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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Orbit Plot
REBOUND comes with a simple way to plot instantaneous orbits of planetary systems. To show how this works, let's setup a test simulation with 4 planets.
Step1:  To plot these initial orbits in the $xy$-plane, we can simply call the OrbitPlot function and give it the simulation as an argument.
Step2:  Note that the OrbitPlot function chooses reasonable limits for the axes for you. 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!).
Step3:  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 nice 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.
Step4:  To get an idea of the three dimensional distribution of orbits, use the slices=True option. This will plot the orbits three times, from different perspectives. You can adjust the dimensions in the z direction using the limz keyword.
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Python Code:
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
Explanation: Orbit Plot
REBOUND comes with a simple way to plot instantaneous orbits of planetary systems. To show how this works, let's setup a test simulation with 4 planets.
End of explanation
%matplotlib inline
fig = rebound.OrbitPlot(sim)
Explanation: To plot these initial orbits in the $xy$-plane, we can simply call the OrbitPlot function and give it the simulation as an argument.
End of explanation
fig = rebound.OrbitPlot(sim, unitlabel="[AU]", color=True, periastron=True)
fig = rebound.OrbitPlot(sim, unitlabel="[AU]", periastron=True, lw=2)
Explanation: Note that the OrbitPlot function chooses reasonable limits for the axes for you. 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!).
End of explanation
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 = rebound.OrbitPlot(sim,color=True,unitlabel="[AU]",lim=2.)
    display(fig)
    plt.close(fig)
    clear_output(wait=True)
Explanation: 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 nice 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.
End of explanation
fig = rebound.OrbitPlot(sim,slices=True,color=True,unitlabel="[AU]",lim=2.,limz=0.36)
Explanation: To get an idea of the three dimensional distribution of orbits, use the slices=True option. This will plot the orbits three times, from different perspectives. You can adjust the dimensions in the z direction using the limz keyword.
End of explanation
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