# Ep - points de Lagrange

import numpy as np
import matplotlib.pyplot as plt

G=6.67e-11
Ms=2e30
Mt=6e24
d=1.5e11
w2=G*Ms/d**3
m=1

# définition de la zone de calcul x, y
x=np.linspace(-3e9,3e9,500)
y=np.linspace(-3e9,3e9,500)
Ep=np.zeros((500,500))

X,Y=np.meshgrid(x,y)

# calcul de l'Ep

TM=(X**2+Y**2)**0.5
SM=((X+d)**2+Y**2)**0.5
Ep=-G*Ms*m/SM-G*Mt*m/TM-0.5*m*SM**2*w2

#-----------------------------------------------------------------------------

plt.figure(figsize=(10,8))
plt.contour(X,Y,-Ep,1000,colors='black')
plt.show()

plt.figure(figsize=(10,8))
plt.plot(x,Ep[250,:],-1.34e9)
plt.axis([-3e9, 3e9, -1.34e9,-1.334e9])
plt.grid()
plt.show()

plt.figure(figsize=(10,8))
plt.plot(x,Ep[:,375])
plt.grid()
plt.show()