with a circular, retrograde, and highly tilted orbit) influences the resonances among the small satellites very strongly. We derive an analytical framework which can be applied to Neptune's satellites and to similar systems. Our numerical simulations explain the current orbital tilts of the small satellites as well as constrain key physical parameters of both Neptune and its moons. Secular orbital interactions during eccentricity damping Long-term periodic changes of orbital shape and orientation occur when two or more planets orbit the same star. The variations of orbital elements are superpositions of the same number of fundamental modes as the number of planets in the system. We investigate how this effect interacts with other perturbations imposed by external disturbances, such as the tides and relativistic effects. Through analytical studies of a system consisting of two planets, we find that an external perturbation exerted on one planet affects the other indirectly. We formulate a general theory for how both orbits evolve in response to an arbitrary externally-imposed slow change in eccentricity.

Geochemistry of crustal formation and evolution

Terrestrial planets produce crusts as they differentiate. The Earth’s bi-modal crust, with a high-standing granitic continental crust and a low-standing basaltic oceanic crust, is unique in our solar system and links the evolution of the interior and exterior of this planet. Here I present geochemical observations to constrain processes accompanying crustal formation and evolution. My approach includes geochemical analyses, quantitative modeling, and experimental studies. The Archean crustal evolution project represents my perspective on when Earth’s continental crust began forming. In this project, I utilized critical element ratios in sedimentary records to track the evolution of the MgO content in the upper continental crust as a function time. The early Archean subaerial crust had >11 wt. % MgO, whereas by the end of Archean its composition had evolved to about 4 wt. % MgO, suggesting a transition of the upper crust from a basalt-like to a more granite-like bulk composition. Driving this fundamental change of the upper crustal composition is the widespread operation of subduction processes, suggesting the onset of global plate tectonics at ~ 3 Ga (Abstract figure). Three of the chapters in this dissertation leverage the use of Eu anomalies to track the recycling of crustal materials back into the mantle, where Eu anomaly is a sensitive measure of the element’s behavior relative to neighboring lanthanoids (Sm and Gd) during crustal differentiation. My compilation of Sm-Eu-Gd data for the continental crust shows that the average crust has a net negative Eu anomaly. This result requires recycling of Eu-enriched lower continental crust to the mantle. Mass balance calculations require that about three times the mass of the modern continental crust was returned into the mantle over Earth history, possibly via density-driven recycling. High precision measurements of Eu/Eu* in selected primitive glasses of mid-ocean ridge basalt (MORB) from global MORs, combined with numerical modeling, suggests that the recycled lower crustal materials are not found within the MORB source and may have at least partially sank into the lower mantle where they can be sampled by hot spot volcanoes. The Lesser Antilles Li isotope project provides insights into the Li systematics of this young island arc, a representative section of proto-continental crust. Martinique Island lavas, to my knowledge, represent the only clear case in which crustal Li is recycled back into their mantle source, as documented by the isotopically light Li isotopes in Lesser Antilles sediments that feed into the fore arc subduction trench. By corollary, the mantle-like Li signal in global arc lavas is likely the result of broadly similar Li isotopic compositions between the upper mantle and bulk subducting sediments in most arcs. My PhD project on Li diffusion mechanism in zircon is being carried out in extensive collaboration with multiple institutes and employs analytical, experimental and modeling studies. This ongoing project, finds that REE and Y play an important role in controlling Li diffusion in natural zircons, with Li partially coupling to REE and Y to maintain charge balance. Access to state-of-art instrumentation presented critical opportunities to identify the mechanisms that cause elemental fractionation during laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) analysis. My work here elucidates the elemental fractionation associated with plasma plume condensation during laser ablation and particle-ion conversion in the ICP.

Detection methods for common problems in solar home systems

Gemstone Team SHINE (Students Helping to Implement Natural Energy)

Analysis of ocean power extraction capabilites of a rotary wave energy conversion system

Gemstone Team WAVES (Water and Versatile Energy Systems)