In this paper a State Transition Matrix for the relative orbital motion expressed in Dromo variables is obtained using linear theory and applied to propagate the uncertainty of Near Earth Asteroids under N-body gravitational perturbation. Dromo is a special perturbation method that offers important advantages both for the numerical propagation and for the analytical treatment of perturbed orbital motion. When applied to linear uncertainty propagation, the proposed method is found to be less complex than non-linear methods, both from the mathematical and the computational point of view, and overcomes fundamental limitations of linear methods based on Cartesian coordinates. A new index is proposed to assess the strength of non-linearities across the size of the uncertainty region during close encounters. When used in combination with the orbit condition code (OCC) proposed by the Minor Planet Center, the index can be used for predicting the evolution of the non-linearities in the uncertainty probability density function and to assess the domain of applicability of the proposed method. Test cases are conducted using real asteroids experiencing multiple close encounters.
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