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.

Doubt, for narrator and orchestra

Doubt is a single-movement composition of roughly twelve minutes for narrator and orchestra (woodwinds, horns, and trumpets in pairs, timpani, percussion, strings). The piece explores the controversial issue of capital punishment. The text was compiled from resources found on the websites of Death Penalty Information Center (http://www.deathpenaltyinfo.org) and Anti-Death Penalty Information (http://www.antideathpenalty.org), as well as excerpts from the Bible. Doubt was conceived of as a dramatic work in which a narrator recites factual information in a direct and unemotional manner and the orchestra provides a response to the mixed emotions elicited by the text. The list of dates and case summaries presented in the middle section of the piece seemed most powerful and effective when recited in a natural speaking voice, which is why I chose not to set the text as song. Also, I chose the orchestral medium rather than a chamber setting because the nature of the topic demanded a larger range of colors and combinations, as well as a louder, fuller sound. Much of the music was composed while deciding which texts to include. Thus the music influenced the choice of text as much as the text suggested the musical setting. The four formal divisions of the piece are delineated primarily by the text. The first section is an orchestral introduction representing various emotional perspectives suggested by the texts. The narrator begins the second section with a Biblical verse over sparse orchestration. The third and main section of the piece begins with a new melody in the low strings that is closely related to the harmonic organization of the piece. The narrator lists dates of convictions, executions, exonerations and facts related to doubtful cases. The third section and the narration conclude with another brief passage from the Bible. The fourth section is a dramatic orchestral coda, bringing back the opening harmonies of juxtaposed perfect fifths. The final chord is full of tension and discord, reflecting the oppositions inherent in the topic of capital punishment: life vs. death, sympathy vs. reproach, pain vs. hope, but above all, doubt about guilt vs. innocence.

Report on Archaeological Investigations Conducted at the St. Mary's Site (18AP45), 107 Duke of Gloucester Street, Annapolis, Maryland, 1987-1990

In celebration of the 250th anniversary of the birth of Charles Carroll of Carrollton, Archaeology in Annapolis was invited to excavate the Carroll House and garden on 107 Duke of Gloucester Street in Annapolis, Maryland. The site, named the St. Mary's Site (18AP45) for the Catholic church on the property, is currently owned by the Redemptorists, a Roman Catholic congregation of priests and brothers who have occupied the site since 1852. Prior to the Redemptorists' tenure, the site was owned by the Carroll family from 1701-1852 and is perhaps best known as the home of Charles Carroll of Carrollton (1737-1832), signer of the Declaration of Independence. Excavations at the site were conducted during four consecutive summer seasons from 1987-1990. The investigation focused on three research questions. The first line of inquiry were questions surrounding the dating, architectural configuration, and artifact deposits of the "frame house," a structure adjoining the west wall of the brick Carroll House via a "passage" and later a three story addition. The frame house was partially demolished in the mid-nineteenth century but the construction was thought to pre-date the brick portion of the house. The second research question was spurred by documentary research which indicated that the property might have been the location of Proctor's Tavern, a late 17th-century tavern which served as the meeting place of the Maryland Provincial Assembly. Archaeological testing hoped to determine its location and, if found, investigate Annapolis' early Euro-American occupation. The third research question focused on the landscape of the site as it was shaped by its occupants over the past three hundred years. The research questions included investigating the stratigraphy, geometry, and architectural and planting features of Charles Carroll of Carrollton's terraced garden built during the 1770s, and investigating the changes to the landscape made by the Redemptorists in the nineteenth and twentieth centuries. While no structural evidence associated with Proctor’s Tavern was uncovered during limited excavations along Spa Creek, the historic shore of Spa Creek was identified, buried beneath deep fill deposits laid down during construction of the Carroll Garden. Features and deposits associated with this period likely remain intact in a waterlogged environment along the southeastern sea wall at the St. Mary’s Site. Evidence of extensive earth moving by Carroll is present in the garden and was identified during excavation and coring. This strongly suggests that the garden landscape visible at the St. Mary’s Site is the intact Carroll Garden, which survives beneath contemporary and late nineteenth century strata. The extant surviving garden should be considered highly sensitive to ground-disturbing activities, and is also highly significant considering demonstrable associations with the Carroll family. Other garden-related features were also discovered, including planting holes, and a brick pavilion or parapet located along Spa Creek to the south of the site. The Duke of Gloucester Street wall was shown to be associated with the Carroll occupation of the site. Finally, intensive archaeological research was directed at the vicinity of a frame house constructed and occupied by the Carrolls to the east of the existing brick house, which was replaced by the Redemptorists in the nineteenth century with a greenhouse. These superimposed buildings were documented in detail and remain highly significant features at the St. Mary’s Site.