diff --git a/src/orbital_mechanics.cpp b/src/orbital_mechanics.cpp
index 9258ba7..8e5f7e3 100644
--- a/src/orbital_mechanics.cpp
+++ b/src/orbital_mechanics.cpp
@@ -166,13 +166,25 @@ OrbitalElements cartesian_to_orbital_elements(Vec3 position, Vec3 velocity, doub
     } else {
         double cos_nu = r_dot_e / (r_mag * e * mu);
         cos_nu = fmax(-1.0, fmin(1.0, cos_nu));
-        true_anomaly = acos(cos_nu);
-        if (vec3_dot(r_vec, v_vec) < 0.0) {
-            true_anomaly = 2.0 * M_PI - true_anomaly;
+        double sin_nu;
+
+        if (fabs(cos_nu) > 1.0 - 1e-10) {
+            Vec3 h_cross_e = vec3_cross(h_vec, e_vec);
+            double denom = r_mag * e * h;
+            if (denom > 1e-10) {
+                sin_nu = vec3_dot(r_vec, h_cross_e) / denom;
+            } else {
+                sin_nu = 0.0;
+            }
+        } else {
+            Vec3 r_cross_h = vec3_cross(r_vec, h_vec);
+            double denom = r_mag * e * h * mu;
+            sin_nu = (denom > 1e-10) ? vec3_dot(r_cross_h, e_vec) / denom : 0.0;
         }
-        // Normalize to (-π, π] range
-        if (true_anomaly > M_PI) {
-            true_anomaly -= 2.0 * M_PI;
+
+        true_anomaly = atan2(sin_nu, cos_nu);
+        if (true_anomaly == -M_PI) {
+            true_anomaly = M_PI;
         }
     }