Spherical coordinate perturbation solutions to relative motion equations: Application to double transformation spherical solution

Perturbation solutions are obtained in spherical coordinates for the spacecraft relative motion problem in the case of a slightly eccentric chief orbit. The use of spherical coordinates eliminates many of the secular terms in the Cartesian coordinate solution and extends the range of validity of these solutions to larger intrack separations. Both the chief eccentricity and the normalized separation are treated as order ϵ. Finally, the third order solution is used in the "double transformation" to improve the accuracy of the "approximate double transformation" Cartesian solution and as an alternative method to obtain the proposed third order spherical solution.