# Orbital Mechanics Simulation - Technical Reference

## Overview
3D orbital mechanics simulation using 2-body gravitational model with sphere of influence (SOI) transitions. Built with C-style C++ and raylib.

## Technical Constraints
- C-style C++ only: structs and functions, no classes or templates
- RK4 (Runge-Kutta 4th order) integration for physics
- Simple rotations (quaternions deferred)
- raylib for 3D visualization
- Single root body systems only (parent_index = -1 for exactly one body)

## Core Data Structures

### Vec3 (physics.h)
```cpp
struct Vec3 {
    double x, y, z;
};
```

### CelestialBody (simulation.h)
```cpp
struct CelestialBody {
    char name[64];
    double mass;              // kg
    double radius;            // meters
    Vec3 local_position;      // position relative to parent (meters)
    Vec3 local_velocity;      // velocity relative to parent (m/s)
    Vec3 position;            // global position (meters from origin)
    Vec3 velocity;            // global velocity (m/s)
    double soi_radius;        // sphere of influence radius (meters)
    int parent_index;         // index of gravitational parent (-1 for root)
    float color[3];           // RGB for rendering
    double eccentricity;      // orbital eccentricity (0 = circular)
    double semi_major_axis;   // meters
};
```

### SimulationState (simulation.h)
```cpp
struct SimulationState {
    CelestialBody* bodies;
    int body_count;
    int max_bodies;
    double time;              // simulation time (seconds)
    double dt;                // time step (seconds)
};
```

### RenderState (renderer.h)
```cpp
struct RenderState {
    Camera3D camera;
    double distance_scale;    // Scale factor for distances
    double size_scale;        // Scale factor for body sizes
    bool show_info;           // Display simulation info
};
```

### OrbitalElements (simulation.h)
```cpp
struct OrbitalElements {
    double time_days;
    double semi_major_axis_au;
    double eccentricity;
    double specific_energy;
    double distance_to_sun_au;
    double distance_to_ref_body_au;
    double velocity_magnitude;
};
```

### AccelerationContext (physics.h)
```cpp
struct AccelerationContext {
    SimulationState* sim;
    CelestialBody* current_body;
    int body_index;
};
```

### OrbitalMetrics (test_utilities.h)
```cpp
struct OrbitalMetrics {
    double kinetic_energy;
    double potential_energy;
    double total_energy;
    double orbital_radius;
    double velocity_magnitude;
    double angular_position;
};
```

### OrbitTracker (test_utilities.h)
```cpp
struct OrbitTracker {
    double initial_angle;
    double previous_angle;
    int quadrant_transitions;
    bool orbit_completed;
    double time_at_completion;
    int body_index;
    double min_time_days;
};
```

## Module Overview

### Physics (physics.cpp/h)
Vector math and gravity calculations. RK4 (Runge-Kutta 4th order) integration with `rk4_step()`. Physics module is independent of simulation structures and accepts direct parameters for improved modularity.

**Key functions:**
- `rk4_step(Vec3* position, Vec3* velocity, double dt, double body_mass, double parent_mass)` - RK4 integration using position/velocity pointers
- `evaluate_acceleration(Vec3 relative_pos, double body_mass, double parent_mass)` - computes gravitational acceleration from parent

### Simulation (simulation.cpp/h)
Simulation state management and updates. SOI detection using Hill sphere: `r_soi = a * (m/M)^(2/5)`.

**Key functions:**
- `find_dominant_body()` - determines which body has gravitational dominance
- `update_soi()` - calculates sphere of influence radius using Hill sphere
- `update_simulation()` - runs one physics step: finds dominant parent, calculates gravity, applies RK4 integration
- `initialize_local_coordinates()` - converts global to local coordinates on load
- `compute_global_coordinates()` - converts local to global coordinates after update
- Dynamic parent switching when bodies cross SOI boundaries (with hysteresis)

**Update Order:**
- Root bodies updated first (in their own frame = global)
- Global coordinates computed for roots
- Child bodies updated in parent's local frame
- Global coordinates computed for all children

### Config Loader (config_loader.cpp/h)
TOML-based config parser using tomlc17 library. Auto-calculates circular orbit velocities and SOI radii.

