def test_from_elements(self):
j = 5
k = 2
Zstar = 0.1
libfac = 0.5
a10 = 3.
a1 = 3.1
G = 2.
m1 = 1.e-7
m2 = 1.e-4
ecom = 0.05
phiecom = 0.7
avars = Andoyer.from_elements(j,
k,
Zstar,
libfac,
a10,
a1,
G,
m1=m1,
m2=m2,
Zcom=ecom,
phiZcom=phiecom)
self.assertAlmostEqual(avars.Zstar, Zstar, delta=1.e-12)
self.assertAlmostEqual(avars.Zcom, ecom, delta=1.e-15)
self.assertAlmostEqual(avars.phiZcom, phiecom, delta=1.e-15)
sim = avars.to_Simulation()
self.assertAlmostEqual(
sim.particles[1].a, a1, delta=3 * ((a1 - a10) / a10)**
2) # should match to O(da/a)^2, atrue=1, a10=a10
def get_resonant(seed, Nplanets=3):
r = random.Random()
r.seed(seed)
Phiprimecrits = [0, 1., -2. / 3.]
pairs = ['inner', 'outer', 'split']
k = r.randint(1, 2)
pairindex = r.randint(0, 2)
pair = pairs[pairindex]
m1 = logunif(r, 1.e-7, 1.e-4)
m2 = logunif(r, 1.e-7, 1.e-4)
eH = ((m1 + m2) / 3.)**(1. / 3.)
ehillstable = 3.5 * eH
jmax = k / (1 - 1 / (1 + 3.5 * eH)**1.5)
if pair == 'split':
if Nplanets == 2:
return # don't want 2planet systems 60 hill radii apart
maxHillradii = 60. # 3rd planet will go in middle so draw up to 60
else:
maxHillradii = 30.
jmin = max(k + 1, k / (1 - 1 / (1 + maxHillradii * eH)**1.5))
jmin = int(np.ceil(jmin))
jmax = int(np.floor(jmax))
if k == 2: # if k = 2, want odd j so we don't get e.g. 8:6 = 4:3
if jmin % 2 == 0: # even
jmin += 1
if jmax % 2 == 0:
jmax -= 1
j = r.randrange(
jmin, jmax + 1,
k) # choose randomly between limits in steps of k e.g. (3,5,7,9)
a1 = 1.
a2 = (float(j) / (j - k))**(2. / 3.)
ecross1 = (a2 - a1) / a1
ecross2 = (a2 - a1) / a2
emin1 = m2 / ecross1**2
emin2 = m1 / ecross2**2
emin = max(
emin1, emin2
) # take as min Z the larger of the kicks a planet gets at conjunction
emin = max(
emin, (m1 + m2)**(1. / k)
) # below mtot^1/k, the resonant term is smaller than the second order mass terms we ignore
emax = min(ecross1, ecross2)
avars = Andoyer(j=j, k=k, X=0, Y=0, m1=m1, m2=m2)
Phiprimecrit = Phiprimecrits[k]
Xcrit = get_Xstarres(k, Phiprimecrit)
Phicrit = 0.5 * Xcrit**2
emin = max(
avars.Phi_to_Z(Phicrit), emin
) # first quantity is value of Z at bifurcation when res first appears
Zstar = logunif(r, emin, emax)
libfac = logunif(r, 3.e-3, 3)
negative = r.randint(0, 1)
if negative:
libfac *= -1
Zcom = logunif(r, emin, emax)
avars = Andoyer.from_elements(j=j,
k=k,
Zstar=Zstar,
libfac=libfac,
m1=m1,
m2=m2,
Zcom=Zcom,
phiZcom=r.uniform(0, 2 * np.pi),
theta=r.uniform(0, 2 * np.pi),
theta1=r.uniform(0, 2 * np.pi))
tmax = r.uniform(0, 10 * avars.tlib)
H = AndoyerHamiltonian(avars)
H.integrate(tmax)
pvars = avars.to_Poincare()
ps = pvars.particles
if Nplanets == 3:
m3 = logunif(r, 1.e-7, 1.e-4)
pvarssorted = Poincare(G=pvars.G)
if pair == "inner":
eH = ((m2 + m3) / 3.)**(1. / 3.)
