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International Journal of Aerospace Engineering
Volume 2015, Article ID 475742, 6 pages
Research Article

Approximate State Transition Matrix and Secular Orbit Model

Flight Dynamics Group, ISRO Satellite Centre, Bangalore 560 017, India

Received 21 September 2014; Revised 24 February 2015; Accepted 24 February 2015

Academic Editor: Christopher J. Damaren

Copyright © 2015 M. P. Ramachandran. 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.


The state transition matrix (STM) is a part of the onboard orbit determination system. It is used to control the satellite’s orbital motion to a predefined reference orbit. Firstly in this paper a simple orbit model that captures the secular behavior of the orbital motion in the presence of all perturbation forces is derived. Next, an approximate STM to match the secular effects in the orbit due to oblate earth effect and later in the presence of all perturbation forces is derived. Numerical experiments are provided for illustration.