import numpy as np
from scipy.integrate import solve_ivp

init_data = [[0.362, +0.380, -1.954, -2.364, +0.461],
             [0.168, +0.032, +0.631, +0.233, -0.608],
             [0.413, +0.280, -0.095, -0.672, -0.369],
             [0.209, -1.669, +0.116, -1.965, +0.237],
             [0.172, +0.376, +0.673, -0.370, +0.723],
             [0.322, -0.583, +0.355, -0.405, +0.831],
             [0.289, -0.619, -0.960, -0.525, -1.366],
             [0.108, +0.626, -1.931, +0.276, +1.698],
             [0.491, +0.499, +0.217, -1.237, +0.084],
             [0.325, +0.781, +1.452, -0.295, -0.827]];

def f(t,y):
    dydt = np.zeros(40)
    ### START YOUR CODE HERE ###


    #### END YOUR CODE HERE ####
    return dydt

def solve_for_gravity(delta_t):
    positions = np.zeros((10,2))
    ### START YOUR CODE HERE ###
    
    
    #### END YOUR CODE HERE ####
    return positions