The orbit of the Earth around the Sun

The_orbit_of_the_Earth_around_the_Sun.py

from numpy import sqrt, arange
import matplotlib.pyplot as plt

G = 6.67384e-11 # Gravitational constant, m3 kg-1 s-2
M = 1.989e30    # Mass of Sun, kg

x = 1.475e11    # Perihelion Sun-Earth distance
y = 0
r = 0

vx = 0
vy = 3.01e4        # Velocity of Earth in perihelion
eps = 8.64573e4    # Seconds in a day

x_list = []
y_list = []

ax = 0
ay = 0

for t in arange(0, 365*eps, eps):
    x = x + vx*eps
    y = y + vy*eps

    x_list.append(x)
    y_list.append(y)

    r = sqrt(x**2 + y**2)

    ax = -G*M*x/r**3
    ay = -G*M*y/r**3

    vx = vx + eps*ax
    vy = vy + eps*ay


x_mi = 1.1*min(x_list)
y_mi = 1.1*min(y_list)
x_ma = 1.1*max(x_list)
y_ma = 1.1*max(y_list)


plt.axis([x_mi, x_ma, y_mi, y_ma])
plt.xlabel('x, meters')
plt.ylabel('y, meters')
plt.title('The orbit of the Earth around the Sun')

plt.plot(0, 0, 'yo', label = 'Sun')
plt.plot(x_list, y_list, 'c.', label = 'Earth')
plt.legend()

plt.grid(True)

plt.show()