Phase 7: Implement parabolic orbit support with union

- 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)

src/config_loader.cpp

@@ -84,24 +84,45 @@ static bool parse_toml_body(toml_datum_t body_table, CelestialBody* body) {
     body->orbit.argument_of_periapsis = 0.0;
     body->orbit.true_anomaly = 0.0;
 
-    // Parse semi_major_axis (required) or altitude (convenience)
+    // Parse semi_major_axis (for elliptical/hyperbolic) or semi_latus_rectum (for parabolic) or altitude (convenience)
     toml_datum_t semi_major = toml_get(orbit_table, "semi_major_axis");
+    toml_datum_t semi_latus = toml_get(orbit_table, "semi_latus_rectum");
     toml_datum_t altitude = toml_get(orbit_table, "altitude");
 
+    // Parse eccentricity first to determine which parameter is required
+    toml_datum_t eccentricity = toml_get(orbit_table, "eccentricity");
+    if (eccentricity.type != TOML_FP64) {
+        printf("Error: Body '%s' missing required 'eccentricity' in orbit table\n", body->name);
+        return false;
+    }
+    body->orbit.eccentricity = eccentricity.u.fp64;
+
+    bool is_parabolic = (fabs(body->orbit.eccentricity - 1.0) < 0.005);
+
+    if (is_parabolic) {
+        // Parabolic orbit - requires semi_latus_rectum
+        if (semi_latus.type != TOML_FP64) {
+            printf("Error: Parabolic orbit for body '%s' requires 'semi_latus_rectum' (not 'semi_major_axis' or 'altitude')\n", body->name);
+            return false;
+        }
+        body->orbit.semi_latus_rectum = semi_latus.u.fp64;
+        if (semi_major.type == TOML_FP64 || altitude.type == TOML_FP64) {
+            printf("Warning: Body '%s' has parabolic eccentricity, 'semi_latus_rectum' used instead of 'semi_major_axis' or 'altitude'\n", body->name);
+        }
+    } else {
+        // Elliptical or hyperbolic - requires semi_major_axis or altitude
         if (semi_major.type == TOML_FP64) {
             body->orbit.semi_major_axis = semi_major.u.fp64;
         } else if (altitude.type == TOML_FP64) {
             // altitude will be added to parent radius in initialization
             body->orbit.semi_major_axis = altitude.u.fp64;
         } else {
-        printf("Error: Body '%s' must have either 'semi_major_axis' or 'altitude' in orbit table\n", body->name);
+            printf("Error: Body '%s' must have either 'semi_major_axis' or 'altitude' in orbit table (non-parabolic orbits)\n", body->name);
             return false;
         }
-
+        if (semi_latus.type == TOML_FP64) {
-    // Parse eccentricity (optional, default 0.0)
+            printf("Warning: Body '%s' has non-parabolic eccentricity, 'semi_latus_rectum' ignored\n", body->name);
-    toml_datum_t eccentricity = toml_get(orbit_table, "eccentricity");
+        }
-    if (eccentricity.type == TOML_FP64) {
-        body->orbit.eccentricity = eccentricity.u.fp64;
     }
 
     // Parse true_anomaly (optional, default 0.0)
@@ -200,12 +221,7 @@ bool load_system_config(SimulationState* sim, const char* filepath) {
             continue;
         }
 
-        if (body->orbit.semi_major_axis == 0.0) {
+        bool is_parabolic = (fabs(body->orbit.eccentricity - 1.0) < 0.005);
-            printf("Error: Body '%s' has invalid semi_major_axis: %.2e (must not be zero)\n",
-                   body->name, body->orbit.semi_major_axis);
-            toml_free(result);
-            return false;
-        }
 
         if (body->orbit.eccentricity < 0.0) {
             printf("Error: Body '%s' has invalid eccentricity: %.2e (must be >= 0)\n",
@@ -214,6 +230,23 @@ bool load_system_config(SimulationState* sim, const char* filepath) {
             return false;
         }
 
