Plotting elliptical orbits

Question

I'm trying to write a code that plots the elliptical paths of an object using the equation for the ellipse r=a(1-e^2)/(1+e*cos(theta)). I'd also like this data to be put into an array for other use.

from numpy import *#Imports Python mathematical functions library
import matplotlib.pyplot as plt #Imports plot library
from pylab import *

a = 5
e = 0.3
theta = 0
while theta <= 2*pi:
    r = (a*(1-e**2))/(1+e*cos(theta))
    print("r = ",r,"theta = ",theta)
    plt.polar(theta, r)
    theta += pi/180

plt.show()

The code spits out correct values for r and theta, but the plot is blank. The polar plot window appears, but there is nothing plotted.

Please help. Thanks in advance.

Answer 1

Do not call plt.polar once for every point. Instead, call it once, with all the data as input:

import numpy as np #Imports Python mathematical functions library
import matplotlib.pyplot as plt #Imports plot library
cos = np.cos
pi = np.pi

a = 5
e = 0.3
theta = np.linspace(0,2*pi, 360)
r = (a*(1-e**2))/(1+e*cos(theta))
plt.polar(theta, r)

print(np.c_[r,theta])

plt.show()

---

By the way, numpy can do the calculation as a two-liner, instead of using a while-loop:

theta = np.linspace(0,2*pi, 360)   # 360 equally spaced values between 0 and 2*pi
r = (a*(1-e**2))/(1+e*cos(theta))  

This defines theta and r as numpy arrays (rather than single values).

Answer 2

I think you need to do points.append([theta,r]) then at the end plt.polar(points) ... that makes a kinda neat design too

from numpy import *#Imports Python mathematical functions library
import matplotlib.pyplot as plt #Imports plot library
from pylab import *

a = 5
e = 0.3
theta = 0

points = []
while theta <= 2*pi:
    r = (a*(1-e**2))/(1+e*cos(theta))
    print("r = ",r,"theta = ",theta)
    points.append((theta, r))
    theta += pi/180
#plt.polar(points) #this is cool but probably not what you want
plt.polar(*zip(*points))
plt.show()