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Instability of fixed, low-thrust drag compensation

McInnes, C.R. (2003) Instability of fixed, low-thrust drag compensation. Journal of Guidance, Control and Dynamics, 26 (4). pp. 655-657. ISSN 0731-5090

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FORCED drag compensation using continuous low-thrust propulsion has been considered for satellites in low Earth orbit. This simple, but nonoptimal, scheme merely requires that the thrust vector is directed opposite to the drag vector and that the magnitude of the two are equal. In principle, the drag force acting on the spacecraft could be determined onboard using accurate accelerometers. However, for small, low-cost spacecraft such sensors may be unavailable.An alternative strategy would be to Ž x the thrust magnitude equal to the expected air drag that would be experienced by the spacecraft. The thrust levelwould be periodically updated based on ground-based orbit determination. In this Engineering Note, it is shown that such a forced circular orbit with a Ž fixed thrust level is exponentially unstable for all physically reasonable atmosphere models.