I'm trying to make it more general code so I can trace even a parabola or hyperbola for $e=1, E=0$ and $e>1, E>0$ respectively. And after achieving that general code I want to make the same code working for perihelion precession motion of Mercury just by adding an additional term ($-A/r^3$) in the energy term. Feel free to change my entire code and energy term.
from numpy import *
import matplotlib.pyplot as plt
L = 9.11*10**38 #L = angular momentum
m = 3.28*10**23 #m = mass of mercury
M = 1.99*10**30 #M = mass of sun
a = 5.8*10**10 #a = semi-major axis
G = 6.674*10**-11 #G = Gravitationl constant
k = G*M*m
E = -k/(2*a) #E = energy
##E = 0
p = L**2/(m*k)
c = 1 + (2*E*L**2)/(m*k**2)
e = sqrt(c) #e = eccentricity
print(e,c)
def fx(x):
r = p/(1 + e*cos(x))
return float(r)
n = 1000
phi =linspace(0,2*pi,n)
radius = zeros([n])
theta = zeros([n])
x = zeros([n])
y = zeros([n])
for i in range(0,n):
radius[i] = fx(phi[i])
theta[i] = 180*phi[i]/pi
for i in range(0,n):
x[i] = radius[i]*cos(phi[i])
for i in range(0,n):
y[i] = radius[i]*sin(phi[i])
print('r =',radius)
print('x =',x)
print('y =',y)
plt.plot(x,y)
plt.show()
import *it can cause unexpected and hard to find problems. Right now your script crashes because $c<0$ and $e=\sqrt{c}$. Have a look at this answer for some equations for bound and unbound orbits, and this answer for a numerical integration example. Feel free to ping me with questions. $\endgroup$