from visual import *
from time import clock
from random import random
# Stars interacting gravitationally
# Program uses numpy arrays for high speed computations
win=600
Nstars = 20 # change this to have more or fewer stars
G = 6.7e-11 # Universal gravitational constant
# Typical values
Msun = 2E30
Rsun = 2E9
Rtrail = 2e8
L = 4e10
vsun = 0.8*sqrt(G*Msun/Rsun)
scene = display(title="Stars", width=win, height=win,
range=2*L, forward=(-1,-1,-1))
xaxis = curve(pos=[(0,0,0), (L,0,0)], color=(0.5,0.5,0.5))
yaxis = curve(pos=[(0,0,0), (0,L,0)], color=(0.5,0.5,0.5))
zaxis = curve(pos=[(0,0,0), (0,0,L)], color=(0.5,0.5,0.5))
Stars = []
colors = [color.red, color.green, color.blue,
color.yellow, color.cyan, color.magenta]
poslist = []
plist = []
mlist = []
rlist = []
for i in range(Nstars):
x = -L+2*L*random()
y = -L+2*L*random()
z = -L+2*L*random()
r = Rsun/2+Rsun*random()
Stars = Stars+[sphere(pos=(x,y,z), radius=r, color=colors[i % 6])]
Stars[-1].trail = curve(pos=[Stars[-1].pos], color=colors[i % 6], radius=Rtrail)
mass = Msun*r**3/Rsun**3
px = mass*(-vsun+2*vsun*random())
py = mass*(-vsun+2*vsun*random())
pz = mass*(-vsun+2*vsun*random())
poslist.append((x,y,z))
plist.append((px,py,pz))
mlist.append(mass)
rlist.append(r)
pos = array(poslist)
p = array(plist)
m = array(mlist)
m.shape = (Nstars,1) # Numeric Python: (1 by Nstars) vs. (Nstars by 1)
radius = array(rlist)
vcm = sum(p)/sum(m) # velocity of center of mass
p = p-m*vcm # make total initial momentum equal zero
dt = 1000.0
Nsteps = 0
pos = pos+(p/m)*(dt/2.) # initial half-step
time = clock()
Nhits = 0
while True:
rate(100)
# Compute all forces on all stars
try: # numpy
r = pos-pos[:,newaxis] # all pairs of star-to-star vectors
for n in range(Nstars):
r[n,n] = 1e6 # otherwise the self-forces are infinite
rmag = sqrt(add.reduce(r*r,-1)) # star-to-star scalar distances
hit = less_equal(rmag,radius+radius[:,newaxis])-identity(Nstars)
hitlist = sort(nonzero(hit.flat)[0]).tolist() # 1,2 encoded as 1*Nstars+2
F = G*m*m[:,newaxis]*r/rmag[:,:,newaxis]**3 # all force pairs
except: # old Numeric
r = pos-pos[:,NewAxis] # all pairs of star-to-star vectors
for n in range(Nstars):
r[n,n] = 1e6 # otherwise the self-forces are infinite
rmag = sqrt(add.reduce(r*r,-1)) # star-to-star scalar distances
hit = less_equal(rmag,radius+radius[:,NewAxis])-identity(Nstars)
hitlist = sort(nonzero(hit.flat)) # 1,2 encoded as 1*Nstars+2
F = G*m*m[:,NewAxis]*r/rmag[:,:,NewAxis]**3 # all force pairs
for n in range(Nstars):
F[n,n] = 0 # no self-forces
p = p+sum(F,1)*dt
# Having updated all momenta, now update all positions
pos = pos+(p/m)*dt
# Update positions of display objects; add trail
for i in range(Nstars):
Stars[i].pos = pos[i]
if Nsteps % 10 == 0:
Stars[i].trail.append(pos=pos[i])
# If any collisions took place, merge those stars
for ij in hitlist:
i, j = divmod(ij,Nstars) # decode star pair
if not Stars[i].visible: continue
if not Stars[j].visible: continue
# m[i] is a one-element list, e.g. [6e30]
# m[i,0] is an ordinary number, e.g. 6e30
newpos = (pos[i]*m[i,0]+pos[j]*m[j,0])/(m[i,0]+m[j,0])
newmass = m[i,0]+m[j,0]
newp = p[i]+p[j]
newradius = Rsun*((newmass/Msun)**(1./3.))
iset, jset = i, j
if radius[j] > radius[i]:
iset, jset = j, i
Stars[iset].radius = newradius
m[iset,0] = newmass
pos[iset] = newpos
p[iset] = newp
Stars[jset].trail.visible = 0
Stars[jset].visible = 0
p[jset] = vector(0,0,0)
m[jset,0] = Msun*1E-30 # give it a tiny mass
Nhits = Nhits+1
pos[jset] = (10.*L*Nhits, 0, 0) # put it far away
Nsteps += 1
|