diff --git a/src/orbital_mechanics.cpp b/src/orbital_mechanics.cpp
index 6f25bd9..10798ad 100644
--- a/src/orbital_mechanics.cpp
+++ b/src/orbital_mechanics.cpp
@@ -119,13 +119,17 @@ OrbitalElements cartesian_to_orbital_elements(Vec3 position, Vec3 velocity, doub
         a = mu / (2.0 * specific_energy);
     }
 
-    double r_dot_e = vec3_dot(r_vec, e_vec) / mu;
+    double r_mag = vec3_magnitude(r_vec);
+    double e_mag = vec3_magnitude(e_vec);
+    double r_dot_e = vec3_dot(r_vec, e_vec);
 
     double true_anomaly;
-    if (e < 1e-10) {
+    if (e < 1e-10 || e_mag < 1e-10) {
         true_anomaly = 0.0;
     } else {
-        true_anomaly = acos(r_dot_e / e);
+        double cos_nu = r_dot_e / (r_mag * e_mag);
+        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;
         }