Interactive Learning

Python Simulations

Modify and run Python code directly in your browser to explore the principles of orbital mechanics.

Before You Begin

Python Prerequisites

Basic Python Knowledge Recommended

These simulations allow you to modify and execute Python code directly in your browser. A basic understanding of Python syntax will help you change parameters, understand calculations, and interpret the results.

No local installation is required

Python runs directly on this page through Pyodide. However, users should be familiar with variables, mathematical operations, functions, lists, and basic Python syntax.

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Simulation Library

Choose a Simulation

Select a simulation, adjust its Python parameters, and compare the numerical and graphical results.

Available Simulations

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Python Library

Available Functions

The following constants and functions are already implemented in the SpaceOrbitLAB Python library and can be used directly in the simulations.

Earth.mu

Earth's standard gravitational parameter in km³/s².

sind(angle)

Computes the sine of an angle expressed in degrees.

cosd(angle)

Computes the cosine of an angle expressed in degrees.

tand(angle)

Computes the tangent of an angle expressed in degrees.

RotX(angle)

Creates a rotation matrix around the X-axis. The angle is expressed in degrees.

RotY(angle)

Creates a rotation matrix around the Y-axis. The angle is expressed in degrees.

RotZ(angle)

Creates a rotation matrix around the Z-axis. The angle is expressed in degrees.

KeplerSolver(M, e)

Solves Kepler's equation from the mean anomaly and eccentricity. Returns the eccentric anomaly and true anomaly.

COE_to_SV(a, e, i, RAAN, argp, nu, mu)

Converts classical orbital elements into inertial position and velocity vectors.

OrbitPropagation_2BN(SV, time_s)

Propagates an orbit by numerically solving Newton's two-body equations of motion.

OrbitPropagation_2BK(a, e, i, RAAN, w, nu0, t_array, mu)

Propagates an elliptical orbit from classical orbital elements using the two-body Keplerian model.

Example


                                from SOL import Earth, RotX, KeplerSolver, COE_to_SV, OrbitPropagation_2BK

Select a simulation from the menu above to display it here.

Simulation 01

Circular Orbit

Change altitude_km to observe how altitude affects orbital velocity and period.

Python Editor circular_orbit.py

import numpy as np
import matplotlib.pyplot as plt

from SOL import Earth

# Earth constants
mu = Earth.mu                 # km³/s²
R_earth = Earth.r1_km         # km

# Change this value
altitude_km = 400.0

# Orbital radius
radius_km = R_earth + altitude_km

# Orbital velocity
velocity_km_s = np.sqrt(
    mu / radius_km
)

# Orbital period
period_s = (
    2 * np.pi
    * np.sqrt(radius_km**3 / mu)
)

print(f"Altitude: {altitude_km:.1f} km")
print(f"Orbital radius: {radius_km:.1f} km")
print(f"Orbital velocity: {velocity_km_s:.3f} km/s")
print(f"Orbital period: {period_s / 60:.2f} minutes")

# Orbit visualization
theta = np.linspace(
    0,
    2 * np.pi,
    800
)

x = radius_km * np.cos(theta)
y = radius_km * np.sin(theta)

fig, ax = plt.subplots(
    figsize=(7, 7)
)

earth = plt.Circle(
    (0, 0),
    R_earth,
    color="#1768a8",
    label="Earth"
)

ax.add_patch(earth)

ax.plot(
    x,
    y,
    color="#ef6b3a",
    linewidth=2.5,
    label="Orbit"
)

ax.scatter(
    [radius_km],
    [0],
    color="#ffffff",
    edgecolor="#091827",
    s=70,
    zorder=5,
    label="Satellite"
)

limit = radius_km * 1.2

ax.set_xlim(
    -limit,
    limit
)

ax.set_ylim(
    -limit,
    limit
)

ax.set_aspect("equal")

ax.set_xlabel(
    "X position (km)"
)

ax.set_ylabel(
    "Y position (km)"
)

ax.set_title(
    "Circular Earth Orbit"
)

ax.grid(
    alpha=0.2
)

ax.legend()

Simulation Result Matplotlib

Run the code to generate the orbit.

Python Output

Waiting for execution…

Simulation 02

Elliptical Orbit

Change semi_major_axis_km and eccentricity to modify the orbit.

Python Editor elliptical_orbit.py

import numpy as np
import matplotlib.pyplot as plt

from SOL import Earth, OrbitPropagation_2BK

# =========================
# ORBITAL PARAMETERS
# =========================

# Semi-major axis [km]
a = 12000.0

# Eccentricity [-]
e = 0.45

# Inclination [deg]
i = 0.0

# Right Ascension of the Ascending Node [deg]
RAAN = 0.0

# Argument of perigee [deg]
w = 0.0

# Initial true anomaly [deg]
nu0 = 0.0

# Earth's gravitational parameter [km^3/s^2]
mu = Earth.mu

# Earth's equatorial radius [km]
R_earth = Earth.r1_km

# =========================
# VALIDATION
# =========================

if a <= 0:
    raise ValueError(
        "The semi-major axis must be positive."
    )

if not 0 <= e < 1:
    raise ValueError(
        "Eccentricity must be between 0 and 1."
    )

# =========================
# ORBITAL PERIOD
# =========================

period_s = 2 * np.pi * np.sqrt(
    a**3 / mu
)

# Time array for one complete orbit
t_array = np.linspace(
    0,
    period_s,
    1000
)

# =========================
# ORBIT PROPAGATION
# =========================

ECI_pos, ECI_vel, nu = OrbitPropagation_2BK(
    a,
    e,
    i,
    RAAN,
    w,
    nu0,
    t_array,
    mu
)

# =========================
# ORBIT INFORMATION
# =========================

periapsis_km = a * (1 - e)
apoapsis_km = a * (1 + e)

print(f"Semi-major axis: {a:.1f} km")
print(f"Eccentricity: {e:.3f}")

print(
    f"Periapsis radius: "
    f"{periapsis_km:.1f} km"
)

print(
    f"Apoapsis radius: "
    f"{apoapsis_km:.1f} km"
)

print(
    f"Periapsis altitude: "
    f"{periapsis_km - R_earth:.1f} km"
)

print(
    f"Apoapsis altitude: "
    f"{apoapsis_km - R_earth:.1f} km"
)

print(
    f"Orbital period: "
    f"{period_s / 60:.2f} minutes"
)

# =========================
# POSITION DATA
# =========================

x = ECI_pos[0, :]
y = ECI_pos[1, :]

# =========================
# VISUALIZATION
# =========================

fig, ax = plt.subplots(
    figsize=(8, 7)
)

# Earth
earth = plt.Circle(
    (0, 0),
    R_earth,
    color="#1768a8",
    label="Earth"
)

ax.add_patch(earth)

# Orbit
ax.plot(
    x,
    y,
    color="#ef6b3a",
    linewidth=2.5,
    label="Orbit"
)

# Initial satellite position
ax.scatter(
    [x[0]],
    [y[0]],
    color="#ffffff",
    edgecolor="#091827",
    s=70,
    zorder=5,
    label="Satellite"
)

# =========================
# GRAPH SETTINGS
# =========================

limit = apoapsis_km * 1.15