Second-order state transition for relative motion near perturbed, elliptic orbits Academic Article uri icon


  • This paper develops a tensor and its inverse, for the analytical propagation of the position and velocity of a satellite, with respect to another, in an eccentric orbit. The tensor is useful for relative motion analysis where the separation distance between the two satellites is large. The use of nonsingular elements in the formulation ensures uniform validity even when the reference orbit is circular. Furthermore, when coupled with state transition matrices from existing works that account for perturbations due to Earth oblateness effects, its use can very accurately propagate relative states when oblateness effects and second-order nonlinearities from the differential gravitational field are of the same order of magnitude. The effectiveness of the tensor is illustrated with various examples. Springer Science+Business Media B.V. 2007.

published proceedings


author list (cited authors)

  • Sengupta, P., Vadali, S. R., & Alfriend, K. T.

citation count

  • 47

complete list of authors

  • Sengupta, Prasenjit||Vadali, Srinivas R||Alfriend, Kyle T

publication date

  • February 2007