Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 659396, 17 pages
Research Article

Semianalytic Integration of High-Altitude Orbits under Lunisolar Effects

1C/Columnas de Hércules 1, ES-11100 San Fernando, Spain
2Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004 Logroño, Spain
3Departamento de Ingeniería Mecánica, Universidad de La Rioja, 26004 Logroño, Spain

Received 6 November 2011; Accepted 20 January 2012

Academic Editor: Josep Masdemont

Copyright © 2012 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.


The long-term effect of lunisolar perturbations on high-altitude orbits is studied after a double averaging procedure that removes both the mean anomaly of the satellite and that of the moon. Lunisolar effects acting on high-altitude orbits are comparable in magnitude to the Earth’s oblateness perturbation. Hence, their accurate modeling does not allow for the usual truncation of the expansion of the third-body disturbing function up to the second degree. Using canonical perturbation theory, the averaging is carried out up to the order where second-order terms in the Earth oblateness coefficient are apparent. This truncation order forces to take into account up to the fifth degree in the expansion of the lunar disturbing function. The small values of the moon’s orbital eccentricity and inclination with respect to the ecliptic allow for some simplification. Nevertheless, as far as the averaging is carried out in closed form of the satellite’s orbit eccentricity, it is not restricted to low-eccentricity orbits.