Operational requirements and the geometry of a station-keeping maneuver

In this paper station-keeping is regarded as the specialization of relative motion referred to a moving, orbiting origin. For this study a well-known linear solution to this problem serves as a base formulation from which the investigation begins.Even though the overall problem could be separated into three parts—necessitating two distinct studies for coverage—this paper examines only the last phase of the operation. That is, it is the continuation, or retention, of a relative motion sub-orbit which is of interest in this analysis.The situation becomes one of determining what is needed to maintain the sub-orbit, and/or to adjust it. In addition, the consequences of these actions, and the results predicted from theory are established, examined, and commented upon. In the presentation of information gathered from this study, various graphs have been prepared; however, these are expressed in a dimensionless format so that the results apply equally to all reasonable reference orbits.For this analysis the separate and combined influences, due to both the initial relative motion state and to a thrusting condition, are examined. Also, the consequences of referencing the acquired sub-orbits to an inertially aligned frame of reference (rather than the familiar rotating one) are illustrated, discussed, and commented upon.Formerly: Sr. Analyst and Manager, Seabrook Office, AMA, Inc., Seabrook, Md., U.S.A.