5.3. Case Study

5.3.1. ISS Ground Track

Source: https://beyond.readthedocs.io/en/latest/examples.html:

#!/usr/bin/env python

"""Script showing the position of the ISS at the time of the TLE
and the ground track for the previous and the next orbit
"""

import sys
from pathlib import Path

import matplotlib.pyplot as plt
import numpy as np

from beyond.io.tle import Tle
from beyond.dates import Date, timedelta


# Parsing of TLE
tle = Tle("""ISS (ZARYA)
1 25544U 98067A   19004.59354167  .00000715  00000-0  18267-4 0  9995
2 25544  51.6416  95.0104 0002419 236.2184 323.8248 15.53730729149833""")

# Conversion into `Orbit` object
orb = tle.orbit()

# Tables containing the positions of the ground track
latitudes, longitudes = [], []
prev_lon, prev_lat = None, None

period = orb.infos.period
start = orb.date - period
stop = 2 * period
step = period / 100

for point in orb.ephemeris(start=start, stop=stop, step=step):

    # Conversion to earth rotating frame
    point.frame = 'ITRF'

    # Conversion from cartesian to spherical coordinates (range, latitude, longitude)
    point.form = 'spherical'

    # Conversion from radians to degrees
    lon, lat = np.degrees(point[1:3])

    # Creation of multiple segments in order to not have a ground track
    # doing impossible paths
    if prev_lon is None:
        lons = []
        lats = []
        longitudes.append(lons)
        latitudes.append(lats)
    elif orb.i < np.pi /2 and (np.sign(prev_lon) == 1 and np.sign(lon) == -1):
        lons.append(lon + 360)
        lats.append(lat)
        lons = [prev_lon - 360]
        lats = [prev_lat]
        longitudes.append(lons)
        latitudes.append(lats)
    elif orb.i > np.pi/2 and (np.sign(prev_lon) == -1 and np.sign(lon) == 1):
        lons.append(lon - 360)
        lats.append(lat)
        lons = [prev_lon + 360]
        lats = [prev_lat]
        longitudes.append(lons)
        latitudes.append(lats)

    lons.append(lon)
    lats.append(lat)
    prev_lon = lon
    prev_lat = lat

img = Path(__file__).parent / "earth.png"

im = plt.imread(str(img))
plt.figure(figsize=(15.2, 8.2))
plt.imshow(im, extent=[-180, 180, -90, 90])

for lons, lats in zip(longitudes, latitudes):
    plt.plot(lons, lats, 'r')

lon, lat = np.degrees(orb.copy(frame='ITRF', form='spherical')[1:3])
plt.plot([lon], [lat], 'ro')

plt.xlim([-180, 180])
plt.ylim([-90, 90])
plt.grid(True, color='w', linestyle=":", alpha=0.4)
plt.xticks(range(-180, 181, 30))
plt.yticks(range(-90, 91, 30))
plt.tight_layout()

if "no-display" not in sys.argv:
    plt.show()  # doctest: +SKIP

5.3.2. ISS Hohmann transfer

https://beyond.readthedocs.io/en/latest/examples.html:

"""Example of Hohmann transfer

The orbit we are starting with is a Tle of the ISS. The amplitude of the maneuver is greatly
exagerated regarding the ISS's capability, but has the convenience to be particularly visual.
"""

import sys

import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d import Axes3D

from beyond.io.tle import Tle
from beyond.dates import timedelta
from beyond.propagators.keplernum import KeplerNum
from beyond.env.solarsystem import get_body
from beyond.orbits.man import ImpulsiveMan
from beyond.orbits.listeners import ApsideListener, find_event


orb = Tle("""ISS (ZARYA)
1 25544U 98067A   18124.55610684  .00001524  00000-0  30197-4 0  9997
2 25544  51.6421 236.2139 0003381  47.8509  47.6767 15.54198229111731""").orbit()

start = orb.date
stop = timedelta(minutes=300)
step = timedelta(seconds=60)

# Changing the propagator to Keplerian, as SGP4 is not able to perform maneuvers
orb.propagator = KeplerNum(step, bodies=get_body("Earth"))

# Research for the next perigee
perigee = find_event(orb.iter(stop=stop, listeners=ApsideListener()), 'Periapsis')

man1 = ImpulsiveMan(perigee.date, (280, 0, 0), frame="TNW")
orb.maneuvers = [man1]

dates1, alt1 = [], []

# Research for the next apogee after the first maneuver
apogee = find_event(orb.iter(start=perigee.date - step * 10, stop=stop, listeners=ApsideListener()), 'Apoapsis')
# apogee = find_event(orb.iter(stop=stop, listeners=ApsideListener()), 'Apoapsis', offset=1)

