def get_galaxies_in_orbit(m_a=10.e11|units.MSun,
m_b=10.e11|units.MSun,
ecc=0.5,
r_min=25.|units.kpc,
t_start=None):
"""
binary galaxy with orbit of given parameters
-- if ecc=>1, start at t_start (p625, t_start=-10=-10*100Myr)
-- if ecc<1, start at apocenter (p644)
"""
converter=nbody_system.nbody_to_si(m_a+m_b,1|units.kpc)
semi = r_min/(1.-ecc)
# relative position and velocity vectors at the pericenter using kepler
kepler = Kepler_twobody(converter)
kepler.initialize_code()
kepler.initialize_from_elements(mass=(m_a+m_b), semi=semi, ecc=ecc, periastron=r_min) # at periastron
# evolve back till initial position
if ( ecc<1. ):
kepler.return_to_apastron()
else:
kepler.transform_to_time(t_start)
# get time of the orbit
t_orbit = kepler.get_time()
rl = kepler.get_separation_vector()
r = [rl[0].value_in(units.AU), rl[1].value_in(units.AU), rl[2].value_in(units.AU)] | units.AU
vl = kepler.get_velocity_vector()
v = [vl[0].value_in(units.kms), vl[1].value_in(units.kms), vl[2].value_in(units.kms)] | units.kms
kepler.stop()
# assign particle atributes
galaxies = Particles(2)
galaxies[0].mass = m_a
galaxies[0].position = (0,0,0) | units.AU
galaxies[0].velocity = (0,0,0) | units.kms
galaxies[1].mass = m_b
galaxies[1].position = r
galaxies[1].velocity = v
# identification
galaxies[0].id = 'a0'
galaxies[1].id = 'b0'
galaxies.move_to_center()
return galaxies, t_orbit
def get_orbit_ini(m0, m1, peri, ecc, incl, omega,
rel_force=0.01, r_disk=50|units.AU):
converter=nbody_system.nbody_to_si(1|units.MSun,1|units.AU)
# semi-major axis
if ecc!=1.0:
semi = peri/(1.0-ecc)
else:
semi = 1.0e10 | units.AU
# relative position and velocity vectors at the pericenter using kepler
kepler = Kepler_twobody(converter)
kepler.initialize_code()
kepler.initialize_from_elements(mass=(m0+m1), semi=semi, ecc=ecc, periastron=peri) # at pericenter
# moving particle backwards to radius r where: F_m1(r) = rel_force*F_m0(r_disk)
#r_disk = peri
r_ini = r_disk*(1.0 + numpy.sqrt(m1/m0)/rel_force)
kepler.return_to_radius(radius=r_ini)
rl = kepler.get_separation_vector()
r = [rl[0].value_in(units.AU), rl[1].value_in(units.AU), rl[2].value_in(units.AU)] | units.AU
vl = kepler.get_velocity_vector()
v = [vl[0].value_in(units.kms), vl[1].value_in(units.kms), vl[2].value_in(units.kms)] | units.kms
period_kepler = kepler.get_period()
time_peri = kepler.get_time()
kepler.stop()
# rotation of the orbital plane by inclination and argument of periapsis
a1 = ([1.0, 0.0, 0.0], [0.0, numpy.cos(incl), -numpy.sin(incl)], [0.0, numpy.sin(incl), numpy.cos(incl)])
a2 = ([numpy.cos(omega), -numpy.sin(omega), 0.0], [numpy.sin(omega), numpy.cos(omega), 0.0], [0.0, 0.0, 1.0])
rot = numpy.dot(a1,a2)
r_au = numpy.reshape(r.value_in(units.AU), 3, 1)
v_kms = numpy.reshape(v.value_in(units.kms), 3, 1)
r_rot = numpy.dot(rot, r_au) | units.AU
v_rot = numpy.dot(rot, v_kms) | units.kms
bodies = Particles(2)
bodies[0].mass = m0
bodies[0].radius = 1.0|units.RSun
bodies[0].position = (0,0,0) | units.AU
bodies[0].velocity = (0,0,0) | units.kms
bodies[1].mass = m1
bodies[1].radius = 1.0|units.RSun
bodies[1].x = r_rot[0]
bodies[1].y = r_rot[1]
bodies[1].z = r_rot[2]
bodies[1].vx = v_rot[0]
bodies[1].vy = v_rot[1]
bodies[1].vz = v_rot[2]
bodies.age = 0.0 | units.yr
bodies.move_to_center()
print "\t r_rel_ini = ", r_rot.in_(units.AU)
print "\t v_rel_ini = ", v_rot.in_(units.kms)
print "\t time since peri = ", time_peri.in_(units.yr)
a_orbit, e_orbit, p_orbit = orbital_parameters(r_rot, v_rot, (m0+m1))
print "\t a = ", a_orbit.in_(units.AU), "\t e = ", e_orbit, "\t period = ", p_orbit.in_(units.yr)
return bodies, time_peri
def get_bodies_in_orbit(m0, m_ffp, m_bp, a_bp, e_bp, phi_bp, inc_bp, lan_bp, b_ffp, r_inf):
#Bodies
bodies = Particles()
##Get BP in orbit
#Binary
star_planet = new_binary_from_orbital_elements(m0, m_bp, a_bp, e_bp, true_anomaly=phi_bp, inclination = inc_bp, longitude_of_the_ascending_node = lan_bp)
#Planet attributes
star_planet.eccentricity = e_bp
star_planet.semimajoraxis = a_bp
