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.

Bridging the Divide Between the Soloist and the Ensemble Player

In conservatories and music schools, the general practice for an aspiring pianist is to focus on solo performance learning mainly solo repertoire. With the advent of the advanced degree in collaborative piano, pianists could submerge themselves in the study of duo sonatas, larger chamber music ensembles, and art song. The appearance of this degree was an important step in the development of pianists, as this kind of work requires specific training and focus to master the vast repertoire involved. However it also more clearly brought out the invisible divide separating the solo pianist from the collaborative pianist, a.k.a. the accompanist. While geniuses such as Bach, Beethoven and Brahms were known to compose and perform all types of music, the appearance of super stars such as Liszt and Paganini helped bring into being the term accompanist and since then music world has tacitly embraced this divide. The goal of my dissertational study is to show that this divide need not exist. The three recitals which comprise this dissertational project were all performed at the University of Maryland, the first on 12 November 2010 at Gildenhom Recital Hall, the second at Ulrich Recital Hall on 10 September 2011, and the third at Gildenhorn Recital Hall on 11 November 2011. The repertoire included Rachmaninoff Prelude in g# minor op. 32 no. 12 and Etude-Tableaux in Eb minor op. 29 no. 5, Brahms Sonata for Piano and Violin in d minor op. 108, Mendelssohn Piano Trio in d minor op. 49, Chopin Sonata No.2 in Bb minor, Franck Sonata for Piano and Violin, Prokofiev Piano Concerto no. 2 in g minor op. 16 with pianist Elizabeth Brown as orchestra, Beethoven Sonata for Piano and Violin in A op 47 (Kreutzer), and Paul Schoenfield Cafe Music. All works with violin and cello were performed with violinist Rebecca Racusin, and cellist Devree Lewis. The recitals were recorded on compact discs and are archived within the Digital Repository at the University of Maryland(DRUM).