Design of Satellite Formations in Orbits of High Eccentricity with Performance Constraints Specified over a Region of Interest

摘要

The Magnetospheric Multiscale (MMS) mission requires a formation of four satellites in a nearly regular tetrahedron throughout a Region of Interest (RoI), defined near the apogee of a highly eccentric reference orbit. In this paper, an approach for determining the differential mean orbital element initial conditions for formations in highly eccentric orbits to maximize a Quality Factor (QF) in a RoI is presented. Previous works on the design of formations in higheccentricity orbits have used numerical integration-based approaches for orbit propagation. We present a fast optimization scheme by using the Gim-Alfriend state transition matrix. Two optimization approaches are presented for the long-term MMS formation design: a single-orbit constrained (SOC) optimization, subject to an along-track drift condition, and a multi-orbit unconstrained (MOU) optimization. A new along-track drift condition is proposed to minimize the along-track drift only in certain portions of the orbit and is shown to produce much more stable long-term behavior of the QF than the previous condition. A verification of the results using the NASA General Mission Analysis Tool is provided. Under ideal conditions, i.e., without errors in the establishment of the initial conditions, the best formation can satisfy the MMS mission QF requirements for over 80 days without corrective action.