#Center on the star
star_planet.position -= star_planet[0].position
star_planet.velocity -= star_planet[0].velocity
cm_p = star_planet.center_of_mass()
cm_v = star_planet.center_of_mass_velocity()
##Get FFP in orbit
#Particle set
m0_ffp = Particles(2)
#Zeros and parabolic velocity
zero_p = 0.0 | nbody_system.length
zero_v = 0.0 | nbody_system.speed
parabolic_velocity = get_parabolic_velocity(m0, m_bp, b_ffp, r_inf)
#Central star
m0_ffp[0].mass = m0
m0_ffp[0].position = (zero_p,zero_p,zero_p)
m0_ffp[0].velocity = (zero_v,zero_v,zero_v)
#Free-floating planet
m0_ffp[1].mass = m_ffp
m0_ffp[1].position = (-r_inf+cm_p[0], b_ffp+cm_p[1], cm_p[2])
m0_ffp[1].velocity = (parabolic_velocity+cm_v[0], cm_v[1], cm_v[2])
#To find the orbital period of the BP
G = (1.0 | nbody_system.length**3 * nbody_system.time**-2 * nbody_system.mass**-1)
orbital_period_bp = 2*math.pi*((a_bp**3)/(G*m0)).sqrt()
#To find the distance and time to periastron
kep = Kepler()
kep.initialize_code()
star_planet_as_one = Particles(1)
star_planet_as_one.mass = m0 + m_bp
star_planet_as_one.position = cm_p
star_planet_as_one.velocity = cm_v
kepler_bodies = Particles()
kepler_bodies.add_particle(star_planet_as_one[0])
kepler_bodies.add_particle(m0_ffp[1])
kep.initialize_from_particles(kepler_bodies)
kep.advance_to_periastron()
time_pericenter = kep.get_time()
kep.stop()
binary = [star_planet_as_one[0], m0_ffp[1]]
sma, e, inclination, long_asc_node, arg_per = my_orbital_elements_from_binary(binary)
m0_ffp.eccentricity = e
m0_ffp.semimajoraxis = sma
#Adding bodies. Order: star, ffp, bp
bodies.add_particle(m0_ffp[0])
bodies.add_particle(m0_ffp[1])
bodies.add_particle(star_planet[1])
return bodies, time_pericenter, orbital_period_bp
def get_orbit_ini(m0,
m1,
peri,
ecc,
incl,
omega,
rel_force=0.01,
r_disk=50 | units.AU):
converter = nbody_system.nbody_to_si(1 | units.MSun, 1 | units.AU)
# semi-major axis
if ecc != 1.0:
semi = peri / (1.0 - ecc)
else:
semi = 1.0e10 | units.AU
# relative position and velocity vectors at the pericenter using kepler
kepler = Kepler_twobody(converter)
kepler.initialize_code()
kepler.initialize_from_elements(mass=(m0 + m1),
semi=semi,
ecc=ecc,
periastron=peri) # at pericenter
# moving particle backwards to radius r where: F_m1(r) = rel_force*F_m0(r_disk)
#r_disk = peri
r_ini = r_disk * (1.0 + numpy.sqrt(m1 / m0) / rel_force)
kepler.return_to_radius(radius=r_ini)
rl = kepler.get_separation_vector()
r = [
rl[0].value_in(units.AU), rl[1].value_in(units.AU), rl[2].value_in(
units.AU)
] | units.AU
vl = kepler.get_velocity_vector()
v = [
vl[0].value_in(units.kms), vl[1].value_in(units.kms), vl[2].value_in(
units.kms)
] | units.kms
period_kepler = kepler.get_period()
time_peri = kepler.get_time()
kepler.stop()
# rotation of the orbital plane by inclination and argument of periapsis
a1 = ([1.0, 0.0,
0.0], [0.0, numpy.cos(incl),
-numpy.sin(incl)], [0.0,
numpy.sin(incl),
numpy.cos(incl)])
a2 = ([numpy.cos(omega), -numpy.sin(omega),
0.0], [numpy.sin(omega), numpy.cos(omega), 0.0], [0.0, 0.0, 1.0])
rot = numpy.dot(a1, a2)
r_au = numpy.reshape(r.value_in(units.AU), 3, 1)
v_kms = numpy.reshape(v.value_in(units.kms), 3, 1)
r_rot = numpy.dot(rot, r_au) | units.AU
v_rot = numpy.dot(rot, v_kms) | units.kms
bodies = Particles(2)
bodies[0].mass = m0
bodies[0].radius = 1.0 | units.RSun
bodies[0].position = (0, 0, 0) | units.AU
bodies[0].velocity = (0, 0, 0) | units.kms
bodies[1].mass = m1
bodies[1].radius = 1.0 | units.RSun
bodies[1].x = r_rot[0]
bodies[1].y = r_rot[1]
bodies[1].z = r_rot[2]
bodies[1].vx = v_rot[0]
bodies[1].vy = v_rot[1]
bodies[1].vz = v_rot[2]
bodies.age = 0.0 | units.yr
bodies.move_to_center()
print "\t r_rel_ini = ", r_rot.in_(units.AU)
print "\t v_rel_ini = ", v_rot.in_(units.kms)
print "\t time since peri = ", time_peri.in_(units.yr)
a_orbit, e_orbit, p_orbit = orbital_parameters(r_rot, v_rot, (m0 + m1))
print "\t a = ", a_orbit.in_(
units.AU), "\t e = ", e_orbit, "\t period = ", p_orbit.in_(units.yr)
return bodies, time_peri
