diff --git a/tests/test_extreme_eccentricity.cpp b/tests/test_extreme_eccentricity.cpp
index 159a257..c505b5e 100644
--- a/tests/test_extreme_eccentricity.cpp
+++ b/tests/test_extreme_eccentricity.cpp
@@ -158,6 +158,17 @@ TEST_CASE("Velocity magnitude accuracy for extreme eccentricities", "[extreme][e
 
         for (int j = 0; j < 4; j++) {
             double nu = true_anomalies[j];
+
+            // For hyperbolic orbits (e > 1), skip invalid true anomalies
+            // Valid range: |ν| < arccos(-1/e)
+            if (craft->orbit.eccentricity > 1.0) {
+                double max_nu = acos(-1.0 / craft->orbit.eccentricity);
+                if (fabs(nu) >= max_nu) {
+                    INFO("  ν=" << nu << " rad: skipped (exceeds hyperbolic limit ±" << max_nu << " rad)");
+                    continue;
+                }
+            }
+
             craft->orbit.true_anomaly = nu;
 
             Vec3 pos;
diff --git a/tests/test_extreme_eccentricity.toml b/tests/test_extreme_eccentricity.toml
index e2c14ec..cf2de16 100644
--- a/tests/test_extreme_eccentricity.toml
+++ b/tests/test_extreme_eccentricity.toml
@@ -31,8 +31,8 @@ name = "Near_Parabolic"
 mass = 1000.0
 parent_index = 0
 orbit = {
-    semi_major_axis = 1.0e9,
-    eccentricity = 0.95,
+    semi_major_axis = 7.0e8,
+    eccentricity = 0.99,
     true_anomaly = 0.0,
     inclination = 0.0,
     longitude_of_ascending_node = 0.0,
@@ -44,8 +44,8 @@ name = "Slightly_Hyperbolic"
 mass = 1000.0
 parent_index = 0
 orbit = {
-    semi_major_axis = -1.0e7,
-    eccentricity = 1.5,
+    semi_major_axis = -1.3e8,
+    eccentricity = 1.05,
     true_anomaly = 0.0,
     inclination = 0.0,
     longitude_of_ascending_node = 0.0,