2body.py

# 2Body.py
# a 2 star system based on Piet Hut
# and Jun Makino's MSA text with
# Modifications by Stan Blank for
# use in Python OpenGL/GLUT

from OpenGL.GL import *
from OpenGL.GLU import *
from OpenGL.GLUT import *
from numpy import *
import sys

#  Set the width and height of the window
global width
global height

#  Initial values
width = 500
height = 500
		
# initial values for position, velocity components, and time increment
global vx1, vy1, vz1, x1, y1, z1, r2, r3, ax1, ay1, az1, dt
global vx2, vy2, vz2, x2, y2, z2, ax2, ay2, az2, G

# initial x,y,z positions for both stars
x1 = 1.0
y1 = 0.0
z1 = 0.0
x2 = -1.0
y2 = 0.0
z2 = 0.0

# initial vx,vy,vz velocities for both stars
vx1 = 0.0
vy1 = -0.128571428
vz1 = 0.0
vx2 = 0.0
vy2 = 0.3
vz2 = 0.0

# initial masses for both stars
m1 = 0.7
m2 = 0.3
rad1 = 0.1*m1
rad2 = 0.1*m2

# arbitrary "Big G" gravitational constant
G = 1.0

# calculate distance and r**3 denominator for universal gravitation
r2 = (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2) + (z1-z2)*(z1-z2)
r3 = r2*sqrt(r2)

# calculate acceleration components along x,y,z axes
ax1 = -G*(x1-x2)*m2/r3
ay1 = -G*(y1-y2)*m2/r3
az1 = -G*(z1-z2)*m2/r3
ax2 = -G*(x2-x1)*m1/r3
ay2 = -G*(y2-y1)*m1/r3
az2 = -G*(z2-z1)*m1/r3

#This value keeps a smooth orbit on my workstation
#Smaller values slow down the orbit, higher values speed things up
dt = 0.001

def init():
	glClearColor(0.0, 0.0, 0.0, 1.0)
	glEnable(GL_DEPTH_TEST)
	
def plotFunc():
	glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT)
	
	# plot the first star (m1) position
	glPushMatrix()
	glTranslatef(x1,y1,z1)
	glColor3ub(245, 230, 100)
	#glColor3ub(245, 150, 30)
	glutSolidSphere(rad1, 10, 10)
	glPopMatrix()
	
	# plot the second star (m2) position
	glPushMatrix()
	glTranslatef(x2,y2,z2)
	glColor3ub(245, 150, 30)
	#glColor3ub(245, 230, 100)
	glutSolidSphere(rad2, 10, 10)
	glPopMatrix()
	
	# swap the drawing buffers
	glutSwapBuffers()
	
def Reshape(  w,  h):
	
	# To insure we don't have a zero height
	if h==0:
		h = 1
	
	#  Fill the entire graphics window!
	glViewport(0, 0, w, h)
	
	#  Set the projection matrix... our "view"
	glMatrixMode(GL_PROJECTION)
	glLoadIdentity()
	
	gluPerspective(45.0, 1.0, 1.0, 1000.0)	
	gluLookAt(0.0, 0.0, 5.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0)

	#  Set the matrix for the object we are drawing
	glMatrixMode(GL_MODELVIEW)
	glLoadIdentity()
	
def keyboard(key, x, y):
	#  Allows us to quit by pressing 'Esc' or 'q'
	if key == chr(27):
		sys.exit()
	if key == "q":
		sys.exit()

def orbits():
	global vx1, vy1, vz1, x1, y1, z1, r2, r3, ax1, ay1, az1
	global vx2, vy2, vz2, x2, y2, z2, ax2, ay2, az2
	
	# calculate front half of velocity vector components
	vx1 += 0.5*ax1*dt
	vy1 += 0.5*ay1*dt
	vz1 += 0.5*az1*dt
	vx2 += 0.5*ax2*dt
	vy2 += 0.5*ay2*dt
	vz2 += 0.5*az2*dt
	
	# calculate x,y,z positions for both stars
	x1 += vx1*dt
	y1 += vy1*dt
	z1 += vz1*dt
	x2 += vx2*dt
	y2 += vy2*dt
	z2 += vz2*dt
	
	# calculate the new r**3 denominator for each star position
	r2 = (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2) + (z1-z2)*(z1-z2)
	r3 = r2*sqrt(r2)
	
	# calculate the new acceleration components
	ax1 = -G*(x1-x2)*m2/r3
	ay1 = -G*(y1-y2)*m2/r3
	az1 = -G*(z1-z2)*m2/r3
	ax2 = -G*(x2-x1)*m1/r3
	ay2 = -G*(y2-y1)*m1/r3
	az2 = -G*(z2-z1)*m1/r3
	
	# calculate the back half velocity components
	vx1 += 0.5*ax1*dt
	vy1 += 0.5*ay1*dt
	vz1 += 0.5*az1*dt
	vx2 += 0.5*ax2*dt
	vy2 += 0.5*ay2*dt
	vz2 += 0.5*az2*dt
	
	#send calculated x,y,z star positions to the display
	glutPostRedisplay()
	
def main():
	global width
	global height
	
	glutInit(sys.argv)
	glutInitDisplayMode(GLUT_RGB|GLUT_DOUBLE)
	glutInitWindowPosition(100,100)
	glutInitWindowSize(width,height)
	glutCreateWindow("2 Body Problem")
	glutReshapeFunc(Reshape)
	glutDisplayFunc(plotFunc)
	glutKeyboardFunc(keyboard)
	glutIdleFunc(orbits)
	
	init()	
	glutMainLoop()

main()