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()