William Davis - Summer '08 REU in Mathematics

Student Head of the Celestial Mechanics Group
Last edited by: William Davis - July 29, 2008 - wldavis2@illinois.edu

illiSol: A Modern Orrery

The illiSol Project initially began in Spring 2008 as my final project for Dr. Francis' Math 198 course, which covered topics of mathematical visualization. illiSol was an effort to create a visualization of the Sol star system, with accurate scale orbits. All of this was possible with a system of equations provided by Jet Propulsion Labs, and was built using OpenGL in Syzygy. A standalone executable and the source code are available in the downloads section, though no compilation has as of yet been made on any UNIX machine.

The application features a number of beautifying elements. For one, Stuart Levy's OpenGL Stars form the background, though as of this writing, they are neither oriented correctly nor do they move correctly based on user input. The planets are also textured with raw image files, and are mapped so that higher resolution images are used when the planets are viewed from a closer distance - this is a feature of OpenGL, and though not entirely efficient, serves our purposes well. Some satellites (moons) are included with some of the planets, but these are neither texture mapped nor do they follow correct orbits.

The issue of scale has always been a question to seriously ponder, as the Integrated Systems Laboratory discovered in porting the popular FOSS Celestia into the virtual environments. illiSol deals with this by allowing the user to adjust scale, both time and spatial, according to their whim. In the case of time, users can speed up and slow down, or even freeze time (which begins from the launch date of the Voyager II mission). For the desktop application, there is also the option for the user to go back one Earth-year in time.

More problematic is the issue of spatial scale, as the Sun is so drastically huge in comparison to everything else in the solar system. illiSol attempts to tackle this problem by allowing non-uniform scaling techniques, where the user can scale the planets and the sun by different proportions, but still has the option to return to "true scale". Indeed, after playing around with the application for a short time, one can see that this is still an imperfect method, as not all distances are scaled in the same way - ultimately, individual planetary systems begin to run into each other.

There are still improvements to be made to illiSol, to make it a truely useful visualization. A recent modification has made virtual environment traversal of the orrery much more user friendly, although the build on this website still has a more desktop-friendly navigation system included. That said, here are some of the area that should see improvement this summer:

  • Orient Stuart Levy's OpenGL Stars correctly
  • Integrate said Stars so that they move correctly based on user input
  • An improved navigation system for the desktop
  • Add a local light source to Sol (the Sun) so that correct shading applies to the planets and their elements
  • Add planetary rotation to the application - this shouldn't be too hard
  • Put the moons in their correct orbits - this may or may not come to fruition, depending on time constraints

Update July 7, 2008: Two of the above have been implemented, although the application has not been tested recently in the cluster setting.

  • The stars now move correctly based on user input
  • Lighting as been added to the application, so that the planets actually appear spherical.

Update July 10, 2008: I have begun writing a paper detailing the history and mathematics behind illiSol. I will post a current copy of it each day I work on it.

  • July 10, 2008 - Set up the LaTeX file and began writing. Completed the Introduction and Overview sections.
  • July 17, 2008 - Worked on a large portion of the History section, which is actually turning out to be more if a historical mathematics section. Included are some pictures that I've made in Inkscape (.svg files). Unfortunately, there's no easy way to get .svg files in LaTeX, so I've shrunk them using GIMP and saved them as PNG images.
  • July 18, 2008 - Finished subsection proving direction of planetary acceleration in the Historical Mathematics section, and reworded part of the same section to be clearer.
  • July 21, 2008 - Finished writing the Historical Mathematics section and started in on the Modern Methods for Computing Orbits section. I've also had to redevelop a few of my images as my understanding of one of the Keplerian Elements was incorrect.
  • July 25, 2008 -In the Modern Methods section, I have begun a moderately in depth explanation of the Keplerian Elements of an elliptical orbit. I plan to tie this in with the JPL equations, write a bibliography, and proof it sometime this weekend.
  • July 26, 2008 -The first draft of the body of the paper is finished, including a Summary, Conclusion, and Acknowledgements section. The only writing portion left to be done is the bibliography, and some proof reading is necessary as well.
  • July 29, 2008 -Final Paper! Any suggestions are welcome, and will be added if appropriate (although the changes may not make it onto this website).
    Final Paper PDF

Update July 14, 2008: Today I created an image to aid in visualizing the Keplerian Elements that JPL uses in their documentation. To understand the elements they use (Inclination, Mean Longitude, Longitude of Perihelion, and Longitude of Ascending Node), take a look at this picture.

  • Removed!

Update July 21, 2008: Today I recreated the image aiding visualization of the Keplerian Elements that is linked above from the 14th.