# Adding the second maneuver to the orbit
man2 = ImpulsiveMan(apogee.date, (270, 0, 0), frame="TNW")
orb.maneuvers.append(man2)

print(man1.date)
print(man2.date)

# Propagation throught the two maneuvers
ephem = orb.ephem(start=start, stop=stop, step=step)

# graphs
plt.figure()

data = np.array(ephem)
dates = [x.date for x in ephem]
# Altitude in km
alt = (np.linalg.norm(data[:, :3], axis=1) - orb.frame.center.body.r) / 1000
events_dates = [perigee.date, apogee.date]
events_alt = (np.linalg.norm([perigee[:3], apogee[:3]], axis=1) - orb.frame.center.body.r) / 1000

plt.plot(dates, alt)
plt.plot([events_dates[0]], [events_alt[0]], 'ro', label="perigee")
plt.plot([events_dates[1]], [events_alt[1]], 'ko', label="apogee")

plt.ylabel("altitude (km)")
plt.legend()
plt.grid(linestyle=':', alpha=0.4)
plt.tight_layout()

fig = plt.figure()
ax = plt.gca(projection='3d')
ax.view_init(elev=52, azim=140)

x, y, z = zip(perigee[:3], apogee[:3])

plt.plot(data[:, 0], data[:, 1], data[:, 2])
plt.plot([perigee[0]], [perigee[1]], [perigee[2]], 'ro')
plt.plot([apogee[0]], [apogee[1]], [apogee[2]], 'ko')

if "no-display" not in sys.argv:
    plt.show()  # doctest: +SKIP

5.3.3. COVID-19

• Data Source: https://github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_data/csse_covid_19_time_series

• https://www.youtube.com/watch?v=54XLXg4fYsc

• https://github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_data/csse_covid_19_time_series

• https://aatishb.com/covidtrends/?location=Poland

• https://aatishb.com/covidtrends/?location=Brazil&location=China&location=India&location=Poland&location=Russia&location=US

• https://youtu.be/xtZYKcOdJp0?t=168

import matplotlib.pyplot as plt
import pandas as pd

# CONFIRMED = 'https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_global.csv'
# RECOVERED = 'https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_recovered_global.csv'
# DEATHS = 'https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_deaths_global.csv'

CONFIRMED = 'https://python3.info/_static/covid19-confirmed.csv'
RECOVERED = 'https://python3.info/_static/covid19-recovered.csv'
DEATHS = 'https://python3.info/_static/covid19-deaths.csv'

confirmed = pd.read_csv(CONFIRMED)
deaths = pd.read_csv(DEATHS)
recovered = pd.read_csv(RECOVERED)


def plot(name: str) -> None:
    # Select matching country
    c = confirmed['Country/Region'] == name
    d = deaths['Country/Region'] == name
    r = recovered['Country/Region'] == name

    # Merge data and discard not needed columns
    df = pd.concat([
        confirmed.loc[c].transpose()[4:],
        deaths.loc[d].transpose()[4:],
        recovered.loc[r].transpose()[4:]
    ], axis=1, keys=['Confirmed', 'Deaths', 'Recovered'])

    # Set columns and index
    df.columns = df.columns.droplevel(1)
    df.index = pd.to_datetime(df.index)
    df.sort_index(ascending=True, inplace=True)

    # Create figure and axis objects
    fig, ax = plt.subplots(
        nrows=3,
        ncols=1,
        sharex=True,
        sharey=False,
        gridspec_kw={'height_ratios': [2, 1, 1]},
        figsize=(15, 5))

    # Set layout for 'Confirmed' cases
    ax[0].plot(df['Confirmed'], color='red')
    ax[0].set_ylim(ymin=0, ymax=None)
    ax[0].set_ylabel('Confirmed')
    ax[0].grid(True, which='major')

    # Set layout for 'Deaths' cases
    ax[1].plot(df['Deaths'], color='black')
    ax[1].set_ylim(ymin=0, ymax=None)
    ax[1].set_ylabel('Deaths')
    ax[1].grid(True, which='major')

    # Set layout for 'Recovered' cases
    ax[2].plot(df['Recovered'], color='green')
    ax[2].set_ylim(ymin=0, ymax=None)
    ax[2].set_ylabel('Recovered')
    ax[2].grid(True, which='major')

    # Set general layout for figure (all axis)
    fig.tight_layout()
    plt.setp(ax[2].get_xticklabels(), rotation=45, horizontalalignment='right')
    plt.show()  # doctest: +SKIP

plot('Poland')
plot('Germany')
plot('France')
plot('Spain')
plot('Italy')