def simulation(par):
saturn_a, saturn_e = par
rebound.reset()
rebound.set_integrator("whfast-nocor")
rebound.set_dt(5.)
# These parameters are only approximately those of Jupiter and Saturn.
rebound.add_particle(m=1.)
rebound.add_particle(m=0.000954, a=5.204, anom=0.600, omega=0.257, e=0.048)
rebound.add_particle(m=0.000285, a=saturn_a, anom=0.871, omega=1.616, e=saturn_e)
rebound.move_to_center_of_momentum()
rebound.init_megno(1e-16)
rebound.integrate(5e2*2.*np.pi) # integrator for 500 years
return [rebound.get_megno(),1./(rebound.get_lyapunov()*2.*np.pi)] # returns MEGNO and Lypunov timescale in years
def simulation(par):
saturn_a, saturn_e = par
rebound.reset()
rebound.set_min_dt(0.1)
# These parameters are only approximately those of Jupiter and Saturn.
sun = rebound.Particle(m=1.)
rebound.particle_add(sun)
jupiter = rebound.particle_add(primary=sun,m=0.000954, a=5.204, anom=0.600, omega=0.257, e=0.048)
saturn = rebound.particle_add(primary=sun,m=0.000285, a=saturn_a, anom=0.871, omega=1.616, e=saturn_e)
rebound.move_to_center_of_momentum()
rebound.megno_init(1e-16)
rebound.integrate(1e4*2.*np.pi)
return [rebound.get_megno(),1./(rebound.get_lyapunov()*2.*np.pi)] # returns MEGNO and Lypunov timescale in years
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
def simulation(integrator):
print("Running "+integrator)
with open(integrator+".txt","w") as f:
rebound.reset()
rebound.set_integrator(integrator)
rebound.set_dt(0.2)
rebound.add_particle(m=1.)
rebound.add_particle(m=0.01, a=1,e=0.1)
rebound.add_particle(m=0.01, a=2.)
rebound.move_to_center_of_momentum()
rebound.init_megno(1e-10)
particles = rebound.get_particles()
times = np.logspace(2,5,num=1000)
for t in times:
rebound.integrate(t,0)
print("%e %e %e %e %e %e %e %e\n" %(rebound.get_t(), rebound.get_megno(), particles[0].x, particles[1].x, particles[2].x, particles[3].x, particles[4].x, particles[5].x),file=f)
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]
# Set variables (defaults are G=1, t=0, dt=0.01)
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, run, trial = par
rebound.reset()
k = 0.01720209895
Gfac = 1./k
rebound.set_dt(dt)
rebound.set_integrator(integrator)
rebound.set_force_is_velocitydependent(0)
massfac = 1.
rebound.add_particle(m=1.00000597682, x=-4.06428567034226e-3, y=-6.08813756435987e-3, z=-1.66162304225834e-6, vx=+6.69048890636161e-6*Gfac, vy=-6.33922479583593e-6*Gfac, vz=-3.13202145590767e-9*Gfac) # Sun
rebound.add_particle(m=massfac/1407.355, x=+3.40546614227466e+0, y=+3.62978190075864e+0, z=+3.42386261766577e-2, vx=-5.59797969310664e-3*Gfac, vy=+5.51815399480116e-3*Gfac, vz=-2.66711392865591e-6*Gfac) # Jupiter
rebound.add_particle(m=massfac/3501.6, x=+6.60801554403466e+0, y=+6.38084674585064e+0, z=-1.36145963724542e-1, vx=-4.17354020307064e-3*Gfac, vy=+3.99723751748116e-3*Gfac, vz=+1.67206320571441e-5*Gfac) # Saturn
rebound.add_particle(m=massfac/22869., x=+1.11636331405597e+1, y=+1.60373479057256e+1, z=+3.61783279369958e-1, vx=-3.25884806151064e-3*Gfac, vy=+2.06438412905916e-3*Gfac, vz=-2.17699042180559e-5*Gfac) # Uranus
rebound.add_particle(m=massfac/19314., x=-3.01777243405203e+1, y=+1.91155314998064e+0, z=-1.53887595621042e-1, vx=-2.17471785045538e-4*Gfac, vy=-3.11361111025884e-3*Gfac, vz=+3.58344705491441e-5*Gfac) # Neptune
N = rebound.get_N()
particles = rebound.get_particles()
np.random.seed(run)
for i in xrange(N):
particles[i].m *= 1.+1e-3*np.random.rand()
particles[i].x *= 1.+1e-3*np.random.rand()
particles[i].y *= 1.+1e-3*np.random.rand()
particles[i].z *= 1.+1e-3*np.random.rand()
particles[i].vx *= 1.+1e-3*np.random.rand()
particles[i].vy *= 1.+1e-3*np.random.rand()
particles[i].vz *= 1.+1e-3*np.random.rand()
def move_to_heliocentric():
particles = rebound.get_particles()
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():
particles = rebound.get_particles()
com_vx = 0.
com_vy = 0.
com_vz = 0.
if integrator=="wh" or integrator=="mercury" or integrator[0:7]=="swifter":
mtot = 0.
for i in xrange(0,N):
com_vx += particles[i].vx*particles[i].m
com_vy += particles[i].vy*particles[i].m
com_vz += particles[i].vz*particles[i].m
mtot += particles[i].m
com_vx /= mtot
com_vy /= mtot
com_vz /= mtot
E_kin = 0.
E_pot = 0.
for i in xrange(N):
dvx = particles[i].vx - com_vx
dvy = particles[i].vy - com_vy
dvz = particles[i].vz - com_vz
E_kin += 0.5*particles[i].m*(dvx*dvx + dvy*dvy + dvz*dvz)
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 -= particles[i].m*particles[j].m/np.sqrt(r2)
return E_kin+E_pot
times = np.logspace(np.log10(orbit),np.log10(tmax),Ngrid)
if integrator=="wh" or integrator=="mercury" or integrator[0:7]=="swifter":
move_to_heliocentric()
else:
rebound.move_to_center_of_momentum()
ei = energy()
es = []
runtime = 0.
for t in times:
rebound.integrate(t,exactFinishTime=0,keepSynchronized=0)
ef = energy()
e = np.fabs((ei-ef)/ei)+1.1e-16
es.append(e)
runtime += rebound.get_timing()
integrator, run, trial = par
print integrator.ljust(13) + " %9.5fs"%(runtime) + "\t Error: %e" %( e)
es = np.array(es)
return [times, es]
