The Orbital Dynamics of Synchronous Satellites: Irregular Motions in the 2 : 1 Resonance

Abstract

The orbital dynamics of synchronous satellites is studied. The 2 : 1 resonance is considered; in other words, the satellite completes two revolutions while the Earth completes one. In the development of the geopotential, the zonal harmonicsJ20andJ40and the tesseral harmonicsJ22andJ42are considered. The order of the dynamical system is reduced through successive Mathieu transformations, and the final system is solved by numerical integration. The Lyapunov exponents are used as tool to analyze the chaotic orbits.

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“…Figura 3 -Diferenças entre as aproximações W1, W2, e W3 , sendo que W1 foi obtida com critério de parada ϵ = 10 -8 , W2 uma expressão obtida com n=10 termos em 7 The space between the Earth and the Moon has several artificial satellites and distinct objects in some resonance. Synchronous satellites in circular or elliptical orbits have been extensively studied in literature, due to the research of resonant orbits characterizing the dynamics of these satellites (see [SAMPAIO et al, 2012a[SAMPAIO et al, , 2012b[SAMPAIO et al, , 2014 and references here in)…”

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“…The space between the Earth and the Moon has several artificial satellites and distinct objects in some resonance. Synchronous satellites in circular or elliptical orbits have been extensively studied in literature, due to the research of resonant orbits characterizing the dynamics of these satellites (see [SAMPAIO et al, 2012a[SAMPAIO et al, , 2012b[SAMPAIO et al, , 2014 and references here in)…”

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“…Synchronous satellites in circular or elliptical orbits have been extensively studied in literature, due to the research of resonant orbits characterizing the dynamics of these satellites (see [6][7][8] and references here in)…”