def simulation(par):
saturn_a, saturn_e = par
rebound.reset()
rebound.integrator = "whfast-nocor"
rebound.min_dt = 5.
rebound.dt = 1.
# These parameters are only approximately those of Jupiter and Saturn.
sun = rebound.Particle(m=1.)
rebound.add(sun)
jupiter = rebound.add(primary=sun,
m=0.000954,
a=5.204,
anom=0.600,
omega=0.257,
e=0.048)
saturn = rebound.add(primary=sun,
m=0.000285,
a=saturn_a,
anom=0.871,
omega=1.616,
e=saturn_e)
rebound.move_to_com()
rebound.init_megno(1e-16)
rebound.integrate(1e3 * 2. * np.pi)
return [
rebound.calculate_megno(),
1. / (rebound.calculate_lyapunov() * 2. * np.pi)
] # returns MEGNO and Lypunov timescale in years
def simulation(par):
saturn_a, saturn_e = par
rebound.reset()
rebound.integrator = "whfast-nocor"
rebound.dt = 5.
# These parameters are only approximately those of Jupiter and Saturn.
rebound.add(m=1.)
rebound.add(m=0.000954, a=5.204, anom=0.600, omega=0.257, e=0.048)
rebound.add(m=0.000285, a=saturn_a, anom=0.871, omega=1.616, e=saturn_e)
rebound.move_to_com()
rebound.init_megno(1e-16)
rebound.integrate(5e2*2.*np.pi) # integrator for 500 years
return [rebound.calculate_megno(),1./(rebound.calculat_lyapunov()*2.*np.pi)] # returns MEGNO and Lypunov timescale in years
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
def simulation(integrator):
print("Running "+integrator)
with open(integrator+".txt","w") as f:
rebound.reset()
rebound.integrator = integrator
rebound.dt = 0.2
rebound.add(m=1.)
rebound.add(m=0.01, a=1,e=0.1)
rebound.add(m=0.01, a=2.)
rebound.move_to_com()
rebound.init_megno(1e-10)
particles = rebound.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.t, rebound.calculate_megno(), particles[0].x, particles[1].x, particles[2].x, particles[3].x, particles[4].x, particles[5].x),file=f)
def simulation(par):
saturn_a, saturn_e = par
rebound.reset()
rebound.integrator = "whfast-nocor"
rebound.min_dt = 5.
rebound.dt = 1.
# These parameters are only approximately those of Jupiter and Saturn.
sun = rebound.Particle(m=1.)
rebound.add(sun)
jupiter = rebound.add(primary=sun,m=0.000954, a=5.204, anom=0.600, omega=0.257, e=0.048)
saturn = rebound.add(primary=sun,m=0.000285, a=saturn_a, anom=0.871, omega=1.616, e=saturn_e)
rebound.move_to_com()
rebound.init_megno(1e-16)
rebound.integrate(1e3*2.*np.pi)
return [rebound.calculate_megno(),1./(rebound.calculate_lyapunov()*2.*np.pi)] # returns MEGNO and Lypunov timescale in years
def simulation(par):
saturn_a, saturn_e = par
rebound.reset()
rebound.integrator = "whfast-nocor"
rebound.dt = 5.
# These parameters are only approximately those of Jupiter and Saturn.
rebound.add(m=1.)
rebound.add(m=0.000954, a=5.204, anom=0.600, omega=0.257, e=0.048)
rebound.add(m=0.000285, a=saturn_a, anom=0.871, omega=1.616, e=saturn_e)
rebound.move_to_com()
rebound.init_megno(1e-16)
rebound.integrate(5e2 * 2. * np.pi) # integrator for 500 years
return [
rebound.calculate_megno(),
1. / (rebound.calculat_lyapunov() * 2. * np.pi)
] # returns MEGNO and Lypunov timescale in years
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
def simulation(integrator):
print("Running " + integrator)
with open(integrator + ".txt", "w") as f:
rebound.reset()
rebound.integrator = integrator
rebound.dt = 0.2
rebound.add(m=1.)
rebound.add(m=0.01, a=1, e=0.1)
rebound.add(m=0.01, a=2.)
