Model for Linearized Satellite Relative Motion About a J(2)-Perturbed Mean Circular Orbit
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A set of linearized relative motion equations are derived with respect to a mean circular reference orbit by using expressions for the secular drift rates and the short-period variations of the chief's orbital elements has been reported. A mean circular reference orbit and a rotating reference frame are chosen to express the relative motion equations in the phase space comprising the relative position and velocity vectors. The long-period terms for elliptic orbits can be ignored for simplifying the STM, especially for prediction times less than the perigee rotation period. The fidelity of the model has been verified on several test cases and by comparisons of the in-track errors with those associated with linearization of the two-body gravitational field. The developed model can be used for rapid mission analysis and the design and evaluations of formation control strategies.
