Astronomy and Astrophysics – Astrophysics
Scientific paper
Dec 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011sf2a.conf..673l&link_type=abstract
SF2A-2011: Proceedings of the Annual meeting of the French Society of Astronomy and Astrophysics Eds.: G. Alecian, K. Belkacem,
Astronomy and Astrophysics
Astrophysics
Third-Body, Disturbing Function, Hansen-Like Coefficients, Elliptic Motion, High Eccentricity, Closed-Form, Variational Integrators
Scientific paper
Many spacecrafts are or will be placed in highly eccentric orbits around telluric planets of the Solar system. Such eccentricities allow to cover a wide range of altitudes, mainly for planetology purposes. There are also orbits with very high eccentricity around the Earth, especially the GTO (Geostationary Transfer Orbit) and orbits of some space debris. In this case, the motion is strongly perturbed by the luni-solar attraction. For various reasons which will be recalled, the traditional tools of celestial mechanics are not well adapted to the particular dynamic of highly eccentric orbits. Therefore, it is necessary to develop specific techniques for this configuration. This concerns numerical as well as analytical tools. We will show how to construct the expression of the disturbing function due to the presence of an external body, well-suited for highly eccentric orbits. Expansion of the elliptic motion in closed-form by using Fourier series in multiple of the eccentric anomaly will be presented. On the other hand, classical methods of numerical integration have often a poor efficiency. We will show the interest of geometric integrators and in particular the variational integrators.
Lion G.
Métris Gilles
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