Orbit Plot (iPython)

with 4 planets.

import rebound
sim = rebound.Simulation()
sim.add(m=1)
sim.add(m=0.1, e=0.041, a=0.4, inc=0.2, f=0.43, Omega=0.82, omega=2.98)
sim.add(m=1e-3, e=0.24, a=1.0, pomega=2.14)
sim.add(m=1e-3, e=0.24, a=1.5, omega=1.14, l=2.1)
sim.add(a=-2.7, e=1.4, f=-1.5,omega=-0.7) # hyperbolic orbit

To plot these initial orbits in the \(xy\)-plane, we can simply call the OrbitPlot function and give it the simulation as an argument.

%matplotlib inline
fig, ax = rebound.OrbitPlot(sim)
../_images/OrbitPlot_3_0.png

There are various ways to customize the plot. Have a look at the arguments used in the following examples, which are pretty much self-explanatory (if in doubt, check the documentation!).

fig, ax = rebound.OrbitPlot(sim, unitlabel="[AU]", color=True, periastron=True, xlim=[-2,2], ylim=[-2.5,1.5])
../_images/OrbitPlot_5_0.png
fig, ax = rebound.OrbitPlot(sim, orbit_type="solid", lw=2)
../_images/OrbitPlot_6_0.png
fig, ax = rebound.OrbitPlot(sim, fancy=True, color=True, lw=2)
../_images/OrbitPlot_7_0.png

Note that all orbits are draw with respect to the center of mass of all interior particles. This coordinate system is known as Jacobi coordinates. It requires that the particles are sorted by ascending semi-major axis within the REBOUND simulation’s particle array.

From within iPython/Jupyter one can also call the OrbitPlot routine in a loop, thus making an animation as one steps through a simulation. This is a one way of keeping track of what is going on in a simulation without having to wait until the end. To do that we need to import the display and clear_output function from iPython first. We’ll also need access to the clear function of matplotlib. Then, we run a loop, updating the figure as we go along.

from IPython.display import display, clear_output
import matplotlib.pyplot as plt
sim.move_to_com()
for i in range(3):
    sim.integrate(sim.t+0.31)
    fig, ax = rebound.OrbitPlot(sim,color=True,unitlabel="[AU]",xlim=[-2,2.],ylim=[-2,2.])
    display(fig)
    plt.close(fig)
    clear_output(wait=True)
../_images/OrbitPlot_10_0.png

To get an idea of the three dimensional distribution of orbits, use the slices option. This will plot the orbits three times, from different perspectives. You can size of the z direction by changing the value of slices. For example, slices=0.5 corresponds to plots half the size of the main plot.

fig = rebound.OrbitPlot(sim,slices=0.5,xlim=[-2.,2],ylim=[-2.,2])
../_images/OrbitPlot_12_0.png

The axes on the plots are automatically aligned with each other. The aspect of all plots is equal (a circular orbit will be a circle).

Advanced Plotting

One important caveat to keep in mind is that OrbitPlot plots osculating Kepler orbits in Jacobi coordinates. This can lead to spurious plots in some general cases, e.g., when a particle is in orbit around a particle with non-zero index:

sim = rebound.Simulation()
sim.add(m=1.) #Star A
sim.add(m=1., a=1.) #Star B
sim.add(a=2.) #Planet ABb
sim.add(a=0.2, primary=sim.particles[1]) #Bb,
sim.move_to_com()
fig = rebound.OrbitPlot(sim)
../_images/OrbitPlot_15_0.png

Circumbinary Planet ABb is plotted correctly in orbit around the center of mass of A and B, but Bb’s Jacobi orbit is also around the center of mass of the interior particles, which corresponds to a hyperbolic orbit. It’s important to note that while the plot looks incorrect, IAS15 would correctly integrate their motions.

There’s no way to generically assign specific primaries to particular particles, since this concept becomes ill defined near the boundaries of different bodies’ Hill spheres bodies and particles could for example switch primaries in a given simulation. But it’s straightforward to make custom plots since version 3.5.10:

import matplotlib.pyplot as plt
import numpy as np
fig, ax = plt.subplots(figsize=(8,8))
ps = sim.particles

# manually set plot boundaries
lim = 2.3
ax.set_xlim([-lim, lim])
ax.set_ylim([-lim, lim])

# plot the stars and planets with separate symbols
linewidth=1.

for star in ps[:2]:
    ax.scatter(star.x, star.y, s=35*linewidth, marker='*', facecolor='black', zorder=3)

for planet in ps[2:]:
    ax.scatter(planet.x, planet.y, s=10*linewidth, facecolor='black', zorder=3)

# Now individually plot orbit trails with appropriate orbit

from rebound.plotting import fading_line

ABb = ps[2] # circumbinary planet, use default jacobi coordinates
o = np.array(ABb.sample_orbit())
lc = fading_line(o[:,0], o[:,1], linewidth=linewidth)
ax.add_collection(lc)

Bb = ps[3] # planet in orbit around B, assign it as primary
o = np.array(Bb.sample_orbit(primary=ps[1]))
lc = fading_line(o[:,0], o[:,1], linewidth=linewidth)
ax.add_collection(lc)
<matplotlib.collections.LineCollection at 0x115af7c50>
../_images/OrbitPlot_17_1.png