https://doi.org/10.1140/epjs/s11734-025-01868-6
Regular Article
On the spin-orbit phase-space of an artificial satellite
1
Grupo de Dinâmica Orbital e Planetologia, São Paulo State University-UNESP, 12516-410, Guaratinguetá, Brazil
2
Observatório Nacional/MCTI, 20921-400, Rio de Janeiro, Brazil
3
São Paulo State University-UNESP, IGCE-DEMAC, 13506-900, Rio Claro, Brazil
a
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Received:
30
April
2025
Accepted:
17
August
2025
Published online:
23
August
2025
Abstract
Artificial satellites are usually in a spin-orbit synchronous state, keeping the same face pointed towards the Earth. In this work, we study the spin-orbit dynamics of an elongated satellite under the gravitational attraction of the Earth, without any kind of altitude control. The shape of the satellite is characterized by the asphericity parameter 
where 
are the principal moments of inertia. Using the Poincaré surface of section technique, we explore the spin-orbit phase space of the satellite for two representative values of 
The orbital eccentricity is a crucial parameter in such a study. Then, the dynamics is explored for a range of eccentricity values. The location and size of the main spin-orbit resonances are identified. We pay special attention to the 1:1 synchronous spin-orbit resonance. The periodic orbit associated to the 1:1 resonance bifurcates at a critical value of 
and an analytical model is capable of reproducing its topological evolution. For practical purposes, there is a limiting amplitude of oscillation of the satellite that meets the mission requirements for synchronous behavior. To exemplify this, a case is assumed in which the satellite must remain pointing to the Earth’s surface. For a wide range of the maximum eccentricity is estimated as a function of the satellite altitude, and an analysis of the parameters that would be compatible with such mission requirements is presented.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
