# FROM ORDER TO CHAOS IN EARTH SATELLITE ORBITS

## Abstract

We consider Earth satellite orbits in the range of semimajor axes where the perturbing effects of Earth’s oblateness and lunisolar gravity are of comparable order. This range covers the medium-Earth orbits (MEO) of the Global Navigation Satellite Systems and the geosynchronous orbits (GEO) of the communication satellites. We recall a secular and quadrupolar model, based on the Milankovitch vector formulation of perturbation theory, which governs the long-term orbital evolution subject to the predominant gravitational interactions. We study the global dynamics of this two-and-a-half degrees-of-freedom Hamiltonian system by means of the fast Lyapunov indicator (FLI), used in a statistical sense. Specifically, we characterize the degree of chaoticity of the action space using angle-averaged normalized FLI maps, thereby overcoming the angle dependencies of the conventional stability maps. Emphasis is placed upon the phase-space structures near secular resonances, which are of primary importance to the space debris community. We confirm and quantify the transition from order to chaos in MEO, stemming from the critical inclinations and find that highly inclined GEO orbits are particularly unstable. Despite their reputed normality, Earth satellite orbits can possess an extraordinarily rich spectrum of dynamical behaviors and, from a mathematical perspective, have all the complications that make themmore »

- Authors:

- Department of Mathematics, University of Rome Tor Vergata, I-00133 Rome (Italy)
- IMCCE/Observatoire de Paris, Université Lille1, F-59000 Lille (France)
- IFAC-CNR, 50019 Sesto Fiorentino, Florence (Italy)

- Publication Date:

- OSTI Identifier:
- 22662951

- Resource Type:
- Journal Article

- Journal Name:
- Astronomical Journal (Online)

- Additional Journal Information:
- Journal Volume: 152; Journal Issue: 5; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1538-3881

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; CHAOS THEORY; COMPARATIVE EVALUATIONS; DEGREES OF FREEDOM; GRAVITATION; GRAVITATIONAL INTERACTIONS; HAMILTONIANS; INCLINATION; ORBITS; PERTURBATION THEORY; PHASE SPACE; PLANETS; SATELLITES; STABILITY

### Citation Formats

```
Gkolias, Ioannis, Gachet, Fabien, Daquin, Jérôme, and Rosengren, Aaron J., E-mail: gkolias@mat.uniroma2.it.
```*FROM ORDER TO CHAOS IN EARTH SATELLITE ORBITS*. United States: N. p., 2016.
Web. doi:10.3847/0004-6256/152/5/119.

```
Gkolias, Ioannis, Gachet, Fabien, Daquin, Jérôme, & Rosengren, Aaron J., E-mail: gkolias@mat.uniroma2.it.
```*FROM ORDER TO CHAOS IN EARTH SATELLITE ORBITS*. United States. doi:10.3847/0004-6256/152/5/119.

```
Gkolias, Ioannis, Gachet, Fabien, Daquin, Jérôme, and Rosengren, Aaron J., E-mail: gkolias@mat.uniroma2.it. Tue .
"FROM ORDER TO CHAOS IN EARTH SATELLITE ORBITS". United States. doi:10.3847/0004-6256/152/5/119.
```

```
@article{osti_22662951,
```

title = {FROM ORDER TO CHAOS IN EARTH SATELLITE ORBITS},

author = {Gkolias, Ioannis and Gachet, Fabien and Daquin, Jérôme and Rosengren, Aaron J., E-mail: gkolias@mat.uniroma2.it},

abstractNote = {We consider Earth satellite orbits in the range of semimajor axes where the perturbing effects of Earth’s oblateness and lunisolar gravity are of comparable order. This range covers the medium-Earth orbits (MEO) of the Global Navigation Satellite Systems and the geosynchronous orbits (GEO) of the communication satellites. We recall a secular and quadrupolar model, based on the Milankovitch vector formulation of perturbation theory, which governs the long-term orbital evolution subject to the predominant gravitational interactions. We study the global dynamics of this two-and-a-half degrees-of-freedom Hamiltonian system by means of the fast Lyapunov indicator (FLI), used in a statistical sense. Specifically, we characterize the degree of chaoticity of the action space using angle-averaged normalized FLI maps, thereby overcoming the angle dependencies of the conventional stability maps. Emphasis is placed upon the phase-space structures near secular resonances, which are of primary importance to the space debris community. We confirm and quantify the transition from order to chaos in MEO, stemming from the critical inclinations and find that highly inclined GEO orbits are particularly unstable. Despite their reputed normality, Earth satellite orbits can possess an extraordinarily rich spectrum of dynamical behaviors and, from a mathematical perspective, have all the complications that make them very interesting candidates for testing the modern tools of chaos theory.},

doi = {10.3847/0004-6256/152/5/119},

journal = {Astronomical Journal (Online)},

issn = {1538-3881},

number = 5,

volume = 152,

place = {United States},

year = {2016},

month = {11}

}