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.

Algae-Based Purification of Landfill Biogas Using a CO2 Removal System and Helical Photobioreactor in Series

Biogas is a mixture of methane and other gases. In its crude state, it contains carbon dioxide (CO2) that reduces its energy efficiency and hydrogen sulfide (H2S) that is toxic and highly corrosive. Because chemical methods of removal are expensive and environmentally hazardous, this project investigated an algal-based system to remove CO2 from biogas. An anaerobic digester was used to mimic landfill biogas. Iron oxide and an alkaline spray were used to remove H2S and CO2 respectively. The CO2-laden alkali solution was added to a helical photobioreactor where the algae metabolized the dissolved CO2 to generate algal biomass. Although technical issues prevented testing of the complete system for functionality, cost analysis was completed and showed that the system, in its current state, is not economically feasible. However, modifications may reduce operation costs.