A satellite orbits Earth in an elliptical path, reaching its closest point (perigee) 300 km above Earths surface and farthest point (apogee) 1200 km above. If Earths radius is 6371 km, what is the semi-major axis of the orbit in kilometers?

["What’s the True Path of a Satellite Over Earth? The Semi-Major Axis of Its Elliptical Orbit", "In today’s data-driven world, understanding how satellites move above our planet isn’t just a niche curiosity—it’s essential for tracking space trends, supporting communications, and even monitoring environmental shifts. With growing interest in satellite technology, from global internet constellations to precision navigation systems, this elliptical orbit—reaching perigee at 300 km and apogee at 1,200 km—has sparked widespread curiosity. Is this distant path really as complex as it sounds? And how can knowing the semi-major axis of this orbit deepen your insight into satellite dynamics?", "This orbit, shaped by gravity and momentum, reveals more than just altitude numbers—it highlights the balance between speed and distance in celestial mechanics. The semi-major axis is a key metric that defines the average distance from Earth’s center, offering a clear measure of the satellite’s scale. For those tracking orbital mechanics, understanding this value provides insight into mission design, coverage patterns, and the energy required to maintain the orbit.", "### A Satellite’s Elliptical Journey: Perigee, Apogee, and Scale", "A satellite orbiting Earth in an elliptical path follows a natural gravitational equilibrium. At perigee—its closest point to Earth, only 300 km above the surface—the satellite moves fastest, driven by strong gravitational pull. At apogee, 1,200 km above Earth, the path widens and speed slows. This variation in distance defines the ellipse’s shape.", "The Earth’s radius stands at 6,371 km, a fixed reference point. Perigee altitude adds 300 km (6,671 km from center); apogee reaches 1,200 km above surface (7,571 km total). Yet what truly defines the orbit’s extent is the semi-major axis—a mathematical average of the closest and farthest points, projected outward from Earth’s center.", "### How Do We Calculate the Semi-Major Axis? A Step-by-Step Insight", "The semi-major axis (often abbreviated as a) lies at the heart of orbital mechanics. It represents the longest diameter of the ellipse, halved and measured perpendicularly from center to the midpoint of the elongated path. For elliptical satellite orbits, it is found by averaging perigee and apogee distances from Earth’s center—not just surface height.", "Using the formula: \n\[\na = \frac{(R_{\ ext{Earth, center, perigee}} + R_{\ ext{Earth, center, apogee}})}{2}\n\]", "Substituting values: \n- Perigee distance from center: 6,371 + 300 = 6,671 km \n- Apogee distance from center: 6,371 + 1,200 = 7,571 km", "\[\na = \frac{6,671 + 7,571}{2} = \frac{14"]