**Key functions:**
- `parse_toml_body()` - parses individual body entries
- `calculate_initial_velocities()` - sets circular orbit velocities using vis-viva equation
- `calculate_soi_radii()` - computes sphere of influence for all bodies

**Config format details:**
- TOML array of tables: `[[bodies]]`
- Comments start with `#`
- `parent_index = -1` indicates root body (star)
- Supports nested orbits (planets with moons)

**Config format (TOML):**
```toml
[[bodies]]
name = "Sun"
mass = 1.989e30
radius = 6.96e8
position = { x = 0.0, y = 0.0, z = 0.0 }
parent_index = -1
color = { r = 1.0, g = 1.0, b = 0.0 }
eccentricity = 0.0
semi_major_axis = 0.0

[[bodies]]
name = "Earth"
mass = 5.972e24
radius = 6.371e6
position = { x = 1.496e11, y = 0.0, z = 0.0 }
parent_index = 0
color = { r = 0.0, g = 0.5, b = 1.0 }
eccentricity = 0.0
semi_major_axis = 1.496e11
```

### Renderer (renderer.cpp/h)
Raylib 3D visualization with logarithmic distance scaling and size scaling for visibility.

**Orbit rendering:**
- Elliptical orbits: e < 0.98
- Parabolic orbits: 0.98 ≤ e ≤ 1.02 (uses escape trajectory formula)
- Hyperbolic orbits: e > 1.02 (shows asymptotic behavior)
- `render_parabolic_orbit()` renders escape paths with true anomaly range: -π*0.95 to π*0.95

### Test Utilities (test_utilities.cpp/h)
Test helper functions for orbital mechanics validation.

**Key functions:**
- `calculate_kinetic_energy()` - computes kinetic energy of a body
- `calculate_potential_energy_pair()` - computes gravitational potential energy between two bodies
- `calculate_system_total_energy()` - sums total energy of entire system
- `calculate_orbital_metrics()` - returns comprehensive orbital state metrics
- `create_orbit_tracker()` - initializes orbit completion tracking
- `update_orbit_tracker()` - tracks orbital progress and detects completion
- `compare_double()` / `compare_vec3()` - floating-point comparison with tolerance

### Local Coordinate Frames (simulation.cpp/h)
Hierarchical coordinate system for improved numerical precision in nested orbits.

**Key functions:**
- `initialize_local_coordinates()` - initializes local frame positions/velocities from global coordinates
- `compute_global_coordinates()` - computes global positions/velocities from local frames

**Benefits:**
- Eliminates large offsets in floating-point calculations (moon at 3.8×10⁸ m instead of 1.5×10¹¹ m)
- Isolates moon orbits from planetary perturbations
- Maintains full floating-point precision for small orbital changes
- Improved Earth-Moon orbital stability (20% drift → stable)

**Implementation Details:**
- Dual coordinate storage: both local and global coordinates maintained
- Parent bodies treated as origin in child's reference frame during integration
- RK4 integration operates on local coordinates
- Global coordinates computed after each physics step for rendering and SOI checks

### Main Program (main.cpp)
GUI-only application with interactive 3D visualization.
- Initializes simulation with MAX_BODIES=100, TIME_STEP=60 seconds
- Runs 100 physics steps per frame (adjustable with speed multiplier)
- Game loop: input handling → camera update → physics update (if not paused) → rendering
- Supports speed multiplier (2x/0.5x per keypress, min 0.125x)
- Default config: `tests/configs/solar_system.toml`

**Controls:**
- Arrow keys: Rotate and zoom camera
- Space: Pause/Resume
- +/-: Speed up/slow down simulation
- I: Toggle info display
- ESC: Quit

## Build System

### Makefile Targets
- `make` - Build raylib (first time) and compile sources to `orbit_sim`
- `make rebuild` - Clean and rebuild
- `make clean` - Remove build artifacts
- `make clean-all` - Clean everything including raylib
- `make run` - Build and run the simulation
- `make test` - Run full automated test suite
- `make test-build` - Build test executable

### Dependencies
- g++ (C++14)
- raylib (built automatically from `ext/raylib/src`)
- tomlc17 (included in `ext/tomlc17/src`)
- Catch2 (for testing)
- libX11, libGL, libpthread (system libraries)

### Test Infrastructure
- **Framework**: Catch2 for unit testing
- **Test Configs**: `tests/configs/` contains test scenarios
  - `solar_system.toml` - Full solar system with moons
  - `earth_circular.toml`, `mars_circular.toml` - Simple orbital tests
  - `parabolic_comet.toml` - Parabolic orbit (e=1.0)
  - `hyperbolic_comet.toml` - Hyperbolic orbit (e>1.0)
  - `soi_transition.toml` - SOI crossing test (3-body system)
- **Test Files**:
  - `test_energy.cpp` - Energy conservation validation
  - `test_moon_orbits.cpp` - Moon orbital stability tests
  - `test_orbital_period.cpp` - Orbital period verification
  - `test_parabolic_orbit.cpp` - Parabolic orbit tests
  - `test_hyperbolic_orbit.cpp` - Hyperbolic orbit tests
  - `test_soi_transition.cpp` - SOI transition validation

