import matplotlib.pyplot as plt
from numpy import linspace, sin, cos, pi

period = {
    "mercury": 87.96926,
    "venus": 224.7008,
    "earth": 365.25636,
    "mars": 686.97959,
    "ceres": 1680.22107,
    "jupiter": 4332.8201,
    "saturn": 10755.699,
    "uranus": 20687.153,
    "neptune": 60190.03,
}

dist = lambda T: T ** (2 / 3)  # Kepler


def plot_orbit(planet1, planet2, periods=10):
    T1 = period[planet1]
    T2 = period[planet2]
    d1 = dist(T1)
    d2 = dist(T2)

    theta = linspace(0, 2 * pi * periods, 1000)
    x = d1 * cos(T2 * theta / T1) - d2 * cos(theta)
    y = d1 * sin(T2 * theta / T1) - d2 * sin(theta)

    plt.gca().set_aspect("equal")
    plt.axis("off")
    plt.plot(x, y)
    plt.show()


plot_orbit("venus", "earth", 8)
plot_orbit("jupiter", "saturn", 4)
plot_orbit("uranus", "earth", 57)
plot_orbit("mercury", "venus", 9)