Linearized relative orbital motion model about an oblate body without averaging

A new linearized differential equation model and solution for spacecraft relative motion about an oblate body is obtained without averaging the perturbing acceleration, and presented for the case of near-zero chief orbit eccentricity. The model is stand-alone and does not require integration of the chief orbit, while the time-explicit solution depends only on initial chief orbital elements, time since epoch and node crossing, and the deputy’s initial conditions in the chief Hill frame. The resulting model outperforms previous models obtained via averaging, and has a similar error to the GA-STM for zero initial chief orbit eccentricity.