diff --git a/tests/test_integration.cpp b/tests/test_integration.cpp
index 53983b4..452e487 100644
--- a/tests/test_integration.cpp
+++ b/tests/test_integration.cpp
@@ -44,4 +44,56 @@ TEST_CASE("Vector math utilities", "[utilities]") {
         double actual_mag = vec3_magnitude(unit);
         REQUIRE(compare_double(actual_mag, expected_mag, 1e-10));
     }
+
+    SECTION("Vector dot product") {
+        double dot = vec3_dot(a, b);
+        REQUIRE(compare_double(dot, 32.0, 1e-10));
+    }
+
+    SECTION("Vector cross product") {
+        Vec3 cross = vec3_cross(a, b);
+        REQUIRE(compare_double(cross.x, -3.0, 1e-10));
+        REQUIRE(compare_double(cross.y, 6.0, 1e-10));
+        REQUIRE(compare_double(cross.z, -3.0, 1e-10));
+    }
+}
+
+TEST_CASE("Acceleration calculation", "[physics][acceleration]") {
+    Vec3 force = {10.0, 20.0, 30.0};
+    double mass = 5.0;
+
+    Vec3 accel = calculate_acceleration(force, mass);
+
+    REQUIRE(compare_double(accel.x, 2.0, 1e-10));
+    REQUIRE(compare_double(accel.y, 4.0, 1e-10));
+    REQUIRE(compare_double(accel.z, 6.0, 1e-10));
+}
+
+TEST_CASE("Gravitational acceleration evaluation", "[physics][gravity]") {
+    Vec3 position = {1.0, 0.0, 0.0};
+    double body_mass = 1000.0;
+    double parent_mass = 1e10;
+
+    Vec3 accel = evaluate_acceleration(position, body_mass, parent_mass);
+
+    double expected_magnitude = G * parent_mass / (1.0 * 1.0);
+    REQUIRE(compare_double(vec3_magnitude(accel), expected_magnitude, 1e-10));
+    REQUIRE(compare_double(accel.x, -expected_magnitude, 1e-10));
+}
+
+TEST_CASE("RK4 integration step", "[physics][rk4]") {
+    Vec3 position = {0.0, 1.0, 0.0};
+    Vec3 velocity = {sqrt(G * 1e10 / 1.0), 0.0, 0.0};
+    double dt = 1.0;
+    double body_mass = 1.0;
+    double parent_mass = 1e10;
+
+    double initial_distance = vec3_magnitude(position);
+
+    rk4_step(&position, &velocity, dt, body_mass, parent_mass);
+
+    double final_distance = vec3_magnitude(position);
+
+    REQUIRE(final_distance > 0.9 * initial_distance);
+    REQUIRE(final_distance < 1.1 * initial_distance);
 }