claudes_game/docs/session_summaries/2026-01-30-newton-raphson-propagation-planning.md

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

   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