# Comparing Hohmann and bielliptic transfers¶

[1]:

from astropy import units as u

from matplotlib import pyplot as plt
import numpy as np

from mpl_toolkits.axes_grid1.inset_locator import mark_inset, zoomed_inset_axes

from poliastro.bodies import Earth
from poliastro.maneuver import Maneuver
from poliastro.twobody import Orbit

[2]:

ZOOM = True

R = np.linspace(2, 75, num=100)
Rstar = [15.58, 40, 60, 100, 200, np.inf]

hohmann_data = np.zeros_like(R)
bielliptic_data = np.zeros((len(R), len(Rstar)))

orb_i = Orbit.circular(Earth, 1.8 * u.km)
r_i = orb_i.a
v_i = np.sqrt(orb_i.v @ orb_i.v)
for ii, r in enumerate(R):
r_f = r * r_i
man = Maneuver.hohmann(orb_i, r_f)
hohmann_data[ii] = (man.get_total_cost() / v_i).decompose().value
for jj, rstar in enumerate(Rstar):
r_b = rstar * r_i
man = Maneuver.bielliptic(orb_i, r_b, r_f)
bielliptic_data[ii, jj] = (
(man.get_total_cost() / v_i).decompose().value
)

idx_max = np.argmax(hohmann_data)

ylims = (0.35, 0.6)

/home/docs/checkouts/readthedocs.org/user_builds/poliastro/envs/latest/lib/python3.9/site-packages/poliastro/core/maneuver.py:49: NumbaPerformanceWarning: '@' is faster on contiguous arrays, called on (array(float64, 1d, A), array(float64, 1d, A))
r_i = norm(r_i)

[3]:

fig, ax = plt.subplots(figsize=(8, 6))

(l,) = ax.plot(R, hohmann_data, lw=2)
for jj in range(len(Rstar)):
ax.plot(R, bielliptic_data[:, jj], color=l.get_color())
ax.vlines([11.94, R[idx_max]], *ylims, color="0.6")

if ZOOM:
ax_zoom = zoomed_inset_axes(
ax, 4, loc=4, axes_kwargs={"facecolor": "0.97"}
)
ax_zoom.plot(R, hohmann_data, lw=2)
for jj in range(len(Rstar)):
ax_zoom.plot(R, bielliptic_data[:, jj], color=l.get_color())
ax_zoom.vlines([11.94, R[idx_max]], *ylims, color="0.6")

ax_zoom.set_xlim(11.0, 16.0)
ax_zoom.set_ylim(0.52, 0.545)
ax_zoom.set_xticks([])
ax_zoom.set_yticks([])
ax_zoom.grid(False)
ax_zoom.set_title("4x zoom")
mark_inset(ax, ax_zoom, loc1=1, loc2=3, fc="none", ec="0.3")

ax.set_xlabel("R")
ax.set_ylabel("Relative change in velocity")
ax.set_ylim(*ylims)
ax.set_xlim(2, 75)
ax.set_title("Hohmann vs bielliptic transfers")

fig.savefig("hohmann-bielliptic-transfers.png")