Every point on a corotating tether feels two competing effective forces: Earth's gravity pulling it inward, GM/r², and the centrifugal effect of spinning once per sidereal day pushing it outward, ω²r. They cancel exactly at geostationary radius (r_GEO ≈ 42,164 km) — below it gravity wins, above it the spin wins. Cutting the cable at radius r and summing the net force on everything beyond that cut gives the tension it must carry:
f(r) = ω²r − GM/r²
T(r) = ∫ᵣ^top λ(r′)·f(r′) dr′ + Mc·f(top)
Tension peaks exactly at GEO and tapers toward zero at both the ground anchor and the counterweight tip. A uniform cable keeps a constant cross-section, so its stress σ = T/A follows that same peaked curve — if it exceeds the material's tensile strength (divided by the safety factor), the cable snaps at GEO. A tapered cable instead keeps stress constant everywhere by thickening exactly where tension peaks, which is the only way real proposals stay buildable — but the ratio of its widest to narrowest cross-section (the taper ratio) explodes unless the material's strength-to-density ratio is very high.
- Counterweight mass — a mass anchored beyond GEO whose outward pull is what keeps the whole tether in tension; too little and the cable goes slack.
- Anchor altitude — how far past GEO the counterweight sits; farther out means more leverage (less mass needed) but more cable to build.
- Material — steel and even carbon fiber require an astronomical taper ratio to survive; only a material with a very high strength-to-density ratio, like carbon nanotubes, keeps the taper modest — which is why every real proposal depends on them.
Real-world relevance: this is exactly the calculation that makes engineers doubt near-term space elevators — the tether has to survive its own weight against gravity and its own outward pull from spin, simultaneously, for tens of thousands of kilometers.