CALIBRATION OF LINEARIZED SOLUTIONS FOR SATELLITE RELATIVE MOTION

The motion of a deputy satellite relative to a chief satellite can be described with either Cartesian coordinates or orbital-element differences. For close proximity, both descriptions can be linearized. An underappreciated fact is that the linearized descriptions are equivalent: the linearized transformation between the two solves the linearized dynamics. This suggests a calibrated initial condition for linearized Cartesian propagation that is related to the orbital-element differences by the linearized transformation. This calibration greatly increases the domain of validity of the linearized approximation, and provides far greater accuracy in matching the nonlinear solution over a larger range of separations.