Energy and orbital stability in a partially-deployed earth space elevator

The Earth Space Elevator is an ingenious concept aimed at providing easy access to space, eliminating the need for rockets and potentially reducing drastically the launch costs. Technical advancements that could make the Space Elevator possible, among others, would be the availability of long carbon nanotubes or other superstrong and light material. This paper aims at addressing issues related with the stability of the system when the elevator is partially deployed starting from a nucleus in geostationary orbit (GEO). As noted by various authors, the energy increase needed to keep the orbital centre (where the gravity and centrifugal forces balance out) at GEO altitude during deployment while the tether is lengthened leads to an orbit with a positive orbital energy, i.e., the circular orbit has an energy level pertaining to a hyperbolic orbit. This situation leads to the instability of the unanchored system that would tend to escape from the geostationary orbit. The paper illustrates the change in orbital energy during assembly for a system made of a cylindrical tether and then investigate the stability of the coupled orbital and attitude motion in the orbital plane before anchoring. The analysis leads to the conclusion that the orbital motion instability ensues well before the orbital energy of the unperturbed system becomes positive.