vz=-2.17699042180559e-5) # Uranus
rebound.add(m=1. / 19314.,
x=-3.01777243405203e+1,
y=+1.91155314998064e+0,
z=-1.53887595621042e-1,
vx=-2.17471785045538e-4,
vy=-3.11361111025884e-3,
vz=+3.58344705491441e-5) # Neptune
rebound.add(m=0,
x=-2.13858977531573e+1,
y=+3.20719104739886e+1,
z=+2.49245689556096e+0,
vx=-1.76936577252484e-3,
vy=-2.06720938381724e-3,
vz=+6.58091931493844e-4) # Pluto
# Set the center of momentum to be at the origin
rebound.move_to_com()
# timestep counter
steps = 0
# Integrate until t=1e6 (unit of time in this example is days)
while rebound.t < 1e6:
rebound.step()
steps += 1
# Print particle positions every 100 timesteps
if steps % 100 == 0:
for p in rebound.particles:
# time x y z
print(rebound.t, p.x, p.y, p.z)
def simulation(par):
integrator = par
rebound.reset()
k = 0.01720209895
G = k*k
rebound.set_G(G)
rebound.set_dt(dt)
rebound.set_integrator(integrator)
rebound.add_particle(m=1.00000597682, x=-4.06428567034226e-3, y=-6.08813756435987e-3, z=-1.66162304225834e-6, vx=+6.69048890636161e-6, vy=-6.33922479583593e-6, vz=-3.13202145590767e-9) # Sun
rebound.add_particle(m=1./1047.355, x=+3.40546614227466e+0, y=+3.62978190075864e+0, z=+3.42386261766577e-2, vx=-5.59797969310664e-3, vy=+5.51815399480116e-3, vz=-2.66711392865591e-6) # Jupiter
# rebound.add_particle(m=1./3501.6, x=+6.60801554403466e+0, y=+6.38084674585064e+0, z=-1.36145963724542e-1, vx=-4.17354020307064e-3, vy=+3.99723751748116e-3, vz=+1.67206320571441e-5) # Saturn
# rebound.add_particle(m=1./22869., x=+1.11636331405597e+1, y=+1.60373479057256e+1, z=+3.61783279369958e-1, vx=-3.25884806151064e-3, vy=+2.06438412905916e-3, vz=-2.17699042180559e-5) # Uranus
# rebound.add_particle(m=1./19314., x=-3.01777243405203e+1, y=+1.91155314998064e+0, z=-1.53887595621042e-1, vx=-2.17471785045538e-4, vy=-3.11361111025884e-3, vz=+3.58344705491441e-5) # Neptune
# rebound.add_particle(m=0, x=-2.13858977531573e+1, y=+3.20719104739886e+1, z=+2.49245689556096e+0, vx=-1.76936577252484e-3, vy=-2.06720938381724e-3, vz=+6.58091931493844e-4) # Pluto
N = rebound.get_N()
def move_to_heliocentric():
particles = rebound.get_particles()
for i in xrange(1,N):
particles[i].x -= particles[0].x
particles[i].y -= particles[0].y
particles[i].z -= particles[0].z
particles[i].vx -= particles[0].vx
particles[i].vy -= particles[0].vy
particles[i].vz -= particles[0].vz
particles[0].x = 0.
particles[0].y = 0.
particles[0].z = 0.
particles[0].vx = 0.
particles[0].vy = 0.
particles[0].vz = 0.
def energy():
if integrator=="wh":
rebound.move_to_center_of_momentum()
particles = rebound.get_particles()
E_kin = 0.
E_pot = 0.
for i in xrange(N):
E_kin += 0.5*particles[i].m*(particles[i].vx*particles[i].vx + particles[i].vy*particles[i].vy + particles[i].vz*particles[i].vz)
for j in xrange(i+1,N):
dx = particles[i].x-particles[j].x
dy = particles[i].y-particles[j].y
dz = particles[i].z-particles[j].z
r2 = dx*dx + dy*dy + dz*dz
E_pot -= G*particles[i].m*particles[j].m/np.sqrt(r2)
if integrator=="wh":
move_to_heliocentric()
return E_kin+E_pot
rebound.move_to_center_of_momentum()
es = []
ei = energy()
for time in xrange(Nsteps):
rebound.step()
ef = energy()
e = (ei-ef)
es.append(e)
ei = ef
es = np.array(es)
print integrator + " done."
