Extensible Simulation of Planets and Comets

A Thesis Presentation By:Natalie Wiser-Orozco

November 14, 2008

Committee Members:Dr. Keith SchubertDr. Ernesto GomezDr. 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 4th 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 SystemNow 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: http://code.google.com/p/extensiblesimulationofplanetsandcomets/

http://www.otsegoville.com/Thesis

References

Johannes Kepler http://en.wikipedia.org/wiki/Johannes_Kepler Web.

Isaac Newton http://en.wikipedia.org/wiki/Isaac_Newton Web.