Hill.py

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Tue May 28 11:50:24 2019
@author: nolte
Blog site: https://galileo-unbound.blog/2019/07/19/getting-armstrong-aldrin-and-collins-home-from-the-moon-apollo-11-and-the-three-body-problem/
"""

import numpy as np
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
from scipy import integrate
from matplotlib import pyplot as plt
from matplotlib import cm
import time
import os

plt.close('all')

womega = 1
R = 1
eps = 1e-6

M1 = 1
M2 = 1/10
chsi = M2/M1

x1 = -M2*R/(M1+M2)
x2 = x1 + R


def poten(y,c):
    
    rp0 = np.sqrt(y**2 + c**2);
    thetap0 = np.arctan(y/c);
        
    rp1 = np.sqrt(x1**2 + rp0**2 - 2*np.abs(rp0*x1)*np.cos(np.pi-thetap0));
    rp2 = np.sqrt(x2**2 + rp0**2 - 2*np.abs(rp0*x2)*np.cos(thetap0));
    V = -M1/rp1 -M2/rp2 - E;
     
    return [V]

def flow_deriv(x_y_z,tspan):
    x, y, z, w = x_y_z
    
    r1 = np.sqrt(x1**2 + x**2 - 2*np.abs(x*x1)*np.cos(np.pi-z));
    r2 = np.sqrt(x2**2 + x**2 - 2*np.abs(x*x2)*np.cos(z));
        
        
    yp = np.zeros(shape=(4,))
    yp[0] = y
    yp[1] = -womega**2*R**3*(np.abs(x)-np.abs(x1)*np.cos(np.pi-z))/(r1**3+eps) - womega**2*R**3*chsi*(np.abs(x)-abs(x2)*np.cos(z))/(r2**3+eps) + x*(w-womega)**2
    yp[2] = w
    yp[3] = 2*y*(womega-w)/x - womega**2*R**3*chsi*abs(x2)*np.sin(z)/(x*(r2**3+eps)) + womega**2*R**3*np.abs(x1)*np.sin(np.pi-z)/(x*(r1**3+eps))
    
    return yp
                

r0 = 0.64
v0 = 0.3
theta0 = 0
vrfrac = 1

rp1 = np.sqrt(x1**2 + r0**2 - 2*np.abs(r0*x1)*np.cos(np.pi-theta0))
rp2 = np.sqrt(x2**2 + r0**2 - 2*np.abs(r0*x2)*np.cos(theta0))
V = -M1/rp1 - M2/rp2
T = 0.5*v0**2
E = T + V

vr = vrfrac*v0
W = (2*T - v0**2)/r0


y0 = [r0, vr, theta0, W]

tspan = np.linspace(1,2000,20000)

y = integrate.odeint(flow_deriv, y0, tspan)

xx = y[1:20000,0]*np.cos(y[1:20000,2]);
yy = y[1:20000,0]*np.sin(y[1:20000,2]);


plt.figure(1)
lines = plt.plot(xx,yy)
plt.setp(lines, linewidth=0.5)
plt.show()