Update implementation_plan.md to reflect current code: RK4 integration, TOML config format, add missing structures, move completed features

docs/implementation_plan.md

@@ -5,7 +5,7 @@
 
 ## Technical Constraints
 - C-style C++ only: structs and functions, no classes or templates
-- Euler integration for physics
+- RK4 (Runge-Kutta 4th order) integration for physics
 - Simple rotations (quaternions deferred)
 - raylib for 3D visualization
 
@@ -55,22 +55,60 @@ struct RenderState {
 };
 ```
 
+### OrbitalElements (bodies.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;
+};
+```
+
 ## Module Overview
 
 ### Physics (physics.cpp/h)
-Vector math and gravity calculations. Euler integration with `euler_step()`.
+Vector math and gravity calculations. RK4 (Runge-Kutta 4th order) integration with `rk4_step()`.
 
 ### Bodies (bodies.cpp/h)
 Simulation state management and updates. SOI detection using Hill sphere: `r_soi = a * (m/M)^(2/5)`
 
 ### Config Loader (config_loader.cpp/h)
-Text-based config parser. Auto-calculates circular orbit velocities and SOI radii.
-
-**Config format:**
-```
-# name mass(kg) radius(m) x(m) y(m) z(m) parent_index r g b
-Sun 1.989e30 6.96e8 0 0 0 -1 1.0 1.0 0.0
-Earth 5.972e24 6.371e6 1.496e11 0 0 0 0.0 0.5 1.0
+TOML-based config parser using tomlc17 library. Auto-calculates circular orbit velocities and SOI radii.
+
+**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)
@@ -82,13 +120,17 @@ Raylib 3D visualization with logarithmic distance scaling and size scaling for v
 - Phase 1-4: Core physics, simulation, config loading, and rendering
 - Raylib integration with 3D camera
 - Distance and size scaling for visualization
-- Config file system with solar_system.txt
+- TOML config file system with solar_system.toml, example_binary_star.toml, test_simple.toml
+- RK4 (Runge-Kutta 4th order) integration for improved accuracy
+- Time scaling controls (speed up/slow down simulation)
+- Pause/resume functionality
+- Orbital elements calculation
+- Binary/multiple star system support with barycentric orbits
 
 ### 🔨 Remaining/Future Work
-- Time scaling controls (speed up/slow down)
-- Pause/resume functionality
-- Additional config files (binary star, etc.)
-- Time step tuning for stability
+- More accurate integration methods (Newton-Raphson propagation)
+- Interactive body selection
+- Reference frame switching
 
 ## Technical Notes
 
@@ -103,6 +145,7 @@ Raylib 3D visualization with logarithmic distance scaling and size scaling for v
 - May need multiple physics sub-steps per render frame
 
 ## Future Enhancements
-- More accurate integration (RK4, Verlet), NOTE: try Newton-Raphson propagation method with testing first
+- More accurate integration methods (Newton-Raphson propagation)
 - Interactive body selection
 - Reference frame switching
+- 3D orbital visualization with inclination