The tether co-rotates with Earth at Ω = 2π / 86164 s. A climber moving outward at radial speed vr in this rotating frame feels a Coriolis acceleration acor = 2Ω·vr, directed tangentially (east–west) — it always pushes westward while ascending. The tether reacts elastically, so the whole rod tilts about its anchor by a small angle φ that obeys a driven, damped torsional oscillator:
φ'' = 2Ω·v_r / r(t) − 2ζω₀·φ' − ω₀²·φ
r(t) = climber's distance from Earth's center
ω₀ = 2π / T (T = "restoring period" slider — stiffer tether ⇒ shorter T)
ζ = damping ratio (how quickly tether sway is absorbed)
The driving term 2Ω·v_r/r shrinks as the climber gets farther out, so deflection is strongest low down and settles toward a smaller quasi-static value φ ≈ (2Ω·v_r/r)/ω₀² as altitude grows (the exact fixed point of the ODE above when φ″ = φ′ = 0) — the mechanism real space-elevator engineering studies use to size the westward thrust or tether pre-lean needed to keep a climbing vehicle from swinging the whole structure out of alignment.
- Climber speed — sets vr; faster climbs mean a stronger, more sustained Coriolis push.
- Restoring period — a stiffer (shorter-period) tether resists sway more and settles to a smaller deflection.
- Damping ratio — how quickly any oscillation in the tilt dies out; near 0 the tether can overshoot and ring.
- Time acceleration — a real climb takes days, so simulated time is sped up to watch the full ascent from surface to counterweight.
Below geostationary radius (≈35,786 km altitude) gravity dominates and the tether hangs in tension; beyond it centrifugal effects dominate and the counterweight keeps the cable taut outward — the "below/above GEO" readout tracks which regime the climber is in. This is the same equatorial-plane tilt geometry as the 3D view, flattened into a plan view you can pan and zoom instead of orbiting a camera.