Formiga, J. K. S.; Moraes, R. V. Orbital characteristics of artificial satellites in… ORBITAL CHARACTERISTICS OF ARTIFICIAL SATELLITES IN RESONANCE AND THE CORRESPONDENT GEOPOTENCIAL COEFFICIENTS Jorge Kennety. S. Formiga Space Mechanics and Control Division – DMC - National Institute for Space Research – INPE; Avenida dos Astronautas, 1758 – P.O. Box 515; 12201-940 - São José dos Campos, S.P., Brazil jkennety@dem.inpe.br Rodolpho Vilhena de Moraes The State São Paulo University – UNESP; Avenida Ariberto P. Da Cunha, 333 – P.O. Box 205; 125116-410 - Guaratinguetá, S.P., Brazil rodolpho@feg.unesp.br Abstract: the purpose of this work is to present the orbital eccentricities and inclinations characteristics for some real artificial satellites, some of them already inactive, whose mean motions are commensurable with the Earth’s rotation period. The correspondent geopotential coefficients for each considered resonance are also presented. 1 Introduction The influence of resonances in the translational and the rotational motion of artificial satellite has been studied covering several aspects such as: a) considering commensurabilities of the satellite’s orbital motion with the planet’s rotational motion (see, for instance, including internal cited references, Gedeon et al., 1967; Sochilina, 1982; Grosso, 1980; Ely and Howell, 1996; Lima Jr., 2000; Klokocnik et al., 2003); b) considering critical inclination (Allan, 1965; Gedeon, 1969; Delhaise and Henrard, 1991); c) considering lunisolar perturbations (Cook, 1962; Hughes 1980; Breiter, 2001; Lima Jr et al, 2001; Deleflie et al. 2005), d) including sun-syncronous orbits (Hough, 1981); e) considering solar radiation pressure (Polyakova, 1963; Ferraz-Mello, 1979; Vilhena de Moraes, 1979; El- Saftawi, 2004); f) considering spin-orbit coupling (Beletskii, 1975; Hamill and Blitzer, 1974; Vilhena de Moraes and Silva, 1990); g) considering frequencies related with the rotational motion (Hitzl and Breakwell, 1970; Modi and Pand, 1975), and including vibrations of some parts of the satellites (Pringle, 1973; Cochran and Holloway, 1980). The resonance considered here is the commensurability between n, the satellite’s mean motion, and E ω , the mean angular rate of rotation of the Earth, that is, 0 q pn E ≈ ω − where p and q are integers . Of course, due to the non-uniform distribution of the Earth’s mass, it must be also considered the precession of the angular keplerian elements. The long period behaviour of the orbital elements, considering perturbations due to this resonance, is distinct for each pair (p,q) and for satellites in orbits of small or great eccentricities and or inclinations (Formiga, 2005). In this work, it is exhibited several actual examples of such satellites. The knowledge of real cases is important for the construction of theories with orbital maintenance or surveillance purposes when resonance is taking into account. Since the magnitude of the orbital perturbations due to a resonance depends on the harmonic coefficients, it is also presented here, for each considered resonance, the corresponding main harmonics coefficients. Journal of Aerospace Engineering, Sciences and Applications, May – Aug. 2008, Vol. I, No 2 33