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.

Surface Insulation Resistance Degradation and Electrochemical Migration on Printed Circuit Boards

Widespread adoption of lead-free materials and processing for printed circuit board (PCB) assembly has raised reliability concerns regarding surface insulation resistance (SIR) degradation and electrochemical migration (ECM). As PCB conductor spacings decrease, electronic products become more susceptible to these failures mechanisms, especially in the presence of surface contamination and flux residues which might remain after no-clean processing. Moreover, the probability of failure due to SIR degradation and ECM is affected by the interaction between physical factors (such as temperature, relative humidity, electric field) and chemical factors (such as solder alloy, substrate material, no-clean processing). Current industry standards for assessing SIR reliability are designed to serve as short-term qualification tests, typically lasting 72 to 168 hours, and do not provide a prediction of reliability in long-term applications. The risk of electrochemical migration with lead-free assemblies has not been adequately investigated. Furthermore, the mechanism of electrochemical migration is not completely understood. For example, the role of path formation has not been discussed in previous studies. Another issue is that there are very few studies on development of rapid assessment methodologies for characterizing materials such as solder flux with respect to their potential for promoting ECM. In this dissertation, the following research accomplishments are described: 1). Long-term temp-humidity-bias (THB) testing over 8,000 hours assessing the reliability of printed circuit boards processed with a variety of lead-free solder pastes, solder pad finishes, and substrates. 2). Identification of silver migration from Sn3.5Ag and Sn3.0Ag0.5Cu lead-free solder, which is a completely new finding compared with previous research. 3). Established the role of path formation as a step in the ECM process, and provided clarification of the sequence of individual steps in the mechanism of ECM: path formation, electrodeposition, ion transport, electrodeposition, and filament formation. 4). Developed appropriate accelerated testing conditions for assessing the no-clean processed PCBs' susceptibility to ECM: a). Conductor spacings in test structures should be reduced in order to reflect the trend of higher density electronics and the effect of path formation, independent of electric field, on the time-to-failure. b). THB testing temperatures should be modified according to the material present on the PCB, since testing at 85oC can cause the evaporation of weak organic acids (WOAs) in the flux residues, leading one to underestimate the risk of ECM. 5). Correlated temp-humidity-bias testing with ion chromatography analysis and potentiostat measurement to develop an efficient and effective assessment methodology to characterize the effect of no-clean processing on ECM.