MTH4332 Planetary dynamics

Part 1 - The discovery of extrasolar planets has revived interest in topics such as planet formation and the stability of planetary systems. Both these areas require a sound knowledge of celestial mechanics, a subject which occupied the minds of some of the top mathematicians in the 19th and early 20th centuries. These days workers in the field tend to take advantage of high-speed computers to solve the N-body equations of motion which describe the evolution of planetary systems, but this method is restricted by the huge parameter space involved (arbitrary eccentricities, separations, masses, orientations) and doesn't lend itself to a deep understanding of the processes responsible for stability etc. In this set of lectures we will study planetary dynamics mostly from the analytical point of view, using techniques from classical mechanics and chaos theory to understand stability. Some numerical work will also be included in order to verify the analytical results.

Part 2 - The second half of the course relates to the way in which the solid planets of our solar system, and, in fact, solid planets in general, evolve internally from formation until their thermal death. We will examine how plate tectonics works on the Earth: from the kinematic theory defined by observations at the Earth's surface to the underlying processes of mantle convection which produce plate motions. This will be contrasted with the other planets and moons of the solar system where surface evolution is quite different, often difficult to understand, and much harder to constrain by observations. Students will have a good understanding of the fluid dynamics of mantle flow and way seismology, gravity, bathymetry, heat flow and magnetic intensity data can be used to probe mantle structure, and will understand the geological processes, kinematics and dynamics of different convective styles manifest in the lithosphere, and be able to relate this knowledge to the global pattern of planetary evolution. Prerequisites