Real orbital mechanics: net acceleration = ω²r − μ/r² (centrifugal minus gravity). Below geostationary altitude (GEO, 42,164 km) gravity wins and the cable must carry the climber's weight; above GEO, centrifugal force wins and the structure is flung outward — that's why a real space elevator needs a counterweight beyond GEO to keep the whole cable in tension. The tension curve is a numerical integral of that same force balance along the cable.