The rigid-body dynamics of tethers in space
Three fundamental tether motions were considered for payload orbital transfer with tethers: hanging, prograde libration and prograde motorised spin. The symmetrical double-ended motorised spinning tether performed best and was most efficient, improving by two orders of magnitude on the librating tether which in turn improved on the hanging tether by roughly a factor of two. An upper payload using long tethers with a motorised tether on a circular orbit can be transferred from a low to a geostationary Earth orbit by employing relatively high motor torque and a safety factor on the tether strength close to unity. Two common literature results, the constant efficiency index of seven for a hanging tether upper payload release and the maximum efficiency index of fourteen for an upper payload released from a prograde librating tether, were found to be a lower bound and quite readily breached, respectively. Orbit circularisation through tether release was found to be feasible with retrograde librating tethers. When the point of release does not occur along the local vertical then a non-optimum release of the payload was found to severely reduce the performance of payload transfer with tethers. Consequently, a very precise and accurately timed release is important for the success of payload orbital transfer with tethers since missing the point of release by a single degree with a spinning tether, say, can cause the payload to miss its required target. The best design for the outrigger system to provide the necessary resistive torque is to utilise the gravity gradient and tap the outrigger system within the gravitational potential well. In this manner the outrigger tether length can be significantly reduced and the outrigger end masses can be minimised, thus saving valuable launch mass and cost, as well as exposing less tether surface area to the space environment. With current materials the maximum ?V to be expected with a motorised tether is between 600-1400 m/s depending on the tether length and payload mass. The duration of the spin-up lasts approximately between half and a full Earth day but may vary by an hour, say, depending on the initial conditions and orbit eccentricity. Ensuring the motor torque axis remains perpendicular to the orbital plane was found to be vital otherwise the spin-up time is greatly increased. The motorised tether has the ability to shift the datum of a hanging tether, which may have useful applications in Earth monitoring or tethered Interferometry. Out-of-plane initial angular displacements or the motor torque axis not remaining perpendicular to the orbital plane caused the motorised tether to precess. Furthermore, the motion of the motorised tether with a constant motor torque was found to be regular, but quasi-periodic, which implies that the payload cannot be reliably delivered at perigee along the local vertical.