A semi-analytical approach to study resonances effects on the orbital motion of artificial satellites

Abstract

A semi-analytical approach is proposed to study resonances effects on the orbital motion of artificial satellites or space debris orbiting the Earth. Applying successive Mathieu transformations, the order of dynamical system is reduced and the final system is solved by numerical integration. In the simplified dynamical model, we can choose the resonance to be considered as critical angle. Simulations are presented showing the variations of the orbital elements of bodies orbiting in the neighbourhood of the 2:1, 14:1 and 15:1 resonance condition. The half-width of the separatrix is calculated through a linearized model which describes the behavior of the dynamical system in a neighborhood of each critical angle. A semi-analytical approach is proposed to study resonances effects on the orbital motion of artificial satellites or space debris orbiting the Earth. Applying successive Mathieu transformations, the order of dynamical system is reduced and the final system is solved by numerical integration. In the simplified dynamical model, we can choose the resonance to be considered as critical angle. Simulations are presented showing the variations of the orbital elements of bodies orbiting in the neighbourhood of the 2:1, 14:1 and 15:1 resonance condition. The half-width of the separatrix is calculated through a linearized model which describes the behavior of the dynamical system in a neighborhood of each critical angle.