On the dynamics of space debris: 1:1 and 2:1 resonances

TL;DR

This paper analyzes the dynamics of space debris in Earth's 1:1 and 2:1 resonances using Hamiltonian formalism, revealing equilibrium points, stability features, and chaotic regions relevant for satellite operations.

Contribution

It introduces an effective Hamiltonian-based method to study and map the resonant regions of space debris, including equilibria and stability, validated against comprehensive Cartesian models.

Findings

Identification of equilibria and libration islands in resonant regions

Mapping of stable and chaotic zones using Fast Lyapunov Indicators

Validation of analytical results with Cartesian coordinate models

Abstract

We study the dynamics of the space debris in the 1:1 and 2:1 resonances, where geosynchronous and GPS satellites are located. By using Hamiltonian formalism, we consider a model including the geopotential contribution for which we compute the secular and resonant expansions of the Hamiltonian. Within such model we are able to detect the equilibria and to study the main features of the resonances in a very effective way. In particular, we analyze the regular and chaotic behavior of the 1:1 and 2:1 resonant regions by analytical methods and by computing the Fast Lyapunov Indicators, which provide a cartography of the resonances. This approach allows us to detect easily the location of the equilibria, the amplitudes of the libration islands and the main dynamical stability features of the resonances, thus providing an overview of the 1:1 and 2:1 resonant domains under the effect of Earth's oblateness. The results are validated by a comparison with a model developed in Cartesian coordinates, including the geopotential, the gravitational attraction of Sun and Moon and the solar radiation pressure.