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.

THE PHYSICS OF IDEAS: INFERRING THE MECHANICS OF OPINION FORMATION FROM MACROSCOPIC STATISTICAL PATTERNS

In a microscopic setting, humans behave in rich and unexpected ways. In a macroscopic setting, however, distinctive patterns of group behavior emerge, leading statistical physicists to search for an underlying mechanism. The aim of this dissertation is to analyze the macroscopic patterns of competing ideas in order to discern the mechanics of how group opinions form at the microscopic level. First, we explore the competition of answers in online Q&A (question and answer) boards. We find that a simple individual-level model can capture important features of user behavior, especially as the number of answers to a question grows. Our model further suggests that the wisdom of crowds may be constrained by information overload, in which users are unable to thoroughly evaluate each answer and therefore tend to use heuristics to pick what they believe is the best answer. Next, we explore models of opinion spread among voters to explain observed universal statistical patterns such as rescaled vote distributions and logarithmic vote correlations. We introduce a simple model that can explain both properties, as well as why it takes so long for large groups to reach consensus. An important feature of the model that facilitates agreement with data is that individuals become more stubborn (unwilling to change their opinion) over time. Finally, we explore potential underlying mechanisms for opinion formation in juries, by comparing data to various types of models. We find that different null hypotheses in which jurors do not interact when reaching a decision are in strong disagreement with data compared to a simple interaction model. These findings provide conceptual and mechanistic support for previous work that has found mutual influence can play a large role in group decisions. In addition, by matching our models to data, we are able to infer the time scales over which individuals change their opinions for different jury contexts. We find that these values increase as a function of the trial time, suggesting that jurors and judicial panels exhibit a kind of stubbornness similar to what we include in our model of voting behavior.

An Assessment of Professional Development for Astronomy and Physics Faculty: Expanding Our Vision of How to Support Faculty's Learning About Teaching

In this thesis, we will explore approaches to faculty instructional change in astronomy and physics. We primarily focus on professional development (PD) workshops, which are a central mechanism used within our community to help faculty improve their teaching. Although workshops serve a critical role for promoting more equitable instruction, we rarely assess them through careful consideration of how they engage faculty. To encourage a shift towards more reflective, research-informed PD, we developed the Real-Time Professional Development Observation Tool (R-PDOT), to document the form and focus of faculty's engagement during workshops. We then analyze video-recordings of faculty's interactions during the Physics and Astronomy New Faculty Workshop, focusing on instances where faculty might engage in pedagogical sense-making. Finally, we consider insights gained from our own local, team-based effort to improve a course sequence for astronomy majors. We conclude with recommendations for PD leaders and researchers.