Trajectory

t.py

from math import pi, sin, cos
from numpy import array, vstack
from numpy.linalg import norm

from pylab import plot, savefig

R = 10.
M = 1.
G = 1.
phi = 30 * 180. / pi
v0_magnitude = 0.1
r = array([0, 0, R])
v = v0_magnitude * array([cos(pi), 0, sin(pi)])
trajectory = []

dt = 0.1
t = 0
while t < 100:
    trajectory.append(r.copy())
    a = -G * M * r / norm(r)**3
    v += a * dt
    r += v * dt
    t += dt

trajectory = vstack(trajectory)
plot(trajectory[:, 0], trajectory[:, 2])
savefig("trajectory.png")

trajectory.png