This thesis is a tour of topics in theoretical astrophysics, unified by their diversity and their pursuit of physical understanding of astrophysical phenomena.In the first chapter, we raise the possibility of the detection of white dwarfs in transit surveys for extrasolar Earths, and discuss the peculiarities of detecting these more massive objects.A population synthesis calculation of the gravitational wave background from extragalactic binary stars is then presented. In this study, we establish a firm understanding of the uncertainties in such a calculation and provide a valuable reference for planning the Laser Interferometer Space Antenna mission.The long-established problem of cosmic ray confinement to the Galaxy is addressed in another chapter. We introduce a new wave damping mechanism, due to the presence of background turbulence, that prevents the confinement of cosmic rays by the resonant streaming instability.We also investigate the spokes in Saturn's B ring, an electrodynamic mystery that is being illuminated by new data sent back from the Cassini spacecraft. In particular, we present assessments of the presence of charged dust near the rings, and the size of currents and electric fields in the ring system. We make inferences from the Cassini discovery of oxygen ions above the rings. In addition, the previous leading theory for spoke formation is demonstrated to be unphysical.In the final chapter, we explain the wayward motions of Prometheus and Pandora, two small moons of Saturn. Previously found to be chaotic as a result of mutual interactions, we account for their behavior by analogy with a parametric pendulum. We caution that this behavior may soon enter a new regime.
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