Design and operation of tethered satellite systems

A mathematical model of a class of motions of a chain of material points (i.e., a tethered satellite system) in the gravitational field of a planet is presented. This class is defined by the requirement that the rectilinear form of the chain be conserved for any type of relative motion. Design and transformation rules are obtained for the motion of the chain in circular orbit with orientation along the radius vector. For a more general case of motion, the design problem is divided into a dynamic one and a geometric one, and general laws governing the deployment of the system into the class of motions under consideration are established. Analytical formulas for evaluating system parameters in various modes of operation are presented.