+        if (is_parabolic) {
+            // For parabolic orbits, semi_latus_rectum must be positive
+            if (body->orbit.semi_latus_rectum <= 0.0) {
+                printf("Error: Body '%s' has parabolic orbit but non-positive semi_latus_rectum: %.2e\n",
+                       body->name, body->orbit.semi_latus_rectum);
+                toml_free(result);
+                return false;
+            }
+        } else {
+            // For elliptical/hyperbolic orbits, semi_major_axis must be non-zero
+            if (body->orbit.semi_major_axis == 0.0) {
+                printf("Error: Body '%s' has invalid semi_major_axis: %.2e (must not be zero)\n",
+                       body->name, body->orbit.semi_major_axis);
+                toml_free(result);
+                return false;
+            }
+
             // For elliptical orbits (e < 1), semi_major_axis must be positive
             if (body->orbit.eccentricity < 1.0 && body->orbit.semi_major_axis <= 0.0) {
                 printf("Error: Body '%s' has elliptical orbit but non-positive semi_major_axis: %.2e\n",
@@ -222,6 +255,7 @@ bool load_system_config(SimulationState* sim, const char* filepath) {
                 return false;
             }
         }
+    }
 
     sim->body_count = body_count;
 
@@ -295,25 +329,28 @@ static bool load_spacecraft_from_toml(SimulationState* sim, toml_result_t result
     for (int i = 0; i < sim->craft_count; i++) {
         Spacecraft* craft = &sim->spacecraft[i];
 
-        if (craft->parent_index >= 0 && craft->parent_index < sim->body_count) {
+        bool is_parabolic = (fabs(craft->orbit.eccentricity - 1.0) < 0.005);
+
+        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;
         }
 
-        // Validate semi_major_axis
+        if (is_parabolic) {
+            // For parabolic orbits, semi_latus_rectum must be positive
+            if (craft->orbit.semi_latus_rectum <= 0.0) {
+                printf("Error: Spacecraft '%s' has parabolic orbit but non-positive semi_latus_rectum: %.2e\n",
+                       craft->name, craft->orbit.semi_latus_rectum);
+                return false;
+            }
+        } else {
+            // For elliptical/hyperbolic orbits, validate semi_major_axis
             if (fabs(craft->orbit.semi_major_axis) < 1e-10) {
                 printf("Error: Spacecraft '%s' has invalid semi_major_axis: %.2e (must not be zero)\n",
                        craft->name, craft->orbit.semi_major_axis);
                 return false;
             }
 
-        // Validate eccentricity
-        if (craft->orbit.eccentricity < 0.0) {
-            printf("Error: Spacecraft '%s' has invalid eccentricity: %.3f (must be >= 0)\n",
-                   craft->name, craft->orbit.eccentricity);
-            return false;
-        }
-
             // For elliptical orbits (e < 1), semi_major_axis must be positive
             if (craft->orbit.eccentricity < 1.0 && craft->orbit.semi_major_axis <= 0.0) {
                 printf("Error: Spacecraft '%s' has elliptical orbit but non-positive semi_major_axis: %.2e\n",
@@ -322,6 +359,14 @@ static bool load_spacecraft_from_toml(SimulationState* sim, toml_result_t result
             }
         }
 
+        // Validate eccentricity
+        if (craft->orbit.eccentricity < 0.0) {
+            printf("Error: Spacecraft '%s' has invalid eccentricity: %.3f (must be >= 0)\n",
+                   craft->name, craft->orbit.eccentricity);
+            return false;
+        }
+    }
+
     printf("Loaded %d spacecraft from %s\n", craft_count, sim->config_name);
     return true;
 }
@@ -359,24 +404,45 @@ static bool parse_toml_spacecraft(toml_datum_t craft_table, Spacecraft* craft) {
     craft->orbit.argument_of_periapsis = 0.0;
     craft->orbit.true_anomaly = 0.0;
 
-    // Parse semi_major_axis (required) or altitude (convenience)
+    // Parse semi_major_axis (for elliptical/hyperbolic) or semi_latus_rectum (for parabolic) or altitude (convenience)
     toml_datum_t semi_major = toml_get(orbit_table, "semi_major_axis");
+    toml_datum_t semi_latus = toml_get(orbit_table, "semi_latus_rectum");
     toml_datum_t altitude = toml_get(orbit_table, "altitude");
 