rebound.move_to_com()
rebound.init_megno(1e-10)
particles = rebound.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.t, rebound.calculate_megno(), particles[0].x,
particles[1].x, particles[2].x, particles[3].x,
particles[4].x, particles[5].x),
file=f)
import rebound
import os.path
filename = "cache.bin"
solar_system_objects = [
"Sun", "Mercury", "Venus", "Earth", "Mars", "Jupiter", "Saturn", "Uranus",
"Neptune", "C/2014 Q2"
]
if os.path.isfile(filename):
rebound.load(filename)
else:
# Get data from NASA Horizons
rebound.add(solar_system_objects)
rebound.move_to_com()
# Let's save it for next time
# Note: rebound.save() only saves the particle data, not the integrator settings, etc.
rebound.save("cache.bin")
rebound.integrator = "whfast"
rebound.set_dt = 0.01
rebound.status()
import numpy as np
Nout = 1000
times = np.linspace(0, 16. * np.pi, Nout) # 8 years
x = np.zeros((rebound.N, Nout))
y = np.zeros((rebound.N, Nout))
ps = rebound.particles
for ti, t in enumerate(times):
# Import the rebound module
import rebound
# Add particles
# We work in units where G=1.
rebound.add(m=1. ) # Test particle
rebound.add(m=1e-3,x=1.,vy=1. ) # Planet
# Move particles so that the center of mass is (and stays) at the origin
rebound.move_to_com()
# You can provide a function, written in python to REBOUND.
# This function gets called every time the forces are evaluated.
# Simple add any any additional (non-gravitational) forces to the
# particle accelerations. Here, we add a simple drag force. This
# will make the planet spiral into the star.
ps = rebound.particles
def dragforce():
dragcoefficient = 1e-2
for p in ps:
p.ax += -dragcoefficient * p.vx
p.ay += -dragcoefficient * p.vy
p.az += -dragcoefficient * p.vz
# Tell rebound which function to call
rebound.additional_forces = dragforce
# Integrate until t=100 (roughly 16 orbits at 1 AU)
rebound.integrate(100.)
# Output something at the end (the planet will be at ~0.1 AU)
def simulation(par):
import rebound
integrator, dt, run = par
rebound.reset()
k = 0.01720209895
G = k * k
rebound.G = G
rebound.dt = dt
rebound.integrator = integrator
rebound.force_is_velocitydependent = 0
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=1. / 1407.355,
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(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(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(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
N = rebound.N
particles = rebound.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[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():
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 -= G * particles[i].m * particles[j].m / np.sqrt(r2)
return E_kin + E_pot
if integrator == "wh" or integrator == "mercury" or integrator[
0:7] == "swifter":
move_to_heliocentric()
else:
rebound.move_to_com()
ei = energy()
runtime = 0.
rebound.integrate(tmax, exactFinishTime=0)
ef = energy()
e = np.fabs((ei - ef) / ei) + 1.1e-16
runtime += rebound.timing
integrator, dt, run = par
print integrator.ljust(13) + " %9.5fs" % (runtime) + "\t Error: %e" % (e)
return [runtime, e]
import rebound
import reboundxf
import numpy as np
rebound.integrator = "ias15"
rebound.G = 4*np.pi**2
tmax = 1.e4 # years
rebound.add(m=1.)
rebound.add(m=1e-6,a=1.,e=0.5)
#rebound.add(m=1e-6,a=2.,e=0.5)
rebound.move_to_com() # Moves to the center of momentum frame
rebound.additional_forces = reboundxf.forces()
reboundxf.set_e_damping([0.,tmax/10.])#,tmax])
reboundxf.set_migration([0.,0.])#,tmax])
Nout = 1000
e1,e2,a1,a2 = np.zeros(Nout), np.zeros(Nout), np.zeros(Nout), np.zeros(Nout)
times = np.linspace(0.,tmax,Nout)
for i,time in enumerate(times):
rebound.integrate(time)
orbits = rebound.calculate_orbits()
e1[i] = orbits[0].e
#e2[i] = orbits[1].e
a1[i] = orbits[0].a
#a2[i] = orbits[1].a
import matplotlib.pyplot as plt
fig = plt.figure(figsize=(15,5))
ax = plt.subplot(111)
def simulation(par):
import rebound
integrator, dt, run = par
rebound.reset()
k = 0.01720209895
G = k*k
rebound.G = G
rebound.dt = dt
if integrator == "whfast-nocor":
integrator = "whfast"
else:
rebound.integrator_whfast_corrector = 11
rebound.integrator = integrator
rebound.force_is_velocitydependent = 0
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=1./1407.355, 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(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(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(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
N = rebound.N
particles = rebound.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[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():
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 -= G*particles[i].m*particles[j].m/np.sqrt(r2)
return E_kin+E_pot
if integrator=="wh" or integrator=="mercury" or integrator[0:7]=="swifter":
move_to_heliocentric()
else:
rebound.move_to_com()
ei = energy()
runtime = 0.
rebound.integrate(tmax,exact_finish_time=0)
ef = energy()
e = np.fabs((ei-ef)/ei)+1.1e-16
runtime += rebound.timing
integrator, dt, run = par
print integrator.ljust(13) + " %9.5fs"%(runtime) + "\t Error: %e" %( e)
return [runtime, e]
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
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
