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Plan: Add Molniya Orbit Test Case

Overview

Add test cases for highly inclined orbits, specifically focusing on Molniya orbits and generic inclined orbit behavior.

Background - Molniya Orbit Properties

From Wikipedia research, Molniya orbits are designed for high-latitude coverage:

Orbital Period: ~718 minutes (~12 hours, half a sidereal day)
Eccentricity: ~0.74
Inclination: 63.4° (critical value that prevents perigee precession)
Argument of Perigee: 270° (apogee at northernmost point)
Perigee altitude: ~600 km
Apogee altitude: ~39,700 km
Semi-major axis: ~26,600 km

Current Codebase Status

Earth as Root Body

✅ SUPPORTED

Validator checks: parent_index < body_index or -1
Earth can be root if it's first body (index 0)
No special validation prevents this

3D Orientation Support

⚠️ DEFINED BUT NOT APPLIED

inclination, longitude_of_ascending_node, argument_of_periapsis exist in OrbitalElements struct
orbital_elements_to_cartesian() in src/orbital_mechanics.cpp only produces 2D orbits (x, y, z=0)
Documented as "deferred implementation" in technical_reference.md line 114
Config parser supports loading these parameters (src/config_loader.cpp)
Test approach: Tests will expect 3D behavior and fail with [!mayfail] tag

Implementation Plan

Step 1: Create Test Configuration File

File: tests/test_molniya.toml

# Test Configuration: Molniya Orbit
# Earth as root body with highly elliptical, highly inclined satellite orbit

[[bodies]]
name = "Earth"
mass = 5.972e24
radius = 6.371e6
parent_index = -1
color = { r = 0.0, g = 0.5, b = 1.0 }
orbit = {
    semi_major_axis = 0.0,
    eccentricity = 0.0,
    true_anomaly = 0.0
}

[[spacecraft]]
name = "Molniya_Satellite"
mass = 1000.0
parent_index = 0
orbit = {
    semi_major_axis = 26540000.0,
    eccentricity = 0.74,
    true_anomaly = 0.0,
    inclination = 1.107,           # 63.4° in radians
    longitude_of_ascending_node = 0.0,
    argument_of_periapsis = 4.71    # 270° in radians
}

Key points:

Earth is root body (index 0, parent_index = -1)
Spacecraft uses Molniya orbital parameters
3D orientation parameters included even though not applied yet

Step 2: Create Test File

File: tests/test_inclined_orbits.cpp

Test Cases:

Molniya Position Verification (tagged [!mayfail])
- Test satellite position at true_anomaly = 0 (perigee)
- Test satellite position at true_anomaly = π/2
- Test satellite position at true_anomaly = π (apogee)
- Test satellite position at true_anomaly = 3π/2
- Verify radii match polar equation: r = a(1-e²)/(1+e·cos(ν))
- Check z-coordinate ≠ 0 for inclined orbits (will fail until 3D implemented)
- Tolerance: ±10 km (10,000 meters)
Molniya Orbital Period (tagged [!mayfail])
- Verify period matches theoretical calculation from Kepler's 3rd law
- Theoretical period: T = 2π√(a³/μ)
- Use OrbitTracker with minimum time to prevent false completion
- Expected: ~11.96 hours
- Tolerance: ±600 seconds (10 minutes)
Generic Inclined Orbit (tagged [!mayfail])
- Test moderate inclination (45°) with e=0.5, a=10,000 km
- Verify z-coordinate is non-zero (will fail until 3D implemented)
- Verify position magnitude matches orbital radius
- Simpler case to test 3D orientation without Molniya complexity
Inclination Parameter Preservation
- Verify config loader correctly reads and preserves inclination value
- This should PASS (just checking config loading, not physics)
- Ensures 3D parameters are being stored correctly

Constants:

POSITION_TOLERANCE_METERS = 10000.0 (±10 km per user request)
PERIOD_TOLERANCE_SECONDS = 600.0 (±10 minutes)

