Spiral Trajectory of Satellites Subjected to Drag Forces in the Atmosphere

In recent years, interest in rockets and artificial satellites mounted on rockets has been growing, with floating space debris a cause for special concern. Rockets and satellites moving near Earth have circular, elliptical, and hyperbolic orbits if their speeds relative to Earth are given by v = 7.9 km/s, 7.9 km/s < v < 11.2 km/s, and v > 11.2 km/s, respectively.¹ These trajectories are shown to solve the central force field problem in many classic textbooks, and drag forces are often described in university texts on mechanics, but most high school textbooks do not mention them. Most high school students would therefore find it difficult to logically explain a rocket or artificial satellite being unable to maintain circular motion, resulting in a spiral trajectory under a drag force.