Advances in Space Research Journal ~ Volume 43, Issue 10, - download pdf or read online

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

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Valk et al. e. positive, and thus one can cast Eq. (6) into Y ðtÞ ¼ 2 À 1513 M 0 n0 Á g0 1 F 1 ðtÞ À F 2 ðtÞ; t t where F 1 and F 2 are positive functions and F 2 is bounded. We can then conclude that (see Fig. 1) (1) if M 0 n0 Á g0 > 0 then Y ðtÞ approaches 2 from below; (2) if M 0 n0 Á g0 < 0 then Y ðtÞ approaches 2 from above, in fact for large t the first contribution dominates the bounded term F 2 . In this last part we will consider if and under which assumptions the previous results concerning the convergence Y !

Bulirsh and Stoer, 1966; Stoer and Bulirsch, 1980). Let us note that, for the purpose 1512 S. Valk et al. / Advances in Space Research 43 (2009) 1509–1526 of validation, the numerical integrations were also made with a couple of other numerical integrators. However, the Bulirsh–Stoer algorithm seems to be the best compromise between accuracy and efficiency. Moreover, as quoted by Wisdom (1983): What is more important for this study, Benettin et al. (1980) found that the maximum LCE1 did not depend on the precision of their calculation.

Introduction Recent optical surveys in high-altitude orbits, performed by the European Space Agency 1 m telescope on Tenerife (Canary islands), have discovered a new unexpected population of 10 cm sized space debris in near geosynchronous orbits (GEO). , 2005). Following the initial guess of Liou and Weaver (2004) who suggested that this new population may be constituted by GEO objects with high area-to* Corresponding author. be (N. Delsate). mass ratios, recent numerical and analytical investigations were performed to support this assumption (Anselmo and Pardini, 2005; Liou and Weaver, 2005).

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Advances in Space Research Journal ~ Volume 43, Issue 10, Pages 1471-1594, 15 May 2009 by Elsevier


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