Chaotic Dynamics of Planetary Systems

Planets form in protoplanetary disks of gas and dust, which damp their motions onto planar, circular paths. The final stage of planet formation occurs after that gas dissipates, setting off a phase of violent impacts, which determine the final masses and orbital configurations we see today. Our group has been working on understanding the chaotic dynamics leading to these instabilities and to quantitatively predict what subset of orbital configurations could survive to the present day. This a key question if we want to connect theoretical models of formation in the protoplanetary disk to the observational data we have at billion-year ages.

We do this through a mix of analytical chaos theory calculations, numerical integrations, and machine learning models. There are several possible projects:

• Developing analytical models for the orbital resonances dominantly driving chaos in closely spaced planetary systems (Requires having taken Physics 111-Theoretical Mechanics)
• Improving a machine learning model that can predict the stability of a given orbital configuration for a planetary system (No machine learning experience or upper level physics courses required, just a passion for programming and for wanting to understand the physics!)
• Training a differentiable machine learning model to identify and calculate approximately conserved quantities from dynamical integrations. This is separate from chaos, but important for a number of theoretical and observational astronomy applications (Requires either having taken Physics 111-Theoretical Mechanics OR having some experience training differentiable models)

For your essay, please write a short paragraph on a programming project you're proud of, what the biggest challenges were, and how you went about debugging/solving them? I'm more interested in the process than the end result. Doesn't have to be a major project, can be something from CS 5.