import numpy as np
from scipy.integrate import solve_ivp
import matplotlib.pyplot as plt



#Part one Diffeq
def f_part1(t, state, Me, Mm, G):
    xm, ym, vx, vy = state

    dvxdt = -(Me*G*xm)/((xm**2+ym**2)**(3/2))
    dxmdt = vx
    dvydt = -(Me*G*ym)/((xm**2+ym**2)**(3/2))
    dymdt = vy

    return (dxmdt, dymdt, dvxdt, dvydt)


# Initial Conditions
t_min = 0
t_max = 86400*20
numpoints = 200
t = np.linspace(t_min, t_max, numpoints)

xm0 = 384400000
ym0 = 0
vx0 = 0
vy0 = 1017.79

Me = 5.97*(10**24)
Mm = 7.35*(10**22)
G = 6.67*(10**-11)


#Solver
results = solve_ivp(f_part1, (t_min,t_max), (xm0, ym0, vx0, vy0), args=(Me, Mm, G), t_eval=t)


#Graph plotting
ax=plt.axes()    # This creates some axes, so that we
ax.set_aspect(1) # can set the aspect ratio to 1 i.e. 
                 # x and y axes are scaled equally.                                
ax.set_xlabel("x coordinate (m)") # Must label axes (with
ax.set_ylabel("y coordinate (m)") # units) and give
ax.set_title("Orbit of moon around earth") # plot title.
#
ax.plot(results.y[0],results.y[1]) # Make the plot
ax.legend(['Moon'])                # and add a key.
plt.show()


# MyInput = '0'
# while MyInput != 'q':
#     MyInput = input('Enter a choice, "1", "2" or "q" to quit: ')
#     print('You entered the choice: ',MyInput)
#     if MyInput == '1':
#         print('You have chosen part (1): simulation of a lunar orbit')
#         #
#         # put your code for part (1) here
#         #
#     elif MyInput == '2':
#         print('You have chosen part (2): earth-moon-probe system')
#         #
#         # put your code for part (2) here
#         #
#     elif MyInput != 'q':
#         print('This is not a valid choice')
# print('You have chosen to finish - goodbye.')