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

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

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

Attributes of an Ellipse

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

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.

Kepler's Laws Of Planetary Motion

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

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.

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

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

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

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.

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.

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

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

Graphical User Interface (GUI)‏

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.

Python API Structure

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

SIMULATION!

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

References Johannes Kepler Web. Isaac Newton Web.