Instability of fixed, low-thrust drag compensation

FORCED drag compensation using continuous low-thrustpropulsion 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 beunavailable. 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 levelis exponentially unstable for all physically reasonable atmosphere models.