return [es]
def simulation(par):
integrator, mass = par
rebound.reset()
mass = pow(10.,mass)
k = 0.01720209895
G = k*k
rebound.G = G
rebound.dt = 0.
rebound.integrator = integrator
rebound.add(m=1.00000597682, x=-4.06428567034226e-3, y=-6.08813756435987e-3, z=-1.66162304225834e-6, vx=+6.69048890636161e-6, vy=-6.33922479583593e-6, vz=-3.13202145590767e-9) # Sun
rebound.add(m=mass, x=+3.40546614227466e+0, y=+3.62978190075864e+0, z=+3.42386261766577e-2, vx=-5.59797969310664e-3, vy=+5.51815399480116e-3, vz=-2.66711392865591e-6) # Jupiter
rebound.add(m=mass, x=+6.60801554403466e+0, y=+6.38084674585064e+0, z=-1.36145963724542e-1, vx=-4.17354020307064e-3, vy=+3.99723751748116e-3, vz=+1.67206320571441e-5) # Saturn
rebound.add(m=mass, x=+1.11636331405597e+1, y=+1.60373479057256e+1, z=+3.61783279369958e-1, vx=-3.25884806151064e-3, vy=+2.06438412905916e-3, vz=-2.17699042180559e-5) # Uranus
rebound.add(m=mass, x=-3.01777243405203e+1, y=+1.91155314998064e+0, z=-1.53887595621042e-1, vx=-2.17471785045538e-4, vy=-3.11361111025884e-3, vz=+3.58344705491441e-5) # Neptune
N = rebound.N
def move_to_heliocentric():
particles = rebound.particles
for i in xrange(1,N):
particles[i].x -= particles[0].x
particles[i].y -= particles[0].y
particles[i].z -= particles[0].z
particles[i].vx -= particles[0].vx
particles[i].vy -= particles[0].vy
particles[i].vz -= particles[0].vz
particles[0].x = 0.
particles[0].y = 0.
particles[0].z = 0.
particles[0].vx = 0.
particles[0].vy = 0.
particles[0].vz = 0.
def energy():
if integrator=="wh":
rebound.move_to_com()
particles = rebound.particles
E_kin = 0.
E_pot = 0.
for i in xrange(N):
E_kin += 0.5*particles[i].m*(particles[i].vx*particles[i].vx + particles[i].vy*particles[i].vy + particles[i].vz*particles[i].vz)
for j in xrange(i+1,N):
dx = particles[i].x-particles[j].x
dy = particles[i].y-particles[j].y
dz = particles[i].z-particles[j].z
r2 = dx*dx + dy*dy + dz*dz
E_pot -= G*particles[i].m*particles[j].m/np.sqrt(r2)
if integrator=="wh":
move_to_heliocentric()
return E_kin+E_pot
rebound.move_to_com()
ei = energy()
es = 1e-20
for s in xrange(1000):
rebound.step()
ef = energy()
e = np.fabs((ei-ef)/ei)
es = max(es,e)
