Several new uses of satellite tethers are discussed, including: (1) using tether extension to reposition a satellite in orbit without fuel expenditure by extending a mass on the end of a tether; (2) using a tether for energy storage to power the satellite during eclipse; and (3) using a tether for eccentricity pumping to correct perturbations in the orbit and as a means of adding energy to the orbit for boosting and orbital transfer.
Orbital Repositioning of a SatelliteIn trod u c ti on One of the limitations of the working lifetime of a satellite is the expenditure of fuel required for changing and maintaining the orbit. In geosynchronous orbit, the orbit is subject to perturbations, primarily due to the gravitational effects of the sun and the moon. Fuel is also required for relocating a satellite, for example, if a synchronous satellite positioned over Indonesia is desired to be relocated over South America.A tether is a long, flexible cable which connects one part of a satellite with another.Tethers have recently been well covered in the aerospace literature [ref. 1-51. In the equilibrium configuration, as shown in figure 1, the tether is oriented radially outward, with a tension on the tether due to the gravitational gradient (or "tidal") force. Mass of the cable is an important figure. A figure of merit for material strength is the critical length L,, the length of untapered cable that could be suspended in a 1-g gravitational field. One proposed cable material is Kevlar, for one common type of which the critical length is 250 km [6]. The effective acceleration due to the gravity gradient a distance x from the center of mass (CM) is, to first order:where go is the gravity at the Earth's surface, r, is the orbital radius and re is the radius of the earth. At geosynchronous Earth orbit (GEO), 3 rq/r: = 1 . 6 . 1 0 -~ km-1.The minimum mass m, of untapered cable required to support an end mass m, is thus to first order (for x in km):Thus, in GEO a 1000 km long tether can easily be made much less massive than the satellite it supports.Most analyses of tether orbits assume that the center of mass of a tethered satellite system remains in the original orbit [1,2]; %.e., that the angular velocity of the tethered satellite does not change as the tether is extended or retracted. We note that this is true only to the first order approximation in tether length. Briefly, the mass that extends outward experiences an increase in centrifugal force that increases linearly with distance, but the mass that extends inward experiences an increase in gravity that increases faster than linearly. Thus, the center of mass of the orbit is pulled inward, and to conserve angular momentum, the angular velocity of the orbit increases.
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Mathematical AnalysisIn the following discussion we assume a tether of negligible mass in circular orbit.The extension of the analysis to tethers of non-negligible mass is straightforward.Consider a satellite of mass mi consisting of two pieces of mass ml=rn2=m/2 connected by a tether. The init...
