Orbit Visualization Project

Visualization Project Home Page

The Geometry Center
Summer Institute 1996

Undergraduate Research Project By:
Chris Sinclair University of Arizona
Molly Megraw University of Washington

Project Supervisors:
Patrick Worfolk Ph.D. Mathematics
Robert Thurman Ph.D. Mathematics

Project Description:

Our project is motivated by current research interests at the Jet Propulsion Laboratory. The basic ideas behind these interests include:

There are two major components to our work:

  1. Using the Circular Restricted Three-Body Problem to model the sun-earth-spacecraft system, we search for orbits around the fixed points of the system. These orbits are ideal destinations for gathering the desired data.
  2. We search for the stable and unstable manifolds of these orbits; spacecraft trajectories on the manifolds provide efficient paths for travelling from the earch to the orbits and back.

A major contribution of our project is to provide a software tool for visualizing and studying the behavior of system fixed points, families of orbits, and manifolds.

Orbit Visualization Project Table of Contents

  1. Essential background information on the Circular Restricted Three-Body Problem Model
  2. Project Presentation: an outline of the mathematical fundamentals
    1. Computation of the libration points and approximating the orbits
    2. Computation of actual orbits and their stable and unstable manifolds
  3. Tutorial display of our software tool for system computation and visualization

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