Space elevator

A proposed transport system using a cable extending from a planetary surface beyond a synchronous orbit. In a co-rotating model, the outward effective force on the outer portion supports the inner portion. The endpoint loads, distribution of mass, and material strength determine a feasible tension profile; the uniform unloaded space-elevator cable is an ideal limit.

A radial co-rotating cable of constant linear mass density $\lambda$ extends from planetary radius $R$ to $b={\eta }^{\prime }R$, with zero applied endpoint tension. If the geostationary orbit has radius $\eta R$, integration of the effective force gives ${\eta }^{\prime }({\eta }^{\prime }+1)=2{\eta }^3$ for a nonzero cable. At position $r$ its tension is $\lambda [GM(1/R-1/r)-{\omega }^2(r^2-R^2)/2]$. Differentiation shows the maximum at the geostationary orbit. An anchor load or counterweight alters the integrated condition.