Preliminary orbit determination of a tethered satellite using the f and g series

Abstract

A renewed interest in the deployment of tethered satellites has led to a need for a preliminary orbit determination method which is capable of distinguishing tethered satellites from untethered ones. Several of the classical preliminary orbit determination methods, which are used for Keplerian satellites, generally require two or more position vectors along with their respective observation times in order to determine a preliminary orbital element set. These conventional methods, however, are unable to distinguish between Keplerian and tethered satellites, whose motion is modified due to the presence of a tether force. The use of these conventional methods will result in the calculation of inaccurate orbital elements if the observed satellite is part of a tethered satellite system. Modifications have been made to the f and g series preliminary orbit determination method in order to allow for the identification of tethered satellites. These modifications allow for the calculation of a gravitational parameter, in addition to a set of orbital elements, which can be used to distinguish between a tethered satellite and an untethered one. This paper applies this modified f and g series method to the problem of the quick identification of a tethered satellite. The performance of this method is evaluated through scenarios of differing tether lengths, levels of observation error, and orbital eccentricities. Due to the desire for the preliminary orbit determination to be achieved quickly, only short time intervals between observations were considered. A description of how this preliminary orbit information can be used to obtain tether parameters for the subsequent differential correction process is also provided.