Team Number: 009
School Name: Albuquerque Academy
Area of Science: Space Sciences
Project Title: Modeling Solar Systems
For the Super-Computing Challenge this year, we chose a project where we will simulate different types of solar systems, varying factors such factors as number of planets, the position of planets, different masses for the orbiting bodies, the velocities of the planets, etc... Here is a basic summary of the problems that we need to overcome in our project.
First of all, any random solar system may appear to be completely stable with all of the planets having harmonious orbits dictated by the gravitational pull of the sun at the center. At first glance, it would appear that to predict the state of the solar system In the future, all one would have to do is find a planet's orbit and let it run along that path for as long as you want to. However, it is more complicated than that. Newton's law of Gravitation states that all particles of matter are attracted to each other with a force that is proportional to their masses and inversely proportional to the distance between them squared. This means that not only are the planets attracted to the sun, but also to each other, meaning the planets do not move in perfectly predictable ellipses, but also move in other directions towards the other planets. Because the sun is the dominant body in the system, these secondary motions are hardly noticed, but it means that the system must eventually break down over time. Our project's goal is to simulate various solar systems and find out when this happens.
Other problems involve the sheer number of computations that have to be done. For example, say we recalculate the state of the system once every day in the simulation. Each calculation of the state of the system will probably involve 100+ individual calculations, so we are looking at 36500+ calculations for one year. Then, suppose we run the simulation for a billion years, at the minimum. The least amount of calculations involved would then be 36,500,000,000,000. With that amount of calculations, we would need a super-computer with a processor of at least 5.1 terahertz to finish in 2 hours. Hence, the need for a super-computer.
Progress to Date:
Our research has gone quite well so far and we have even begun to code some of the classes necessary for our program. We have done a good deal of research on the interactions of bodies in space, because each body's movement within the program is affected by every other body in the system due to gravitational attraction. We have developed a good mathematical model that takes into account the masses of the orbiting bodies, their velocities, and the gravitational attraction between them To do this we developed a math model that can simulate a planet's response to gravitational forces. Newton developed Calculus so that he could accomplish that. Since no one on our team has any experience in Calculus, our math model is based on a different procedure, which is the way Newton did it at first in his masterpiece, Principia Mathematica. This method is more geometric and involves vectors. First, a gravitational force can be expressed as a vector with a magnitude equal to the fo! rce and a direction that points to the body it is attracted to. The force vector can be translated into an acceleration vector, due to Newton's second law of motion, and that can be turned into a velocity vector. Then, summing that vector with all others, including the planet's original velocity vector yields a resulting vector, which represents the planet's new velocity.
We expect that our program will work successfully in the way that we intend. It should correctly display the results of a user-made solar system after given amount of time (measured in earth years). We also expect that a majority of our efforts will be directed toward finding the exact process of finding and orchestrating the many complex equations involved with our project. This is due to, in part, the universe being naturally complex and, in order for our program to function correctly, we must accurately simulate how astrophysics operate. However, due to the extreme intricacy of our project, we anticipate that the user will have difficulty creating a solar system that will hold together for any long period of time.
Team 009 Bibliography
Delaney, Wesley. Physics Information. Accessed: 23 Oct 2001
Formulas for Rotational Motion. Accessed: 23 Oct 2001
Formulas for Acceleration & Newton's Laws. Accessed: 23 Oct 2001
Geodetic Reference System 1980. Accessed: 23 Oct 2001