import matplotlib.pyplot as plt
import numpy as np

if __name__ == "__main__":
    fig = plt.figure(figsize=(15.2, 8))
    ax = fig.add_subplot(111)

    R = 10
    p0, q0 = [20, 0], [-20, 0]
    k = 275

    dist = lambda p1, p2: np.sqrt( (p1[0]-p2[0])**2 + (p1[1]-p2[1])**2 )
    force = lambda r: - k / r**2

    theta = np.linspace(-np.pi, np.pi, 50)
    for t in theta:
        p1 = [-R * np.cos(t), R * np.sin(t)]
        if t < np.pi * 0.5 and t > -np.pi * 0.5:
            r = dist(q0, p1)
        else:
            r = dist(p0, p1)
        F = force(r)
        ax.arrow(p1[0], p1[1], F * np.cos(t), F * np.sin(t), head_width=0.5, head_length=0.7, fc='k')

    ax.annotate(r"+", xytext=(0,0), size=30, xy=(0,0), ha="center", va="center")
    ax.annotate(r"Satellite", xy=(25,0), xytext=(15,0),
                size=30, va="center",
                arrowprops=dict(arrowstyle="fancy", fc='k'))
    ax.set_xlim(-13, 25)
    ax.set_ylim(-11, 11)
    ax.plot(-R * np.cos(theta), R * np.sin(theta), linewidth=3.)
    ax.axis('off')
    plt.savefig('field tidal.svg', bbox_inches='tight', pad_inches=.15, transparent='true')