A satellite orbits Earth in an elliptical path. At its closest point (perigee), it is 300 km above Earths surface; at farthest point (apogee), 1200 km above. Given Earths radius is 6371 km, what is the semi-major axis of the orbit in kilometers? - Coaching Toolbox
A satellite orbits Earth in an elliptical path. At its closest point (perigee), it is 300 km above the surface; at its farthest point (apogee), 1200 km above. Given Earth’s radius is 6371 km, what is the semi-major axis of the orbit in kilometers?
A satellite orbits Earth in an elliptical path. At its closest point (perigee), it is 300 km above the surface; at its farthest point (apogee), 1200 km above. Given Earth’s radius is 6371 km, what is the semi-major axis of the orbit in kilometers?
Why satellite orbits with elliptical paths are shaping thinking today—from space sustainability debates to global broadband access—this fundamental orbital geometry reveals more than just mechanics. Understanding how satellites move across such varied distances helps clarify their role in telecommunications, weather tracking, and Earth observation. As users increasingly rely on satellite-enabled services, knowing the precise parameters behind these paths builds deeper digital awareness.
Why A satellite orbits Earth in an elliptical path. At its closest point (perigee), it is 300 km above Earths surface; at farthest point (apogee), 1200 km above. Given Earths radius is 6371 km, what is the semi-major axis of the orbit in kilometers?
Understanding the Context
Orbits aren’t always perfect circles—most natural and artificial satellites trace ellipses shaped by gravity and velocity. For a satellite fluctuating between 300 km and 1200 km above Earth’s surface, the semi-major axis represents the average distance from the planet’s center. This average—found by summing perigee and apogee heights, then dividing by two—forms a core metric for satellite engineers and researchers. It reflects not just current position, but the orbital balance that enables stable, predictable motion.
Deriving the semi-major axis starts with perigee and apogee heights: 300 km and 1200 km. Adding these gives 1500 km, the sum across the ellipse’s widest span. Dividing by two isolates the average—1500 ÷ 2 = 750 km. This midpoint marks the orbit’s effective radius from Earth’s center: 6371 km (Earth’s radius) + 750 km = 7121 km. The semi-major axis, therefore, is 7121 kilometers—a key figure in tracking satellite behavior.
How A satellite orbits Earth in an elliptical path. At its closest point (perigee), it is 300 km above Earths surface; at farthest point (apogee), 1200 km above. Given Earths radius is 6371 km, what is the semi-major axis of the orbit in kilometers?
Now, unpack the calculation using standard orbital mechanics. The perigee lies 300 km above Earth, so its distance from Earth’s center is 6371 + 300 = 6671 km. Apogee, at 1200 km above, measures 637
