diff --git a/src/orbital_mechanics.cpp b/src/orbital_mechanics.cpp
index 8e5f7e3..084c39b 100644
--- a/src/orbital_mechanics.cpp
+++ b/src/orbital_mechanics.cpp
@@ -210,13 +210,14 @@ OrbitalElements cartesian_to_orbital_elements(Vec3 position, Vec3 velocity, doub
         Omega = 0.0;
     }
 
-    double e_dot_n = vec3_dot(e_vec, n) / (mu * n_mag);
-
     double omega;
     if (e > 1e-10 && n_mag > 1e-10) {
-        omega = acos(e_dot_n / e);
-        if (e_vec.z < 0.0) {
-            omega = 2.0 * M_PI - omega;
+        double cos_omega = vec3_dot(e_vec, n) / (e * n_mag);
+        Vec3 n_cross_e = vec3_cross(n, e_vec);
+        double sin_omega = vec3_dot(n_cross_e, h_vec) / (e * n_mag * h);
+        omega = atan2(sin_omega, cos_omega);
+        if (omega < 0.0) {
+            omega += 2.0 * M_PI;
         }
     } else {
         omega = 0.0;