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Model of \(J_2\) perturbed satellite relative motion with time-varying differential drag

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Abstract

This work revisits the modeling of the relative motion between satellites flying in near-circular low-Earth-orbits. The motion is described through relative orbital elements and both Earth’s oblateness and differential drag perturbations are addressed. With respect to the former formulation, the description of the \(J_2\) effect is improved by including also the changes that this perturbation produces in both relative mean longitude and relative inclination vector during a drifting phase, when a non-vanishing relative semi-major axis is required. The second major improvement consists in a general empirical formulation to include the mean effects produced by non-conservative perturbations, such as the differential aerodynamic drag acceleration. As a result, in addition to the well-known actions on the relative semi-major axis and on the mean along-track separation, the model is able to reflect the mean variation of the relative eccentricity vector due to atmospheric density oscillations produced by day and night transitions.

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Notes

  1. The relationship between ROEs and the relative Cartesian state is discussed later in Sect. 4.

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Authors and Affiliations

  1. German Space Operations Center, German Aerospace Center, Münchener Straße 20, 82234, Weßling, Germany

    Gabriella Gaias, Jean-Sébastien Ardaens & Oliver Montenbruck

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  1. Gabriella Gaias
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  2. Jean-Sébastien Ardaens
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  3. Oliver Montenbruck
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Correspondence to Gabriella Gaias.

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Gaias, G., Ardaens, JS. & Montenbruck, O. Model of \(J_2\) perturbed satellite relative motion with time-varying differential drag. Celest Mech Dyn Astr 123, 411–433 (2015). https://doi.org/10.1007/s10569-015-9643-2

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  • DOI: https://doi.org/10.1007/s10569-015-9643-2

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