Astronomy, Chaos, Strange Attractors, and the Three Body Problem
Project Description
Thinkers since ancient times have striven to understand the orbits and stability of astronomical systems. A breakthrough in scientific understanding (and a "revolution" in the literal and original sense) culminated with Isaac Newton showing that an orbit in a system with two bodies (e.g., with two stars, a star and a planet, a planet and a moon, etc.) has to be an ellipse. However, neither he nor anybody following him was able to solve the "three body problem", i.e. to determine the motion of a system with only one additional astronomical object. This hasn't been an idle interest: an understanding of the dynamics in a multiple body system is necessary, for example, to better understand whether planets form around other stars and how many and what type of planets form around them. This in turn will give us insight into the question of how many planets outside our solar system might be able to sustain life (or might already have it!). More practical uses include, for example, methods such as the so-called "slingshot effect" for putting satellites into useful orbits. Insights of the last decade now help us understand why the three body problem has been so hard to solve: it turns out that three body systems can exhibit many of the signs of what modern mathematicians call "chaos". (See for example the work of Pekka Heinmki, Harry J. Lehto, Mauri J. Valtonen & Arthur D. Chernin, Three-body dynamics: intermittent chaos with strange attractor, Monthly Notices of the Royal Astronomical Society, 1998.) This project will use computer simulation to investigate the types of chaotic phenomena, such as periodic chaos or strange attractors, which occur in the three body problem with goals towards better understanding both the conditions in which they occur and their likelihood of happening.
Background Needed
Calc II and being comfortable working with computers.