
Team Number: 89 School Name: Portales High School Area of Science: Earth and Space Science Project Title: Planetary Dynamics Project Abstract: http://mode.lanl.k12.nm.us/97.98/abstracts/089.html Interim Report: http://mode.lanl.k12.nm.us/97.98/interims/089.html Final Report: http://mode.lanl.k12.nm.us/97.98/finalreports/089/finalreport.html Program Code: http://mode.lanl.k12.nm.us/~ch089lxw/project.c
Please click on one of the following to go to that section of our Interim Report
I. Abstract
II. Newtonian Mechanics
III. Particle Dynamics Simulation
IV. Super Computer Implementation
V. Computer Graphical Animation
VI. Progress and Result to Date
VII. Apendix (Our Code)
This year's project for the Portales challenge team will be based upon the theories of particle dynamics as applied to calculations of the dynamic behavior of real or hypothetical solar systems comprised of planets, a sun (or multiple orbiting suns), asteroids, comets, moons, and spaceships. The "particles" we will be using may include any object that might affect or be affected by the other objects in the given solar system. In our programming, a user will specify initial conditions for each particle (planets, sun, asteroid, etc.) such as particle mass starting positions (x_{i}, y_{i}, z_{i}), and initial velocities (V_{xi}, V_{yi}, V_{zi}) in a given coordinate system. Other starting conditions could be mass and initial velocity of particles. The program will calculate these data in the context of Newton's Universal Law of Gravitation to find the interparticle forces at word and then calculate new coordinates and new velocities of each particle for a given time interval(DeltaT). The new time interval will represent a new movie frame in our particle dynamics "motion picture". The motion picture of solar system particle dynamics will be produced via computer graphics animation by hooking together many frames representing many successive time increments DeltaT. This way we will find out how the objects within a given solar system act and interact and how changes (both real and hypothetical) can act to perturb the solar system.
Newton’s kinematic equations of motion govern the motions of large bodies at low speeds and
modest accelerations. These equations are listed below in vector form and in vector component
form.
//This code is produced by Liangfei Wang and Dr. John Kenney, III
//Contributions have been made to this code by Gina Weber (lanl) and
// Ron Obenhaus (ENMU).
//Begin Program!
//This file defines the parameters for all C++ commands
#include < iostream.h >
//This file defines the mathematical functions in C++
#include < math.h >
//This file defines the function to output information into files
#include < fstream.h >
main()
{
//Create and open a file named stuff.txt
ofstream newfile ("stuff.txt");
//Initializing number of time intervals, DT, suns, and planets
int t;
float delt;
int i, j;
//Input information
cout << "How many time intervals?" << endl;
cin >> t;
cout << "How many seconds per time interval?" << endl;
cin >> delt;
cout << "How many planets in solar system?" << endl;
cin >> i;
cout << "How many suns in solar system?" << endl;
cin >> j;
//Initializing mass, starting positions, and starting velocities
float mass[i+j];
float xi[i+j][t], yi[i+j][t], zi[i+j][t];
float vix[i+j], viy[i+j], viz[i+j];
//Integer c is the sum of suns and planets
int c = i + j;
//This loop is for entering data for each mass, starting position,
//and starting velocities
for (int a = 1; a <= c; a++)
{
cout << "Enter mass for a planetary body (Sun or Planet) in mass * 10^23" << endl;
cin >> mass[a];
cout << "Enter starting positions (x, y, z):" << endl;
cin >> xi[a][1] >> yi[a][1] >> zi[a][1];
cout << "Enter starting velocities in m/sec (Vx, Vy, Vz)" << endl;
cin >> vix[a] >> viy[a] >> viz[a];
}
//First of the triple loop is the time interval loop
for (int time=1; time <= t; time++)
{
//Initializing forces to 0
//G is Newton's universal constant of gravitation
float rij;
float fix = 0;
float fiy = 0;
float fiz = 0;
double G = (0.00000000006772);
//Second loop is for k=1 to c particles
for (int k = 1; k <= c; k++)
{
//Third loop is for l=1 to c particles
for (int l = 1; l <= c; l++)
{
//Only run equations if l does not equal k
if (l != k)
{
//Compute interparticle positions and force vectors for
//particle i at time step(t1)
rij = sqrt(pow(xi[k]  xi[l],2) + pow(yi[k]  yi[l],2) + pow(zi[k]  zi[l],2));
fix = ((G * mass[k] * mass[l]) / sqrt(pow(rij,5))) * (xi[k][time]  xi[l][time]) + fix;
fiy = ((G * mass[k] * mass[l]) / sqrt(pow(rij,5))) * (yi[k][time]  yi[l][time]) + fiy;
fiz = ((G * mass[k] * mass[l]) / sqrt(pow(rij,5))) * (zi[k][time]  zi[l][time]) + fiz;
vix[k] = (delt * (fix / mass[k])) + vix[k];
viy[k] = (delt * (fiy / mass[k])) + viy[k];
viz[k] = (delt * (fiz / mass[k])) + viz[k];
xi[k][time] = xi[k][time] + (delt * vix[k]) + (1 / 2) * pow(delt,2) * (fix / mass[k]);
yi[k][time] = xi[k][time] + (delt * viy[k]) + (1 / 2) * pow(delt,2) * (fiy / mass[k]);
zi[k][time] = xi[k][time] + (delt * viz[k]) + (1 / 2) * pow(delt,2) * (fiz / mass[k]);
//Output planetary positions to the screen
cout << xi[k][time] << ", " << yi[k][time] << ", " << zi[k][time] << endl;
//Output planetary positions to the file: stuff.txt
newfile << xi[k][time] << " is the x coordinate on the map\n";
newfile << yi[k][time] << " is the y coordinate on the map\n";
newfile << zi[k][time] << " is the z coordinate on the map\n";
newfile << "\n";
//close file: stuff.txt
newfile.close();
}
}
}
}
return 0;
}
//End Program!