import numpy as np
import matplotlib.pyplot as plt

G = 1.0

m1 = 5.0
m2 = 3.0

r1 = np.array([-1.0, 0.0], dtype=float)
r2 = np.array([1.0, 0.0], dtype=float)
v1 = np.array([0.0, 0.5], dtype=float)
v2 = np.array([0.0, -0.5], dtype=float)

dt = 0.01
num_steps = 10000

r1_list = [r1.copy()]
r2_list = [r2.copy()]

for _ in range(num_steps):
    diff = r2 - r1
    dist = np.linalg.norm(diff)
    if dist == 0:
        break 
    force = G * m1 * m2 * diff / dist**3

    v1 += force / m1 * dt
    v2 -= force / m2 * dt

    r1 += v1 * dt
    r2 += v2 * dt

    r1_list.append(r1.copy())
    r2_list.append(r2.copy())

r1_array = np.array(r1_list)
r2_array = np.array(r2_list)

plt.figure(figsize=(8, 8))
plt.plot(r1_array[:, 0], r1_array[:, 1], 'r-', label='Тело 1 (m=5)')
plt.plot(r2_array[:, 0], r2_array[:, 1], 'b-', label='Тело 2 (m=3)')
plt.scatter(r1_array[0, 0], r1_array[0, 1], color='red', s=50, label='Начало (тело 1)')
plt.scatter(r2_array[0, 0], r2_array[0, 1], color='blue', s=50, label='Начало (тело 2)')
plt.noscript('Гравитационное взаимодействие двух тел')
plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.grid(True)
plt.axis('equal')
plt.show()