def plot_range_for_velocity(v_min, v_max, step=500, save_to_file=None):
vx, vy_min, vy_max = [], [], []
for v in range(v_min, v_max, step):
# print v to indicate progress
print(v)
# run sim for desired velocity
sim = Sim(planet_name, capsule_name, 80000)
sim.set_v0(v)
rng = get_angle_range(sim, step=0.01)
if len(rng) > 0: # makes sure that even if it is impossible to land, the program won't crash after hours
# store data
vx.append(v)
vy_min.append(rng[0])
vy_max.append(rng[-1])
# plot
f, ax = plt.subplots(1)
ax.plot(vx, vy_min, 'bo')
ax.plot(vx, vy_max, 'ro')
plt.xlabel('$ v_0 $ [m/s]')
plt.ylabel('$ \phi_0 [°]$')
plt.title(r'Min and max $ \phi_0(v_0) $')
if save_to_file is not None:
plt.savefig(save_to_file)
plt.show()