beta = r.uniform(3.5, 30)
a3 = a2 * (1 + beta * eH)
ecross3 = (a3 - a2) / a3
emin3 = m2 / ecross3**2
e3 = logunif(r, emin3, ecross3)
pvarssorted.add(m=ps[1].m,
M=ps[1].M,
a=ps[1].a,
e=ps[1].e,
gamma=ps[1].gamma,
l=ps[1].l)
pvarssorted.add(m=ps[2].m,
M=ps[2].M,
a=ps[2].a,
e=ps[2].e,
gamma=ps[2].gamma,
l=ps[2].l)
pvarssorted.add(m=m3,
M=1,
a=a3,
e=e3,
gamma=r.uniform(0, 2 * np.pi),
l=r.uniform(0, 2 * np.pi))
elif pair == "outer":
eH = ((m1 + m3) / 3.)**(1. / 3.)
beta = r.uniform(3.5, 30)
a3 = a1 / (1 + beta * eH)
ecross3 = (a1 - a3) / a3
emin3 = m1 / ecross3**2
e3 = logunif(r, emin3, ecross3)
pvarssorted.add(m=m3,
M=1,
a=a3,
e=e3,
gamma=r.uniform(0, 2 * np.pi),
l=r.uniform(0, 2 * np.pi))
pvarssorted.add(m=ps[1].m,
M=ps[1].M,
a=ps[1].a,
e=ps[1].e,
gamma=ps[1].gamma,
l=ps[1].l)
pvarssorted.add(m=ps[2].m,
M=ps[2].M,
a=ps[2].a,
e=ps[2].e,
gamma=ps[2].gamma,
l=ps[2].l)
elif pair == "split":
eH1 = ((m1 + m3) / 3.)**(1. / 3.)
eH2 = ((m2 + m3) / 3.)**(1. / 3.)
amin = a1 * (1 + 3.5 * eH1)
amax = min(a1 * (1 + 30 * eH1), a2 / (1 + 3.5 * eH2))
if amin > amax:
seed += 900000
return get_resonant(
seed=seed) # draw new sample (may not be 'split')
a3 = r.uniform(amin, amax)
ecross3 = min((a3 - a1) / a1, (a2 - a3) / a3)
emin3 = max(m1 / ((a3 - a1) / a3)**2, m2 / ((a2 - a3) / a3)**2)
e3 = logunif(r, emin3, ecross3)
pvarssorted.add(m=ps[1].m,
M=ps[1].M,
a=ps[1].a,
e=ps[1].e,
gamma=ps[1].gamma,
l=ps[1].l)
pvarssorted.add(m=m3,
M=1,
a=a3,
e=e3,
gamma=r.uniform(0, 2 * np.pi),
l=r.uniform(0, 2 * np.pi))
pvarssorted.add(m=ps[2].m,
M=ps[2].M,
a=ps[2].a,
e=ps[2].e,
gamma=ps[2].gamma,
l=ps[2].l)
sim = pvarssorted.to_Simulation()
else:
sim = avars.to_Simulation()
# add inclinations and scale s.t. a1 = 1, Mprimary=1. and G = 4*pi**2
ps = sim.particles
siminc = rebound.Simulation()
siminc.G = 4 * np.pi**2
dscale = ps[1].a
tscale = ps[1].P
mscale = siminc.G * dscale**3 / tscale**2 # ps[0].m + ps[1].m
siminc.add(m=ps[0].m / mscale,
x=ps[0].x / dscale,
y=ps[0].y / dscale,
vx=ps[0].vx / dscale * tscale,
vy=ps[0].vy / dscale * tscale)
for p in ps[1:]:
siminc.add(m=p.m / mscale,
a=p.a / dscale,
e=p.e,
inc=logunif(r, 1.e-3, 1.e-1),
Omega=r.uniform(0, 2 * np.pi),
pomega=p.pomega,
l=p.l)
rH = siminc.particles[-1].a * (siminc.particles[-1].m / 3. /
siminc.particles[0].m)**(1. / 3.)
siminc.particles[-1].r = rH
siminc.move_to_com()
siminc.integrator = "whfast"
siminc.dt = 2. * np.sqrt(3) / 100. * siminc.particles[1].P
siminc.ri_whfast.safe_mode = 0
siminc.collision = "line"
return siminc, j, k, pairindex, Zstar, libfac, Zcom