Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 768973, 12 pages
Research Article

Comparison between Two Methods to Calculate the Transition Matrix of Orbit Motion

1Grupo de Dinâmica Orbital e Planetologia, Departament of Mathematics, FEG/UNESP, CEP 12516-410, Guaratinguetá, SP, Brazil
2DEM-INPE, Avenida dos Astronautas, 1758, CEP 12227-010, São José dos Campos, SP, Brazil

Received 10 June 2011; Accepted 6 September 2011

Academic Editor: Maria Zanardi

Copyright © 2012 Ana Paula Marins Chiaradia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Two methods to evaluate the state transition matrix are implemented and analyzed to verify the computational cost and the accuracy of both methods. This evaluation represents one of the highest computational costs on the artificial satellite orbit determination task. The first method is an approximation of the Keplerian motion, providing an analytical solution which is then calculated numerically by solving Kepler's equation. The second one is a local numerical approximation that includes the effect of 𝐽 2 . The analysis is performed comparing these two methods with a reference generated by a numerical integrator. For small intervals of time (1 to 10 s) and when one needs more accuracy, it is recommended to use the second method, since the CPU time does not excessively overload the computer during the orbit determination procedure. For larger intervals of time and when one expects more stability on the calculation, it is recommended to use the first method.