polaris

polaris --- PythOnLibrary for AstRodynamIcS

polaris is a Python library for preliminary spacecraft trajectory design.

The full documentation can be found here. <--! in development! -->

Installation

Install via pip

pip install astro-polaris

or clone this repository with

$ git clone https://github.com/Yuricst/polaris.git

Dependencies

Core dependencies are

• numba, numpy, pandas, scipy

Although not necessary to run polaris, the following packages are also used within the example scripts and Jupyter notebooks:

• tqdm, plotly

Imports

Subpackages within polaris are imported as

import polaris.SolarSystemConstants as ssc
import polaris.Propagator as prop
import polaris.R3BP as r3bp
import polaris.Keplerian as kepl
import polaris.Coordinates as coord
import polaris.LinearOrbit as lino

For examples, go to ./examples/ to see Jupyter notebook tutorials.

Quick Example

Here is a quick example of constructing a halo orbit in the Earth-Moon system. We first import the module

import numpy as np
import matplotlib.pyplot as plt

import polaris.Propagator as prop
import polaris.R3BP as r3bp

Define the CR3BP system parameters via

param_earth_moon = r3bp.CR3BP('399','301')   # NAIF ID's '399': Earth, '301': Moon
param_earth_moon.mu

We construct an initial guess of a colinear halo orbit at Earth-Moon L2 with z-direction amplitude of 4000 km via the Lindstedt*–*Poincaré method

haloinit = r3bp.get_halo_approx(mu=param_earth_moon.mu, lp=2, lstar=param_earth_moon.lstar, 
                                az_km=4000, family=1, phase=0.0)

We then apply differential correction on the initial guess

p_conv, state_conv, flag_conv = r3bp.ssdc_periodic_xzplane(param_earth_moon, haloinit["state_guess"], 
                                                           haloinit["period_guess"], fix="z", message=False)

We finally propagate the result

prop0 = prop.propagate_cr3bp(param_earth_moon, state_conv, p_conv)

and plot the result

plt.rcParams["font.size"] = 20
fig, axs = plt.subplots(1, 3, figsize=(18, 8))
axs[0].plot(prop0.xs, prop0.ys)
axs[0].set(xlabel='x, canonical', ylabel='y, canonical')
axs[1].plot(prop0.xs, prop0.zs)
axs[1].set(xlabel='x, canonical', ylabel='z, canonical')
axs[2].plot(prop0.ys, prop0.zs)
axs[2].set(xlabel='y, canonical', ylabel='z, canonical')
for idx in range(3):
    axs[idx].grid(True)
    axs[idx].axis("equal")
plt.suptitle('L2 halo')
plt.tight_layout(rect=[0, 0.01, 1, 1.03])
plt.show()

We can also construct the manifolds of this halo orbit; consider for example the case of constructing its stable manifold

mnfpls, mnfmin = r3bp.get_manifold(param_earth_moon, state_conv, p_conv, tf_manif=5.0,
                                   stable=True, force_solve_ivp=False)

we can now plot

plt.rcParams["font.size"] = 20
fig, ax = plt.subplots(1,1, figsize=(12,8))
for branch in mnfpls.branches:
    ax.plot(branch.propout.xs, branch.propout.ys, linewidth=0.8, c='deeppink')
    
for branch in mnfmin.branches:
    ax.plot(branch.propout.xs, branch.propout.ys, linewidth=0.8, c='dodgerblue')

ax.set(xlabel='x, canonical', ylabel='y, canonical', title='Stable manifold of the L2 halo')
plt.grid(True)
plt.axis("equal")
plt.show()