Space Elevator Orbital Mechanics (2D)

The 3D space-elevator scene this page pairs with is built for spectacle: its climber simply linear-interpolates between a fixed anchor and a fixed counterweight height every frame, with no orbital mechanics actually driving that motion despite the title. This 2D companion replaces the decoration with the real physics the concept depends on. At every point along the tether it computes the gravitational acceleration pulling the climber toward Earth (g(r) = GM/r²) and the centrifugal acceleration flinging it outward as Earth's rotation carries the whole tether around (ω²r), then shows their difference as the net force the cable structure has to resist. Below the geostationary radius — where a satellite would need to orbit once per day to stay above the same point on the ground — gravity wins and the tether must pull the climber up to keep it from falling; above that radius, the spin wins and the tether must pull the climber in to keep it from flying off. Sliders let you change the climb speed, move the counterweight's radius (which sets how far beyond geostationary orbit the whole system extends), and speed up or slow down Earth's rotation — watch the live r_geo figure shift as spin changes, exactly as the real cube-root relationship r_geo = (GM/ω²)^(1/3) predicts.