- Add solve_barker_equation() function using cubic formula: D + D³/3 = M
- Integrate Barker's equation into propagate_orbital_elements() for parabolic orbits
- Add 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
- All 93 tests passing (239,872 assertions)
- Add PARABOLIC_TOLERANCE = 1e-3 constant for consistent detection
- Replace inconsistent thresholds (0.005, 0.98, 1.02) across 5 files
- Refactor orbital_elements_to_cartesian() to use semi-latus rectum as primary parameter
- Eliminate 3 separate code branches with unified formulas for all orbit types
- Improve numerical stability for parabolic and near-parabolic orbits
- Reduce code complexity: -23 lines net
New modular API:
- solve_kepler_elliptical(M, e): Newton-Raphson for E - e·sin(E) = M
- solve_kepler_hyperbolic(M, e): Solver for H - e·sinh(H) = M
- eccentric_to_true_anomaly(E, e): Convert eccentric to true anomaly
- hyperbolic_to_true_anomaly(H, e): Convert hyperbolic to true anomaly
- mean_anomaly_to_true_anomaly(M, e): Unified wrapper (dispatches based on e)
Changes:
- Renamed solve_kepler_equation() → solve_kepler_elliptical() for clarity
- Extracted KEPLER_TOLERANCE and KEPLER_MAX_ITERATIONS constants
- Separated hyperbolic solver logic from combined function
- Fixed test_newton_raphson_convergence to verify Kepler's equation
(instead of incorrectly expecting E ≈ M for small e)
- Added TODO comment for future cartesian_to_orbital_elements refactoring
Added 6 test files for Newton-Raphson solver and analytical propagation:
- test_cartesian_to_elements_basic.cpp: Tests state vector ↔ orbital elements conversion
- test_newton_raphson_convergence.cpp: Tests Newton-Raphson solver convergence behavior
- test_analytical_propagation_apsides.cpp: Tests propagation through orbital apsides
- test_analytical_propagation_timesteps.cpp: Tests propagation with various timesteps
- test_extreme_eccentricity.cpp: Tests near-parabolic and hyperbolic orbits
- test_precision_boundaries.cpp: Tests exact boundary value handling
Implemented core orbital mechanics functions:
- solve_kepler_equation(): Newton-Raphson solver with 1e-10 tolerance
- get_initial_trial_value(): Series expansion initial guess
- cartesian_to_orbital_elements(): State vectors to orbital elements conversion
- propagate_orbital_elements(): Analytical propagation using Kepler's equation
Updated test plan document with current progress and remaining tests.
Test status: 66 passed, 14 failed (out of 80 test cases)
- Failing tests are expected: implementation needs debugging
- Config validation issues fixed by adjusting orbital parameters
- Added union in OrbitalElements (semi_major_axis | semi_latus_rectum)
- Updated config_loader to parse and validate semi_latus_rectum for parabolic orbits
- Validation ensures correct parameter (semi_latus_rectum for e≈1, semi_major_axis for other)
- Updated orbital_mechanics.cpp parabolic case: r = p / (1 + cos(ν))
- Updated parabolic_comet.toml to use semi_latus_rectum = 1.496e11
- Tolerance for parabolic detection: |e - 1.0| < 0.005
Note: Parabolic test still fails velocity tolerance check due to floating-point precision
at r=0.5 AU, E ≈ -200 J/kg (not exactly 0)
cinnaboot