Step 3: Update Build System

Add test file to existing test build (Catch2 automatically includes all test_*.cpp files)

Step 4: Expected Behavior

Before 3D Implementation

All tests with [!mayfail] tag will run but failure is acceptable
Position tests: Pass radius check, fail on z-coordinate check
Period test: May pass (period independent of inclination for same orbital energy)
Generic inclined test: Fail on z-coordinate check
Config preservation test: PASS (just checks config loading)

After 3D Implementation

All position tests should PASS
Period test should PASS
Generic inclined test should PASS
Config preservation test should PASS
Remove [!mayfail] tags from passing tests

Implementation Findings

Bug Discovered in Spacecraft Initialization

Location: src/config_loader.cpp lines 257-259

Code:

if (!is_parabolic && craft->parent_index >= 0 && craft->parent_index < sim->body_count) {
    CelestialBody* parent = &sim->bodies[craft->parent_index];
    craft->orbit.semi_major_axis += parent->radius;  // BUG: Always adds parent radius
}

Problem:

For spacecraft, code unconditionally adds parent radius to semi_major_axis
For bodies, this logic does NOT exist (bodies use semi_major_axis as-is)
This creates an inconsistency between body and spacecraft orbital definitions
The logic was intended for altitude parameter convenience but is applied even when semi_major_axis is specified directly

Impact on Molniya Tests:

Config specifies: semi_major_axis = 26,540,000 m
Actual used: 26,540,000 + 6,371,000 = 32,911,000 m
Position errors: 1.7M m at perigee, 11.1M m at apogee
Orbital period: ~16.5 hours instead of expected ~12 hours
All radius-based tests fail with errors far exceeding ±10 km tolerance

Root Cause: The config loader has these paths (simplified):

// For bodies:
if (semi_major_axis.type == TOML_FP64) {
    body->orbit.semi_major_axis = semi_major.u.fp64;  // Used directly
} else if (altitude.type == TOML_FP64) {
    body->orbit.semi_major_axis = altitude.u.fp64;  // Stored as altitude
}

// For spacecraft:
if (semi_major_axis.type == TOML_FP64) {
    craft->orbit.semi_major_axis = semi_major.u.fp64;  // Stored as SMA
} else if (altitude.type == TOML_FP64) {
    craft->orbit.semi_major_axis = altitude.u.fp64;  // Stored as altitude
}

// AFTER loading all spacecraft (line 253-260):
for (int i = 0; i < sim->craft_count; i++) {
    Spacecraft* craft = &sim->spacecraft[i];
    bool is_parabolic = (fabs(craft->orbit.eccentricity - 1.0) < 0.005);
    if (!is_parabolic && craft->parent_index >= 0) {
        CelestialBody* parent = &sim->bodies[craft->parent_index];
        craft->orbit.semi_major_axis += parent->radius;  // ALWAYS adds!
    }
}

Required Fix: The logic should only add parent radius when altitude was specified:

Option A: Track which parameter was used during parsing
Option B: Check if semi_major_axis < parent radius (altitude would be small)
Option C: Only apply this transformation for altitude-based initialization

Additional Issues Found

OrbitTracker Not Completing

Symptom: Molniya period test never completes orbit (tracker->orbit_completed = false)
Possible causes:
1. Minimum time threshold too restrictive (currently 0.01 days = 14.4 minutes)
2. Quadrant transition logic failing for highly elliptical orbits
3. Angle comparison tolerance too tight for large orbital variations
Status: Not investigated yet, secondary priority to config bug

Test File Name Mismatch

Original plan: tests/test_molniya.toml
Actual created: tests/test_inclined_orbits.toml (matches test file name)
Reason: User preference to have config filename match test filename
Status: ✅ RESOLVED (updated config in final implementation)

Test Verification Formula

Orbital Radius at True Anomaly

r = a(1-e²) / (1 + e·cos(ν))

Where:

a = semi-major_axis
e = eccentricity
ν = true_anomaly

Orbital Period (Kepler's 3rd Law)

T = 2π√(a³/μ)