# Dynamical cartography of Earth satellite orbits

## TL;DR

This paper presents a comprehensive numerical study of Earth satellite orbit dynamics over 120 years, mapping stability regions and resonance effects to inform debris removal strategies.

## Contribution

It provides the first detailed dynamical atlas of Earth satellite orbits considering multiple perturbations and resonance interactions over long timescales.

## Key findings

- Identification of stable and chaotic orbital regions
- Resonance overlaps create potential disposal zones
- Impact of increased area-to-mass ratio on stability

## Abstract

We have carried out a numerical investigation of the coupled gravitational and non-gravitational perturbations acting on Earth satellite orbits in an extensive grid, covering the whole circumterrestrial space, using an appropriately modified version of the SWIFT symplectic integrator, which is suitable for long-term (120 years) integrations of the non-averaged equations of motion. Hence, we characterize the long-term dynamics and the phase-space structure of the Earth-orbiter environment, starting from low altitudes (400 km) and going up to the GEO region and beyond. This investigation was done in the framework of the EC-funded "ReDSHIFT" project, with the purpose of enabling the definition of passive debris removal strategies, based on the use of physical mechanisms inherent in the complex dynamics of the problem (i.e., resonances). Accordingly, the complicated interactions among resonances, generated by different perturbing forces (i.e., lunisolar gravity, solar radiation pressure, tesseral harmonics in the geopotential) are accurately depicted in our results, where we can identify the regions of phase space where the motion is regular and long-term stable and regions for which eccentricity growth and even instability due to chaotic behavior can emerge. The results are presented in an "atlas" of dynamical stability maps for different orbital zones, with a particular focus on the (drag-free) range of semimajor axes, where the perturbing effects of the Earth's oblateness and lunisolar gravity are of comparable order. In some regions, the overlapping of the predominant lunisolar secular and semi-secular resonances furnish a number of interesting disposal hatches at moderate to low eccentricity orbits. All computations were repeated for an increased area-to-mass ratio, simulating the case of a satellite equipped with an on-board, area-augmenting device.

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Source: https://tomesphere.com/paper/1904.05825