diff --git a/src/orbital_mechanics.cpp b/src/orbital_mechanics.cpp
index 10a03d0..fb1d124 100644
--- a/src/orbital_mechanics.cpp
+++ b/src/orbital_mechanics.cpp
@@ -240,10 +240,44 @@ OrbitalElements cartesian_to_orbital_elements(Vec3 position, Vec3 velocity, doub
     double r_mag = vec3_magnitude(r_vec);
     double r_dot_e = vec3_dot(r_vec, e_vec);
 
-    // Near-circular: e ≈ 0, true anomaly undefined
+    // Ascending node vector: n = k × h_vec (k is unit Z vector)
+    Vec3 n_vec = {0.0, 0.0, 1.0};
+    Vec3 n = vec3_cross(n_vec, h_vec);
+    double n_mag = vec3_magnitude(n);
+
+    // True anomaly: angle from periapsis to position
     double true_anomaly;
     if (e < 1e-10) {
-        true_anomaly = 0.0;
+        // Circular orbit: no periapsis direction. Use argument of latitude
+        // (position angle in orbital plane) as true anomaly, with omega=0.
+        // For nearly-coplanar orbits, the ascending node is numerically
+        // unstable. Use the inclination to decide which reference to use.
+        double true_anomaly_from_position;
+        double sin_i = (h > 1e-10) ? n_mag / h : 1.0;
+        if (sin_i > 1e-6 && n_mag > 1e-10) {
+            // Well-defined ascending node: compute argument of latitude
+            double x_AN = n.x / n_mag;
+            double y_AN = n.y / n_mag;
+            // y_AN in orbital plane = (h × n) / |h × n|
+            double h_cross_n_x = h_vec.y * 0.0 - h_vec.z * n.y;
+            double h_cross_n_y = h_vec.z * n.x - h_vec.x * 0.0;
+            double h_cross_n_z = h_vec.x * n.y - h_vec.y * n.x;
+            double hcn_mag = sqrt(h_cross_n_x*h_cross_n_x + h_cross_n_y*h_cross_n_y + h_cross_n_z*h_cross_n_z);
+            if (hcn_mag > 1e-10) {
+                h_cross_n_x /= hcn_mag;
+                h_cross_n_y /= hcn_mag;
+                h_cross_n_z /= hcn_mag;
+            }
+            double r_xAN = r_vec.x * x_AN + r_vec.y * y_AN;
+            double r_yAN = r_vec.x * h_cross_n_x + r_vec.y * h_cross_n_y + r_vec.z * h_cross_n_z;
+            true_anomaly_from_position = atan2(r_yAN, r_xAN);
+        } else {
+            // Nearly coplanar: ascending node is numerically unstable.
+            // Use X-axis as reference. For coplanar orbits this gives
+            // the argument of latitude = atan2(y, x).
+            true_anomaly_from_position = atan2(r_vec.y, r_vec.x);
+        }
+        true_anomaly = normalize_angle(true_anomaly_from_position);
     } else {
         double cos_nu = r_dot_e / (r_mag * e);
         cos_nu = fmax(-1.0, fmin(1.0, cos_nu));
@@ -278,11 +312,6 @@ OrbitalElements cartesian_to_orbital_elements(Vec3 position, Vec3 velocity, doub
         i = 0.0;
     }
 
-    // Ascending node vector: n = k × h_vec (k is unit Z vector)
-    Vec3 n_vec = {0.0, 0.0, 1.0};
-    Vec3 n = vec3_cross(n_vec, h_vec);
-    double n_mag = vec3_magnitude(n);
-
     // Longitude of ascending node from n vector
     double Omega;
     if (n_mag > 1e-10) {
@@ -375,7 +404,6 @@ OrbitalElements propagate_orbital_elements(const OrbitalElements& elements, doub
 
         OrbitalElements result = elements;
         result.true_anomaly = 2.0 * atan(sqrt((1.0 + e) / (1.0 - e)) * tan(E_new / 2.0));
-
         return result;
     } else {  // e >= 1.0 (hyperbolic)
         double n = sqrt(mu / pow(-a, 3.0));