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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 570127, 11 pages
Research Article

Averaging Tesseral Effects: Closed Form Relegation versus Expansions of Elliptic Motion

1C/Columnas de Hercules 1, San Fernando, Spain
2Universidad de La Rioja, Logroño, Spain

Received 7 February 2013; Accepted 26 March 2013

Academic Editor: Antonio F. Bertachini A. Prado

Copyright © 2013 Martin Lara 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.


Longitude-dependent terms of the geopotential cause nonnegligible short-period effects in orbit propagation of artificial satellites. Hence, accurate analytical and semianalytical theories must cope with tesseral harmonics. Modern algorithms for dealing analytically with them allow for closed form relegation. Nevertheless, current procedures for the relegation of tesseral effects from subsynchronous orbits are unavoidably related to orbit eccentricity, a key fact that is not enough emphasized and constrains application of this technique to small and moderate eccentricities. Comparisons with averaging procedures based on classical expansions of elliptic motion are carried out, and the pros and cons of each approach are discussed.