Energy, Momentum, and Angular Momentum | Conserved Quantities | Reading the energy plot | What Orbit Is It Actually On? | A note on the gravitational parameter | Continuing a Run | Editing between segments

The Six Elements | Shape: Semi-Major Axis and Eccentricity | Orientation: Inclination, Longitude of Ascending Node, and Argument of Periapsis | Position: True Anomaly | Hyperbolic Orbits | The Conversion: Elements to Cartesian | Using add_planet() for Quick Setup | Keplerian vs. Cartesian: When to Use Which

The Problem of Scale | Shifting the Reference Frame | How It Works | Keeping vs. Removing the Center Body | Multiple Perspectives on the Same Data | The Barycentric Frame | Analyzing Relative Velocities | A Binary Star System from the Planet's View | Practical Tips

Physics | A radius argument on add_body() | Non-gravitational forces | General-relativistic corrections | Setup helpers | ~~Construct bodies from Keplerian orbital elements~~ ✅ Added in v0.2.0 | ~~A load_solar_system() convenience~~ ✅ Added in v0.2.0 | Quality of life | ~~Save and load simulation state~~ ✅ Added in v0.3.0 | Progress bar for long simulations | Built-in conservation diagnostics ✅ Added in v1.0.0 | Variable time steps ✅ Partly addressed in v1.0.0 | Suggestions Welcome

Gravitational Acceleration | Why Initial Velocity Matters | Gravitational Softening | Numerical Integration Methods | 1. Velocity Verlet (default, method = "verlet") | 2. Euler-Cromer (method = "euler_cromer") | 3. Standard Euler (method = "euler") | Comparing the Three Methods | Keplerian Orbital Elements | From Elements to Cartesian State Vectors | Kepler's Laws and the Simulation | The C++ Engine

Installation | Your First Simulation in 30 Seconds | Customizing the Plot | Watching the Orbit in Motion | Adding More Bodies | Removing Bodies | Inspecting a System | The Output is Just a Tibble | Saving and Sharing Systems | Next Steps

The Full Solar System | The Inner Solar System | The Earth-Moon System | The Sun-Earth System | The Three-Body Problem (Sun-Earth-Moon) | Shifting Your Point of View | The Kepler-16 System: A Real Circumbinary Planet | A Comet Crossing the Inner Solar System | What-If: Circular Mars

Books | Classical Dynamics of Particles and Systems — Stephen T. Thornton & Jerry B. Marion (5th ed., 2004, Brooks/Cole) | Computational Physics — Mark Newman (2012, CreateSpace) | Data Structures & Algorithms in Python — John Canning, Alan Broder & Robert Lafore (2022, Addison-Wesley) | Online Documentation | Rcpp Documentation — CRAN | Acknowledgments

How the 2D/3D Dispatch Works | A Tilted Lunar Orbit | Forcing 3D for Flat Data

The Convention: Central Body at the Origin | Why Velocity Must Be Perpendicular to Position | The Circular Orbit Velocity | What Happens If You Get the Speed Wrong? | Escape Velocity | Which Direction Does the Orbit Go? | Rotating the Whole Setup | When the Central Body Isn't Much Heavier | Recap

Masses | Orbital Distances (Semi-Major Axes) | Mean Orbital Speeds | Using the Constants | Why "Distance" Constants Are Semi-Major Axes

The Raw Output | Custom ggplot2 Visualizations | Custom plotly Visualizations

A Chaotic Triple-Star System | Troubleshooting Unstable Simulations