return es
k = 0.01720209895 # Gaussian constant
rebound.set_G(k*k) # Gravitational constant
# Setup particles (data taken from NASA Horizons)
# This could also be easily read in from a file.
rebound.particle_add( Particle( m=1.00000597682, x=-4.06428567034226e-3, y=-6.08813756435987e-3, z=-1.66162304225834e-6, vx=+6.69048890636161e-6, vy=-6.33922479583593e-6, vz=-3.13202145590767e-9) ) # Sun
rebound.particle_add( Particle( m=1./1047.355, x=+3.40546614227466e+0, y=+3.62978190075864e+0, z=+3.42386261766577e-2, vx=-5.59797969310664e-3, vy=+5.51815399480116e-3, vz=-2.66711392865591e-6) ) # Jupiter
rebound.particle_add( Particle( m=1./3501.6, x=+6.60801554403466e+0, y=+6.38084674585064e+0, z=-1.36145963724542e-1, vx=-4.17354020307064e-3, vy=+3.99723751748116e-3, vz=+1.67206320571441e-5) ) # Saturn
rebound.particle_add( Particle( m=1./22869., x=+1.11636331405597e+1, y=+1.60373479057256e+1, z=+3.61783279369958e-1, vx=-3.25884806151064e-3, vy=+2.06438412905916e-3, vz=-2.17699042180559e-5) ) # Uranus
rebound.particle_add( Particle( m=1./19314., x=-3.01777243405203e+1, y=+1.91155314998064e+0, z=-1.53887595621042e-1, vx=-2.17471785045538e-4, vy=-3.11361111025884e-3, vz=+3.58344705491441e-5) ) # Neptune
rebound.particle_add( Particle( m=0, x=-2.13858977531573e+1, y=+3.20719104739886e+1, z=+2.49245689556096e+0, vx=-1.76936577252484e-3, vy=-2.06720938381724e-3, vz=+6.58091931493844e-4) ) # Pluto
# Set the center of momentum to be at the origin
rebound.move_to_center_of_momentum()
# Get the particle data
# Note: this is a pointer and will automatically update as the simulation progresses
particles = rebound.particles_get()
# timestep counter
steps = 0
# Integrate until t=1e6 (unit of time in this example is days)
while rebound.get_t()<1e6:
rebound.step()
steps += 1
# Print particle positions every 100 timesteps
if steps%100==0:
for i in range(rebound.get_N()):
# time particle id x y z
print rebound.get_t(), i, particles[i].x, particles[i].y, particles[i].z
def simulation(par):
integrator, mass = par
rebound.reset()
mass = pow(10., mass)
k = 0.01720209895
G = k * k
rebound.G = G
rebound.dt = 0.
rebound.integrator = integrator
rebound.add(m=1.00000597682,
x=-4.06428567034226e-3,
y=-6.08813756435987e-3,
z=-1.66162304225834e-6,
vx=+6.69048890636161e-6,
vy=-6.33922479583593e-6,
vz=-3.13202145590767e-9) # Sun
rebound.add(m=mass,
x=+3.40546614227466e+0,
y=+3.62978190075864e+0,
z=+3.42386261766577e-2,
vx=-5.59797969310664e-3,
vy=+5.51815399480116e-3,
vz=-2.66711392865591e-6) # Jupiter
rebound.add(m=mass,
x=+6.60801554403466e+0,
y=+6.38084674585064e+0,
z=-1.36145963724542e-1,
vx=-4.17354020307064e-3,
vy=+3.99723751748116e-3,
vz=+1.67206320571441e-5) # Saturn
rebound.add(m=mass,
x=+1.11636331405597e+1,
y=+1.60373479057256e+1,
z=+3.61783279369958e-1,
vx=-3.25884806151064e-3,
vy=+2.06438412905916e-3,
vz=-2.17699042180559e-5) # Uranus
rebound.add(m=mass,
x=-3.01777243405203e+1,
y=+1.91155314998064e+0,
z=-1.53887595621042e-1,
vx=-2.17471785045538e-4,
vy=-3.11361111025884e-3,
vz=+3.58344705491441e-5) # Neptune
N = rebound.N
def move_to_heliocentric():
particles = rebound.particles
for i in xrange(1, N):
particles[i].x -= particles[0].x
particles[i].y -= particles[0].y
particles[i].z -= particles[0].z
particles[i].vx -= particles[0].vx
particles[i].vy -= particles[0].vy
particles[i].vz -= particles[0].vz
particles[0].x = 0.
particles[0].y = 0.
particles[0].z = 0.
particles[0].vx = 0.
particles[0].vy = 0.
particles[0].vz = 0.
def energy():
if integrator == "wh":
rebound.move_to_com()
particles = rebound.particles
E_kin = 0.
E_pot = 0.
for i in xrange(N):
E_kin += 0.5 * particles[i].m * (
particles[i].vx * particles[i].vx + particles[i].vy *
particles[i].vy + particles[i].vz * particles[i].vz)
for j in xrange(i + 1, N):
dx = particles[i].x - particles[j].x
dy = particles[i].y - particles[j].y
dz = particles[i].z - particles[j].z
r2 = dx * dx + dy * dy + dz * dz
E_pot -= G * particles[i].m * particles[j].m / np.sqrt(r2)
if integrator == "wh":
move_to_heliocentric()
return E_kin + E_pot
rebound.move_to_com()
ei = energy()
es = 1e-20
for s in xrange(1000):
rebound.step()
ef = energy()
e = np.fabs((ei - ef) / ei)
es = max(es, e)
return es
