- Project Background:
The orbit of an essentially mass-less planetoid in a solar system
containing two large masses can be simple or complex depending on the
initial conditions of the orbit and other model parameters.
For example, the particles making up the rings of Saturn have orbits which are
largely influenced by the planet and its largest moon, Titan.
A special case of celestial motion of three bodies is to consider the
two larger masses to be orbiting their common center of mass in a
plane while the planetoid can orbit in three-dimensional space.
- Project Description:
The student would have the opportunity to develop a numerical
simulation of the orbit of the planetoid of the planar restricted
three-body problem.
This simulation would be used to look for regions in parameter space
where the orbit appears to be chaotic.
In order to determine if chaos is present, the student would look at
particular indicators of chaos, such as Poincaré maps, the power
spectrum of the orbit, the autocorrelation function of the orbit, and
the Lyapunov exponents of the orbit.
- Desired Student Background:
Ability to program in a high-level language, preferably Mathematica, C/C++, or FORTRAN, and mathematical knowledge at the
level of MATH 365 Ordinary Differential Equations.