import matplotlib.pyplot as plt
import numpy as np

#############################################
# planet around the sun

plt.clf()

n = 10000
dt = 0.001
G=1.


x=[]
y=[]

x.append(1.)
y.append(0.)
vx=0.
vy=1.

for i in range(1,n):
   x.append(x[i-1] + dt*vx)
   y.append(y[i-1] + dt*vy)
   vx = vx - dt*G*x[i-1]/(x[i-1]**2 + y[i-1]**2)**(1.5) 
   vy = vy - dt*G*y[i-1]/(x[i-1]**2 + y[i-1]**2)**(1.5) 

plt.plot(x,y)
plt.show()