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

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Processo FAPESP: 09/00735-5

Processo FAPESP: 06/04997-6

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 harmonics J(20) and J(40) and the tesseral harmonics J(22) and J(42) are 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.