+    // Parse eccentricity first to determine which parameter is required
+    toml_datum_t eccentricity = toml_get(orbit_table, "eccentricity");
+    if (eccentricity.type != TOML_FP64) {
+        printf("Error: Spacecraft '%s' missing required 'eccentricity' in orbit table\n", craft->name);
+        return false;
+    }
+    craft->orbit.eccentricity = eccentricity.u.fp64;
+
+    bool is_parabolic = (fabs(craft->orbit.eccentricity - 1.0) < 0.005);
+
+    if (is_parabolic) {
+        // Parabolic orbit - requires semi_latus_rectum
+        if (semi_latus.type != TOML_FP64) {
+            printf("Error: Parabolic orbit for spacecraft '%s' requires 'semi_latus_rectum' (not 'semi_major_axis' or 'altitude')\n", craft->name);
+            return false;
+        }
+        craft->orbit.semi_latus_rectum = semi_latus.u.fp64;
+        if (semi_major.type == TOML_FP64 || altitude.type == TOML_FP64) {
+            printf("Warning: Spacecraft '%s' has parabolic eccentricity, 'semi_latus_rectum' used instead of 'semi_major_axis' or 'altitude'\n", craft->name);
+        }
+    } else {
+        // Elliptical or hyperbolic - requires semi_major_axis or altitude
         if (semi_major.type == TOML_FP64) {
             craft->orbit.semi_major_axis = semi_major.u.fp64;
         } else if (altitude.type == TOML_FP64) {
             // altitude will be added to parent radius in initialization
             craft->orbit.semi_major_axis = altitude.u.fp64;
         } else {
-        printf("Error: Spacecraft '%s' must have either 'semi_major_axis' or 'altitude' in orbit table\n", craft->name);
+            printf("Error: Spacecraft '%s' must have either 'semi_major_axis' or 'altitude' in orbit table (non-parabolic orbits)\n", craft->name);
             return false;
         }
-
+        if (semi_latus.type == TOML_FP64) {
-    // Parse eccentricity (optional, default 0.0)
+            printf("Warning: Spacecraft '%s' has non-parabolic eccentricity, 'semi_latus_rectum' ignored\n", craft->name);
-    toml_datum_t eccentricity = toml_get(orbit_table, "eccentricity");
+        }
-    if (eccentricity.type == TOML_FP64) {
-        craft->orbit.eccentricity = eccentricity.u.fp64;
     }
 
     // Parse true_anomaly (optional, default 0.0)

src/orbital_mechanics.cpp

@@ -18,8 +18,9 @@ void orbital_elements_to_cartesian(OrbitalElements elements, double parent_mass,
     } else if (e < 1.0) {
         r = a * (1.0 - e * e) / (1.0 + e * cos(nu));
         v_mag = sqrt(mu * (2.0 / r - 1.0 / a));
-    } else if (fabs(e - 1.0) < 1e-10) {
+    } else if (fabs(e - 1.0) < 0.005) {
-        r = 2.0 * a / (1.0 + cos(nu));
+        double p = elements.semi_latus_rectum;
+        r = p / (1.0 + cos(nu));
         v_mag = sqrt(2.0 * mu / r);
     } else {
         r = a * (1.0 - e * e) / (1.0 + e * cos(nu));

src/orbital_mechanics.h

@@ -4,12 +4,15 @@
 #include "physics.h"
 
 struct OrbitalElements {
-    double semi_major_axis;
+    union {
+        double semi_major_axis;       // for elliptical (e<1) and hyperbolic (e>1)
+        double semi_latus_rectum;     // for parabolic (e≈1)
+    };
     double eccentricity;
+    double true_anomaly;
     double inclination;
     double longitude_of_ascending_node;
     double argument_of_periapsis;
-    double true_anomaly;
 };
 
 void orbital_elements_to_cartesian(OrbitalElements elements, double parent_mass,

tests/configs/parabolic_comet.toml

@@ -9,8 +9,8 @@ radius = 6.96e8
 parent_index = -1
 color = {r = 1.0,g = 1.0,b = 0.0 }
 orbit = {
-    semi_major_axis = 0.0
+    semi_major_axis = 0.0,
-    eccentricity = 0.0
+    eccentricity = 0.0,
     true_anomaly = 0.0
 }
 
@@ -21,7 +21,7 @@ radius = 5.0e3
 parent_index = 0
 color = {r = 0.7,g = 0.8,b = 0.9 }
 orbit = {
-    semi_major_axis = 1.0e30
+    semi_latus_rectum = 1.496e11,
-    eccentricity = 1.0
+    eccentricity = 1.0,
     true_anomaly = 0.0
 }