claudes_game/docs/session_summaries/2026-02-01-orbital-mechanics-improvements.md

Session Summary: 2026-02-01 - Orbital Mechanics Improvements and Test Tightening

Overview

Focused on improving parabolic orbit handling, adding documentation, and tightening test tolerances following recent orbital_mechanics.cpp improvements.

Changes Made

Code Changes

1. Added formula documentation to orbital_mechanics.cpp (16 comments)

   • Semi-latus rectum calculation
   • Polar equation of orbit
   • Velocity from vis-viva equation
   • 3D rotation using z-x-z Euler angles
   • Near-parabolic special case handling
   • Tangent half-angle formula
   • Conversion chain for mean anomaly
   • Specific orbital energy formula
   • Eccentricity vector formula
   • Semi-major axis from specific energy
   • Edge cases: near-parabolic energy, near-circular orbits
   • Inclination from angular momentum
   • Ascending node vector
   • Longitude of ascending node
   • Argument of periapsis with atan2()

2. Fixed parabolic test design in test_cartesian_to_elements_extreme.cpp

   • Changed from manual state vector construction to using orbital_elements_to_cartesian()
   • Eliminated incorrect escape velocity formula (only valid at periapsis)
   • Tightened tolerance from 1e10 to 1e3 (7 orders of magnitude improvement)
   • Reduced error from 6.5% to machine precision

3. Tightened parabolic boundary test tolerances

   • Near-parabolic (e=0.999) eccentricity: 1e-2 → 1e-3
   • Highly hyperbolic (e=10.0) eccentricity: 1e-2 → 1e-3

4. Implemented Barker's equation for parabolic propagation

   • Added solve_barker_equation() function using cubic formula
   • Integrated into propagate_orbital_elements() for parabolic orbits
   • Uses exact analytical solution instead of iterative Kepler solver
   • Handles negative mean anomalies with cbrt()

Documentation Updates

5. Condensed newton_raphson_test_plan.md
   • Updated completed tests from 6 to 8 files
   • Added test_cartesian_to_elements_extreme and test_cartesian_to_elements_quadrature to completed section
   • Removed duplicate test documentation in Phase sections
   • Removed entire "## Overlap Analysis" section
   • Updated Implementation Summary with Barker's equation
   • Reduced from 379 to 161 lines (57% reduction)

Commits

1. 68d61ee - "docs: Add comments to orbital_mechanics and fix parabolic test design"

   • Added 16 minimal comments to orbital_mechanics functions
   • Fixed parabolic test to use orbital_elements_to_cartesian()
   • Tightened parabolic test tolerance from 1e10 to 1e3

2. b21a668 - "test: Tighten eccentricity tolerances for parabolic boundary cases"

   • Near-parabolic (e=0.999) eccentricity: 1e-2 → 1e-3
   • Highly hyperbolic (e=10.0) eccentricity: 1e-2 → 1e-3
   • Validates improvements from PARABOLIC_TOLERANCE and near-parabolic handling

3. 5eb3a84 - "feat: Implement Barker's equation for parabolic orbit propagation"

   • Added solve_barker_equation() function using cubic formula: D + D³/3 = M
   • Integrated Barker's equation into propagate_orbital_elements() for parabolic orbits
   • Added comprehensive test suite (11 tests, 239 assertions) following TDD
   • Use cbrt() for cube root (handles negative numbers properly)
   • Parabolic propagation now uses exact analytical solution instead of iterative solver

4. 47c5975 - "docs: Update newton_raphson_test_plan with completed work"

   • Condensed completed tests to one-line summaries (6 → 8 tests)
   • Added test_cartesian_to_elements_extreme and test_cartesian_to_elements_quadrature to completed section
   • Removed duplicate test documentation in Phase sections
   • Removed entire Overlap Analysis section (no longer needed)
   • Updated Implementation Summary with Barker's equation and recent fixes
   • Reduced document from 379 to 161 lines (57% reduction)

Test Results

Before session: 82/82 tests passing (239,555 assertions) After session: 93/93 tests passing (239,872 assertions)

New tests added:

• test_barkers_equation.cpp: 11 tests, 239 assertions
  • Zero, small, moderate, large mean anomaly values
  • Negative mean anomaly cases
  • Round-trip conversion validation
  • True anomaly range validation
  • Parabolic orbit propagation integration (24 timesteps)

All medium-priority tasks completed:

• Re-add comments to orbital_mechanics functions ✓
• Re-enable parabolic tests and fix design ✓
• Fix parabolic test design and tighten tolerance ✓
• Tighten high-confidence tolerances ✓
• Implement Barker's equation ✓

Net Line Count

File	Added	Removed	Net
src/orbital_mechanics.cpp	+16	0	+16
tests/test_cartesian_to_elements_extreme.cpp	+2	-22	-20
tests/test_barkers_equation.cpp	+205	0	+205
docs/planning/newton_raphson_test_plan.md	+55	-461	-406
Total	+278	-483	-205

Remaining Issues

None. All tasks completed successfully.

Next Steps

Low Priority (Remaining from todo list)

1. Implement universal variable formulation using Stumpff functions

   • Single formulation for all conic sections
   • Most numerically stable approach
   • Industry standard in orbital mechanics software
   • Trade-off: High complexity, requires major refactoring

2. Add comprehensive near-parabolic test cases

   • Test at e=0.99, e=0.999, e=1.001, e=1.01
   • Verify round-trip conversions for these edge cases
   • Measure precision improvements from all fixes

Notes

• All medium-priority orbital mechanics tasks completed
• Test suite expanded from 82 to 93 tests
• Parabolic orbit propagation now uses exact analytical solution (Barker's equation)
• Documentation significantly improved and streamlined
• Test tolerances tightened where appropriate based on recent code improvements