Orbital Mechanics & Astrodynamics — Installation

What You're Setting Up

Overview's circular orbital velocity and period equations are closed-form and hand-calculable. This section sets up a Python environment for those calculations, plus an introduction to GMAT (NASA's General Mission Analysis Tool) — the standard free, open-source tool for real mission design, going beyond this guide's idealized two-body examples into full mission trajectory design and optimization.

Install Python

bash

python3 --version
pip install numpy

Verify Your Setup — Recompute Overview's ISS Example

This reproduces Overview's worked orbital velocity and period calculation (μ = 398,600 km³/s², r = 6,778 km).

python

import math

MU_EARTH = 398600  # km^3/s^2

def orbital_velocity(r, mu=MU_EARTH):
    return math.sqrt(mu / r)

def orbital_period(r, mu=MU_EARTH):
    return 2 * math.pi * math.sqrt(r**3 / mu)

r = 6378 + 400  # Earth radius + ISS altitude, km
v = orbital_velocity(r)
T = orbital_period(r)
print(f"Orbital velocity = {v:.3f} km/s")
print(f"Orbital period = {T:.1f} s ({T/60:.1f} minutes)")

Expected output:
Orbital velocity = 7.669 km/s
Orbital period = 5553.5 s (92.6 minutes)

This matches Overview's hand-computed ~7.669 km/s and ~92.6 minutes
exactly, confirming your environment works and the formulas
transcribe to code identically.

A Second Check — the Try It Satellite

Reproducing Overview's Try It exercise (700 km altitude) as a second, independent check:

python

r2 = 6378 + 700
v2 = orbital_velocity(r2)
T2 = orbital_period(r2)
print(f"Orbital velocity = {v2:.3f} km/s")
print(f"Orbital period = {T2:.1f} s ({T2/60:.1f} minutes)")

Expected output:
Orbital velocity = 7.504 km/s
Orbital period = 5926.2 s (98.8 minutes)

Matches Overview's Try It answer (7.504 km/s, 98.8 minutes) exactly
— slower and longer-period than the lower ISS-altitude orbit,
consistent with Kepler's Third Law.

Install GMAT for Real Mission Design

GMAT (General Mission Analysis Tool) is NASA's free, open-source, actively maintained tool for real space mission design, trajectory optimization, and navigation — used for actual NASA and industry mission planning, not just idealized textbook orbits.

bash

# Download the current release (GMAT is distributed as OS-specific
# bundled installers) from either:
# https://sourceforge.net/projects/gmat/
# https://github.com/nasa/GMAT/releases

(needs verification — recheck against current source: GMAT release versions and installer details change with each release cycle — confirm the current version and installation steps at the links above rather than assuming a fixed version number.)

A Note on Python Astrodynamics Libraries

If searching for a Python-native astrodynamics library beyond the basic formulas above, be aware that poliastro — a once-popular pure-Python astrodynamics library — was archived and became unmaintained in October 2023. hapsira is the actively maintained community fork that continues its development, validated against GMAT and other established astrodynamics software. If you encounter tutorials or examples referencing poliastro specifically, check whether they still work against the current package or whether the hapsira fork is the better current choice before relying on either for real work.

Verify Everything Works

bash

# 1. Confirm the ISS-example check prints 7.669 km/s and 92.6 minutes

# 2. Confirm the second check (700 km altitude) prints 7.504 km/s
#    and 98.8 minutes

# 3. Open GMAT, load one of its built-in mission example scripts
#    (GMAT ships with several), and run it — confirm it produces a
#    real propagated orbit/trajectory output, not just an error

Common Setup Issues

Computed velocity or period doesn't match the expected output

Confirm r is computed as Earth's radius PLUS altitude, not altitude alone — this is the single most common mistake in orbital mechanics calculations generally (Overview's own example is explicit about this: r = 6,378 + 400 = 6,778 km, not just 400 km).

GMAT installer fails or won't launch after installing

Confirm your OS meets GMAT's current documented system requirements (listed in the release's own README) — GMAT is a substantial desktop application with real dependencies, and an installation failure is more often a missing system dependency than a corrupted download.

Confusion between poliastro and hapsira package names in example code found online

Since poliastro is archived (as of October 2023) but plenty of existing tutorials/StackOverflow answers still reference it by name, treat any import poliastro example found online as potentially outdated — check whether hapsira (the maintained fork) is the more current choice for the same functionality before installing either.

What's Set Up

•Python 3 + NumPy — for orbital velocity/period calculations throughout this guide

•GMAT — for real mission trajectory design and optimization beyond this guide's idealized two-body examples

Next Steps

Go to the Fundamentals section to continue building on Kepler's laws with orbital elements and elliptical (non-circular) orbits.