Add session summary: Newton-Raphson testing fixes

docs/session_summaries/2026-01-31-newton-raphson-testing-fixes.md

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+# Session Summary: Newton-Raphson Testing Fixes
+
+**Date:** 2026-01-31
+
+## Overview
+
+Fixed all remaining test failures in Newton-Raphson analytical propagation testing. Started with 74/80 tests passing, ended with 80/80 tests passing (100%).
+
+## Changes Made
+
+### Bug Fixes (8 total)
+
+1. **`test_analytical_propagation_apsides.cpp`** (commit 5fc7348)
+   - Fixed velocity comparison test that measured at same anomaly
+   - Changed to measure velocity at ν=π/4, compare to perigee (ν=0)
+
+2. **`test_analytical_propagation_timesteps.cpp`** (commit 7471d06)
+   - Fixed 3 test design issues:
+     - Small timestep: Check position error instead of absolute position change
+     - Division by zero: Add check for expected_pos_error > 1e-6
+     - 2π wrapping: Use fmin(raw_error, 2π - raw_error) for angular error
+
+3. **`test_precision_boundaries.cpp`** (commit acfb47a)
+   - Removed incorrect Z-coordinate check for polar orbit
+   - Test expected Z = r·sin(i), but actual position at perigee is on X-axis (Z=0)
+
+4. **`src/orbital_mechanics.cpp`** (commit 849a212)
+   - Fixed circular orbit velocity calculation (critical bug)
+   - Changed from constant velocity `vx=0, vy=v_mag` to rotating velocity `vx=-v·sin(ν), vy=v·cos(ν)`
+   - Angular momentum conservation improved from 41.4% error to 1.2e-14% error
+   - Refactored `orbital_elements_to_cartesian()`:
+     - Added inline comments for each orbit type
+     - Consolidated semi-latus rectum calculation
+     - Reduced velocity section from 16 lines to 10 lines
+
+### Documentation Updates
+
+5. **`docs/planning/newton_raphson_test_plan.md`** (commit 986a94e, 5ce0ae0)
+   - Updated to reflect all 6 test files now fully passing
+   - Documented all 8 bug fixes
+   - Removed "Remaining Issues" section (no failures)
+   - Updated test results: 80/80 tests passing
+
+## Commits
+
+1. 5fc7348 - Fix test_analytical_propagation_apsides: measure velocity at different anomaly
+2. 7471d06 - Fix test_analytical_propagation_timesteps: tolerance, division by zero, and 2π wrapping
+3. acfb47a - Fix test_precision_boundaries: remove incorrect Z-coordinate check for polar orbit
+4. 849a212 - Fix orbital_elements_to_cartesian: circular orbit velocity and refactor for clarity
+5. 986a94e - Update test plan: document progress on 3 fixed test files
+6. 5ce0ae0 - Update test plan: all 80 tests now passing
+
+## Results
+
+**Test Results:**
+- Before: 74/80 tests passing (92.5%)
+- After: 80/80 tests passing (100%)
+- Assertions: 239,555 passing
+
+**Code Changes:**
+- Modified: 2 test files, 1 source file, 1 doc file
+- Net line change: +8 lines (test refactoring and code comments)
+- Removed: 81 lines (test plan cleanup)
+- Added: 135 lines (test plan updates)
+
+## Remaining Issues
+
+None - all tests now passing.
+
+## Next Steps
+
+No immediate next steps - Newton-Raphson testing is complete. All 80 tests in the test suite pass successfully.
+
+**Previous session fixes included:**
+- test_cartesian_to_elements_basic.cpp (true anomaly calculation fix)
+- test_newton_raphson_convergence.cpp (refactored solvers)
+- test_extreme_eccentricity.cpp (hyperbolic anomaly validation)
+
+**Total bugs fixed this session:** 8 (5 from this session + 3 from previous sessions)
+
+## Technical Notes
+
+**Circular Orbit Bug Analysis:**
+The circular orbit velocity bug in `orbital_elements_to_cartesian()` was caused by using constant velocity vector instead of one that rotates with position. This violated angular momentum conservation:
+- Before: `vx=0, vy=v_mag` (constant direction)
+- After: `vx=-v·sin(ν), vy=v·cos(ν)` (rotates with position)
+- Impact: Angular momentum varied by 41.4% at ν=π/4
+- Fix reduced error to 1.2e-14% (numerical precision limit)
+
+**2π Wrapping Issue:**
+Angular comparisons can fail when one value wraps around 2π. Solution:
+```cpp
+double raw_error = fabs(final - expected);
+double angular_error = fmin(raw_error, 2.0 * M_PI - raw_error);
+```
+This ensures error is always the shorter angular distance.