Resonances in Ring, Satellite, and Planetary Systems
Hamilton, Douglas P
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In this thesis, we study the origin and evolution of planets, rings, and moons in the context of orbital dynamics. In particular, we investigate the Kepler 36 exoplanet system, which features two known planets whose semimajor axes differ by 0.01 AU but whose densities differ by nearly a factor of 10, in contrast to predictions from standard Solar System evolution theory. We use resonance and perturbation theory to show that these planets could have migrated to their current positions through a swarm of smaller bodies that knocked them progressively closer together.We then develop a set of orbital elements designed to be used for a body orbiting an oblate host such as Saturn. Our corrections properly vanish in the limit that the oblateness terms go to 0, in contrast to the so-called “epicyclic elements,” which do not correctly reduce to their osculating counterparts. We compare the accuracy of our elements to the epicyclic elements as well as a simple numerical fit. We also provide an explicit inverse function for our elements that transforms them back to state vectors. Next, we study the confinement of narrow, eccentric rings. Dozens of these odd structures are known to orbit the three outer planets as well as several small bodies, but simple theory predicts they should spread on timescales as short as tens of years. The standard confinement theory suggests that these rings can be “shepherded” by nearby satellites, but most narrow rings lack such nearby satellites. We argue that by circularizing, eccentric rings can lengthen their spreading timescales by a factor of 100,000. We support our theory with simulations of narrow eccentric ringlets and find that we can self-confine the Titan ringlet at Saturn. Finally, we consider the formation and evolution of Saturn’s largest moon, Titan. No self-consistent theory exists that can explain all of its unusual features, including its enormous mass, “lonely” location within Saturn’s satellite system, and relatively high orbital eccentricity and inclination. We argue that Titan could have formed from a dynamical instability within a resonant chain of moons similar to the modern-day Galilean chain of Io, Europa, and Ganymede at Jupiter. We sim- ulate this process for a wide variety of tidal migration and eccentricity damping strengths along with over a hundred unique possible mass distributions and find that instabilities are rare but possible.