## Orbit Types

### Elliptical Orbits (0 ≤ e < 1)
- Standard planetary and moon orbits
- Eccentricity e = 0 (circular) to e < 1 (elliptical)
- Total energy is negative (bound to parent)
- Velocity follows vis-viva equation: `v² = GM(2/r - 1/a)`

### Parabolic Orbits (e = 1)
- Escape trajectories with exactly escape velocity
- Total energy is zero (marginally unbound)
- Escape velocity: `v² = 2GM/r`
- Rendered using true anomaly range: -π*0.95 to π*0.95
- Used for comets on escape trajectories

### Hyperbolic Orbits (e > 1)
- Fast escape trajectories exceeding escape velocity
- Total energy is positive (unbound)
- Asymptotic velocity: `v∞ = √(2GM/|a|)` where a < 0
- Shows open curve with asymptotic behavior
- Used for high-speed comets and interstellar objects

## Data Flow

### Initialization Sequence
1. Configuration file → `load_system_config()` → populates `SimulationState`
2. `calculate_initial_velocities()` → sets circular orbit velocities for all bodies
3. `calculate_soi_radii()` → computes sphere of influence for each body

### Main Simulation Loop
1. `update_simulation()` → for each body:
   - `find_dominant_body()` → determine gravitational parent based on SOI
   - `evaluate_acceleration()` → compute gravitational force from parent
   - `rk4_step()` → update position/velocity using Runge-Kutta 4th order
2. `render_simulation()` → for each body:
   - `scale_position()` → convert to render coordinates using logarithmic scaling
   - `scale_radius()` → convert to render size using exponential scaling
   - `render_body()` → draw sphere with color

### SOI Transition Mechanics
- Bodies dynamically switch gravitational parents when crossing SOI boundaries
- Uses 0.5x distance hysteresis to prevent oscillation between parents
- `find_dominant_body()` checks all bodies and selects most dominant influence

## Implementation Status

### ✅ Completed
- Phase 1-4: Core physics, simulation, config loading, and rendering
- Raylib integration with 3D camera
- Distance and size scaling for visualization
- TOML config file system with solar system configs (includes Sun + 8 planets + 6 moons)
- RK4 (Runge-Kutta 4th order) integration for improved accuracy
- Time scaling controls (speed up/slow down simulation)
- Pause/resume functionality
- Orbital elements calculation
- **Hierarchical coordinate frames (local + global storage)**
- **Parent-first update order for stability**
- **Parabolic orbit support (e=1.0)**
- **Hyperbolic orbit support (e>1.0)**
- **Physics module refactoring (parameter-based signatures)**
- **Comprehensive test suite (8 test files, 39+ assertions)**
- **Build system with automated testing**
- **UI body selection and information display (raygui integration)**
- **Camera follow feature for selected bodies**
- **Camera follow improvements: distance preservation and proper orbital rotation**

### 🔨 Remaining/Future Work
- More accurate integration methods (Newton-Raphson propagation)
- Reference frame switching
- SOI transition frame transformations (Phase 3 of hierarchical frames)
- Io and Titan orbital stability tuning

## Technical Notes

### Code Style and Architecture
- C-style C++: structs and functions only, no classes or templates
- All headers use include guards
- Memory management uses malloc/free
- Layer separation: Physics, Simulation, Configuration, Rendering layers
- Physics module is independent of simulation structures (parameter-based signatures)

### Scaling for Visualization
- Distance: logarithmic/power-law scaling for solar system scale
- Size: minimum visible radius to prevent tiny bodies from disappearing
- Origin at Sun for simplicity
- Both distance_scale and size_scale are configurable in RenderState

### Physics Considerations
- Timestep: 60 seconds for solar system scale
- Circular orbit velocity: `v = sqrt(G * M / r)`
- Physics steps per frame: 100 (default) with speed multiplier adjustment
- Simulation time per frame: 60s * 100 = 6000 seconds at 1x speed
- SOI (Sphere of Influence) uses Hill sphere approximation: `r_soi = a * (m/M)^(2/5)`
- SOI transitions use 0.5x distance hysteresis to prevent oscillation
- Parabolic orbits use escape velocity: `v² = 2GM/r`
- Hyperbolic orbits have positive total energy and asymptotic velocity

## Future Enhancements
- More accurate integration methods (Newton-Raphson propagation)
- Reference frame switching
- 3D orbital visualization with inclination
- SOI transition frame transformations (Phase 3 of hierarchical frames)
- Camera focus on selected body
- Visual highlighting of selected body in 3D view
- Enhanced UI features (search, multiple selection, orbital metrics)