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+# Session Summary - 2026-01-30 - Newton-Raphson Propagation Planning
+
+## Overview
+Session focused on creating a comprehensive implementation plan for Newton-Raphson analytical propagation to replace RK4 integration, enabling much larger simulation timesteps.
+
+## Changes Made
+
+### New Files Created
+- **docs/newton_raphson_propagation_plan.md** (538 lines)
+  - Complete implementation plan for analytical propagation
+  - 5 implementation phases (30-44 hours estimated)
+  - Hybrid approach: analytical propagation (99% of time) + RK4 during burns (1%)
+  - Detailed algorithms, technical challenges, performance analysis
+  - Migration strategy and success criteria
+
+### Files Modified
+- None (documentation only)
+
+## Commits
+- **c455c78**: Add Newton-Raphson analytical propagation implementation plan
+
+## Results
+
+### Key Insights from Time Step Stability Analysis (Previous Session)
+- RK4 at 60s is very stable (only 22% of stability limit)
+- Mercury orbiter at 200km altitude is limiting factor: 270s max stable dt
+- Io and Moon are very stable with RK4 (>596s max stable dt)
+- Current default (60s) provides excellent margin
+
+### Newton-Raphson vs RK4 Comparison
+| Aspect | Newton-Raphson (Analytical) | RK4 (Numerical) |
+|--------|---------------------------|-----------------|
+| Timestep | Days/weeks | Seconds/minutes |
+| Accuracy | Exact (2-body) | Approximate |
+| Long-term energy | Perfect | Drift accumulates |
+| N-body support | Limited (needs patching) | Native support |
+| Non-gravitational forces | No | Yes |
+| Computational cost | Low (3-5 iterations) | Medium (4 evaluations) |
+
+### Design Decisions Documented
+1. **Hybrid approach**: Use analytical propagation for orbital motion, RK4 during burns
+2. **Burn execution**: Numerical integration (RK4) for flexible timesteps during continuous thrust
+3. **SOI transitions**: Reuse existing infrastructure with orbital element transformations
+4. **Default behavior**: Analytical propagation will be default when implemented
+5. **Initial guess**: Use series expansion formula for faster Newton-Raphson convergence
+   ```cpp
+   E₀ = M + e·sin(M) + (e²/2)·sin(2M)
+   ```
+
+### Expected Performance Gains
+| Scenario | RK4 dt | Analytical dt | Speedup |
+|----------|--------|--------------|---------|
+| Low Earth Orbit | 60s | 3600s (1 hour) | 60x |
+| Geostationary Orbit | 60s | 3600s (1 hour) | 60x |
+| Moon orbit | 60s | 86400s (1 day) | 1440x |
+| Interplanetary | 60s | 172800s (2 days) | 2880x |
+
+## Implementation Phases (Planned)
+
+### Phase 1: Core Mathematical Functions (4-6 hours)
+- `cartesian_to_orbital_elements()` conversion
+- Newton-Raphson solver for Kepler's equation
+- Analytical propagation step function
+
+### Phase 2: Hybrid Integration System (6-8 hours)
+- Propagation mode selection logic
+- Burn execution with numerical integration
+- RK4 with external force support
+
+### Phase 3: SOI Transition Handling (8-12 hours)
+- Orbital element transformation across SOI boundaries
+- Direct conversion vs. Lambert's problem approach
+
+### Phase 4: Burn Command Interface (4-6 hours)
+- Impulsive burn command
+- Finite duration burn command
+
+### Phase 5: Testing and Validation (8-12 hours)
+- Unit tests for all mathematical functions
+- Integration tests for burns and SOI transitions
+- Performance benchmarks
+
+**Total estimated effort: 30-44 hours**
+
+## Remaining Issues
+
+None - this was a planning/documentation session only. No code implementation was performed.
+
+## Next Steps
+
+**Immediate**: None - implementation deferred to future session
+
+**When ready to implement**:
+1. Review docs/newton_raphson_propagation_plan.md
+2. Start with Phase 1 (core math functions)
+3. Implement `cartesian_to_orbital_elements()` first (inverse of existing function)
+4. Add comprehensive unit tests for each function
+5. Validate against existing RK4 results during development
+
+**Future documentation updates** (post-implementation):
+- Update docs/technical_reference.md with new propagation methods
+- Update docs/future_work.md to reflect completed Newton-Raphson implementation
+- Remove "More Accurate Integration Methods" section from future work
+
+## Technical Notes
+
+### Key Challenge: Continuous Burns with Analytical Propagation
+User's proposed solution:
+1. Divide finite-duration burn into small chunks (1-10s each)
+2. For each chunk:
+   - Get state from orbital elements (Newton-Raphson)
+   - Apply thrust numerically (RK4) over chunk dt
+   - Convert back to orbital elements
+3. After burn, resume pure analytical propagation
+
+This approach provides:
+- 10-1000x faster simulation during normal operation
+- Flexible timesteps during burns
+- Seamless transitions between analytical and numerical modes
+
+### Code Modifications Required
+When implementation begins:
+- Add new functions to `physics.h`/`physics.cpp`
+- Modify Spacecraft struct (add burn state fields)
+- Modify `simulation.cpp` (update spacecraft physics logic)
+- Keep RK4 for burn integration (no removal needed)
+- Parallel implementation during migration
+
+## Net Line Count
+- **Added**: +538 lines (docs/newton_raphson_propagation_plan.md)
+- **Modified**: 0 lines
+- **Deleted**: 0 lines
+- **Net**: +538 lines