diff --git a/src/orbits.cpp b/src/orbits.cpp
index 8f3e307..152384a 100644
--- a/src/orbits.cpp
+++ b/src/orbits.cpp
@@ -287,3 +287,18 @@ orbitGetTimeOfFlight(TwoBodySystem sys, double theta_begin, double theta_end)
 
 	return tof_end - tof_begin;
 }
+
+
+// internal
+
+double
+getApoapsis(double a, double e)
+{
+	return a * (1 + e);
+}
+
+double
+getPeriapsis(double a, double e)
+{
+	return a * (1 - e);
+}
diff --git a/tests/orbit_test.cpp b/tests/orbit_test.cpp
index 1d1a575..8a8e483 100644
--- a/tests/orbit_test.cpp
+++ b/tests/orbit_test.cpp
@@ -250,3 +250,28 @@ TEST_CASE("time of flight example 4.2", "[orbits]")
 	double tof = orbitGetTimeOfFlight(sys, theta_1, theta_2);
 	REQUIRE_THAT(tof, WithinAbs(7867.5, 2 * 0.5));
 }
+
+TEST_CASE("orbit shaping example 7.1", "[orbits]")
+{
+	double a = 8500.0;
+	double e = 0.15;
+	double mu = EARTH_GRAVITATIONAL_PARAMETER;
+	double epsilon = orbitGetSpecificEnergy(a, mu);
+
+	double r_apogee = getApoapsis(a, e);
+	REQUIRE_THAT(r_apogee, WithinAbs(9775, 1));
+
+	double r_perigee = getPeriapsis(a, e);
+	REQUIRE_THAT(r_perigee, WithinAbs(7225, 1));
+
+	double v_apogee = orbitGetVelocity(epsilon, mu, r_apogee);
+	REQUIRE_THAT(v_apogee, WithinAbs(5.8873, 1e-4));
+
+	double a_target = r_apogee;
+	double epsilon_target = orbitGetSpecificEnergy(a_target, mu);
+	double v_target = orbitGetVelocity(epsilon_target, mu, r_apogee);
+	REQUIRE_THAT(v_target, WithinAbs(6.3857, 1e-4));
+
+	double delta_v = v_target - v_apogee;
+	REQUIRE_THAT(delta_v, WithinAbs(0.4983, 1e-4));
+}