Modifications to Encke's method for long arc orbit determination solutions

An expanded model is developed that permits the extrapolation of Encke's method for the determination of orbits with long arcs, and the model is used to determine a solution for the Lageos trajectory. Encke's method is reviewed emphasizing the nature of the growth of the Encke ratio and the reliability of extrapolated reference trajectories. The reference-orbit formulation is improved by including parameters that accommodate drag and large-amplitude perodic variations in the orbital elements. The proposed Long Arc Model is expected to provide a maximum Encke ratio that is an order of magnitude more reliable than that given by the secularly precessing ellipse. The computational cost of using the Long Arc Model is shown to compare favorably with that of the true force model, and the long arc solutions are useful for current orbit-determination needs.