1. Extensible Simulation of Planets and Comets
A Thesis Presentation By:
Natalie Wiser-Orozco
November 14, 2008
Committee Members:
Dr. Keith Schubert
Dr. Ernesto Gomez
Dr. Richard Botting

2. Course Of Action Understanding The Movement Of Our Solar System
Orbits
Kepler and Newton
Building The Simulator
Gravitational Functions
Graphical Simulation
Extensibility
Application Programming Interface

3. Orbits Ellipse – Oval-like shape Eccentricity determines flatness
How does mass affect orbit?

4. Attributes of an Ellipse

5. Shoemaker-Levy 9 and Jupiter
S-L9 discovered on March 24th, 1993
Split into fragments on July 8th, 1992
Collided with Jupiter in July of 1994

6. Johannes Kepler Lived from 1571 to 1630
Pioneered modern astronomy by deriving a mathematical model based on detailed observations.
Kepler's three laws of planetary motion.

7. Kepler's Laws Of Planetary Motion

8. Sir Isaac Newton Lived from 1643 to 1727 Laws of motion
Laws of universal gravitation

9. Example of orbit as described by Newton
A body in orbit is “falling” towards the body that is at the foci of the orbit's ellipse.
From this, he derived the law of universal gravitation.

10. Building The Simulator
Implementing the N-Body equation
Developing a graphical simulation
Wrapping it up into a neat package (GUI)‏

11. N-Body Equation Explanation of the equation itself.
Implemented the equation in small steps.
Used Runge-Kutta 4th Order ODE solver.
There were some trials and tribulations along the way.
Finally, success!

12. Explanation of the N-Body Equation
Ordinary Differential Equation
Equivalent First-Order System
Now suitable for solving with
RK4 numeric method.

13. Small Steps Started with previous coursework from CS535
Moved to using data provided by NASA for the initial conditions for a Sun and Earth system.

14. Trials and Tribulations
I had the equation wrong, yielding inaccurate data.
The Moon orbits the Sun?
Needed to add Earth's initial velocity to the Moon's initial velocity.

15. Success! Simple simulations are finally behaving as expected.
Final hurdle – generalizing to be able to calculate trajectories for an arbitrary number of bodies.

16. Developing a Graphical Simulation
Plotting the bodies
Tracing their trajectories.
Texture mapping
Scene Navigation

17. Graphical User Interface (GUI)‏

18. Application Programming Interface (API)‏
Python
Start with base objects for Bodies and Cameras.
Extend the base classes to accommodate new functionality.
Register the extended classes with the Manager classes.
Scilab
Implement different gravitational functions and numeric methods.
Register these scripts with the Utilities class.

19. Python API Structure

20. Scilab API
Register new numeric methods and gravitational functions in the Utilities file, and the GUI handles the rest!

21. SIMULATION!

22. The Code Is open source and can be found online at:

23. References
Johannes Kepler Web.
Isaac Newton Web.