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 INFLUENCE OF MOTIVATION ON EMOTION REGULATION AND MOTOR PERFORMANCE: EXAMINATION OF A NEURO-AFFECTIVE MODEL

Mental stress is known to disrupt the execution of motor performance and can lead to decrements in the quality of performance, however, individuals have shown significant differences regarding how fast and well they can perform a skilled task according to how well they can manage stress and emotion. The purpose of this study was to advance our understanding of how the brain modulates emotional reactivity under different motivational states to achieve differential performance in a target shooting task that requires precision visuomotor coordination. In order to study the interactions in emotion regulatory brain areas (i.e. the ventral striatum, amygdala, prefrontal cortex) and the autonomic nervous system, reward and punishment interventions were employed and the resulting behavioral and physiological responses contrasted to observe the changes in shooting performance (i.e. shooting accuracy and stability of aim) and neuro-cognitive processes (i.e. cognitive load and reserve) during the shooting task. Thirty-five participants, aged 18 to 38 years, from the Reserve Officers’ Training Corp (ROTC) at the University of Maryland were recruited to take 30 shots at a bullseye target in three different experimental conditions. In the reward condition, $1 was added to their total balance for every 10-point shot. In the punishment condition, $1 was deducted from their total balance if they did not hit the 10-point area. In the neutral condition, no money was added or deducted from their total balance. When in the reward condition, which was reportedly most enjoyable and least stressful of the conditions, heart rate variability was found to be positively related to shooting scores, inversely related to variability in shooting performance and positively related to alpha power (i.e. less activation) in the left temporal region. In the punishment (and most stressful) condition, an increase in sympathetic response (i.e. increased LF/HF ratio) was positively related to jerking movements as well as variability of placement (on the target) in the shots taken. This, coupled with error monitoring activity in the anterior cingulate cortex, suggests evaluation of self-efficacy might be driving arousal regulation, thus affecting shooting performance. Better performers showed variable, increasing high-alpha power in the temporal region during the aiming period towards taking the shot which could indicate an adaptive strategy of engagement. They also showed lower coherence during hit shots than missed shots which was coupled with reduced jerking movements and better precision and accuracy. Frontal asymmetry measures revealed possible influence of the prefrontal lobe in driving this effect in reward and neutral conditions. The possible interactions, reasons behind these findings and implications are discussed.