Evaluation and comparison of relative motion theories Academic Article uri icon


  • A modeling error index is introduced for evaluating and comparing the accuracy of various theories of the relative motion of satellites to determine the effect of modeling errors on the various theories. The derived index does not require linearization of the equations of motion, and so nonlinear theories can also be evaluated. The index can be thought of as proportional to the percentage error; consequently, the smaller the index, the more accurate the theory. The results show that not including the reference orbit eccentricity and differential gravitational perturbations has a major effect on the accuracy of the theory, and the nonlinear effects are much smaller except for very large relative motion orbits. The two key parameters in the evaluation are the eccentricity of the reference orbit and the relative motion orbit size. The theories compared are Hill's equations, a small eccentricity state transition matrix, a non-J2 state transition matrix, the Gim-Alfriend state transition matrix, the unit sphere approach, and the Yan-Alfriend nonlinear method. The numerical results show the sequence of the index from high to low should be Hill's equation, non-J2, small eccentricity, Gim-Alfriend state transition matrix index, with the unit sphere approach and the Yan-Alfriend nonlinear method having the lowest index and equivalent performance. Copyright 2004 by Texas A&M University.

published proceedings


author list (cited authors)

  • Alfriend, K. T., & Yan, H.

citation count

  • 68

complete list of authors

  • Alfriend, KT||Yan, H

publication date

  • March 2005