What free Python can do vs Wolfram Mathematica

Capability	Python (free)	Mathematica ($$$)
Orbital mechanics equations	NumPy/SciPy — full coverage	Built-in symbolic + numeric
JPL Horizons ephemeris data	REST API + gzip/json (as shown above)	HorizonsEphemerisData[] function
Unit-aware calculations	Pint library	Built-in Quantity framework
2D/3D trajectory plots	Matplotlib (4-panel dashboard above)	Built-in Graphics3D + Manipulate
Real-time ephemeris data	Astropy + JPL Horizons API	Built-in AstronomicalData[]
Interactive animation	ipywidgets / Plotly	Manipulate[] — seamless
Symbolic algebra	SymPy	Native — Mathematica's core strength
Deployment	Runs anywhere (browser via Pyodide)	Requires Wolfram licence or Cloud

Verdict: Using the same JPL Horizons data source as Wolfram, Python reproduces the Artemis II trajectory with identical data points — 428 state vectors covering the full 10-day mission. The analytical model (Hohmann transfer + patched conics) predicts TLI speed within 3% and flyby distance within 0.4% of reality.

Mathematica's edge is in symbolic manipulation and the seamless Manipulate[] 3D animation. But for numerical computation, data analysis, and reproducibility, Python is fully capable — and this entire blueprint runs in the browser via Pyodide. No server, no licence, no installation.

天体物理学

蓝图 (1)

Artemis II - JPL Horizons Flight Data