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Extra info for Advances in Space Research Journal ~ Volume 43, Issue 10, Pages 1471-1594, 15 May 2009

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Advances in Space Research 43 (2009) 1509–1526 of the scientific community. In the particular case of classical near-geosynchronous objects, the problem has been solved by computing the MEGNO indicator for a family of simulated geostationary, geosynchronous and super-geosynchronous orbits. A classical near-geosynchronous object has a period close to one sidereal day and is subjected to the main gravitational effects of the Earth, including the 1:1 resonance, luni-solar perturbing effects, as well as solar radiation pressure associated to a small area-tomass ratio ðA=m ( 1m2 =kgÞ.

Anselmo, C. 5°, superimposed on a longer term trend driven by third body attraction. An increase in A/M would result in a faster nodal regression and wider amplitude of the inclination oscillation, even though, for any given value of A/M, the nodal rate and the inclination excursion would depend on the initial conditions. 6 years. e. with i > 90°) for some time. For instance, this situation would occur with CR Á A/M P 48 m2/kg in the B1 case (Fig. 22) and with CR Á A/M P 54 m2/kg in the C4 case.

Regarding the numerical computation of the MEGNO indicator, we adopt the same strategy as in Goz´dziewski et al. (2001). To be specific, in addition to the numerical integrations of both the equations of motion and the first order variation equations, we consider the two additional differential equations d d_ Á d y¼ ; dt dÁd d y w¼2 ; dt t ð5Þ which allow to derive the MEGNO indicators as Y ðtÞ ¼ 2 yðtÞ=t; Y ðtÞ ¼ wðtÞ=t: The MEGNO criterion, unlike the common Lyapunov variational methods, takes advantage of the whole dynamical information for the orbits and the evolution of its tangent vector, which results in shorter times of integration to achieve comparable results.

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