In the latest years there has been a growing interest in satellite formation flight and distributed satellite systems, in the context of such missions as space-based radar or interferometry. For example, different strategies and configurations have been proposed to complement SAR constellations with along-track and cross-track interferometry, and mission analyses have been carried out in the framework of several on-going projects. This recent flurry of research lead to the development of several sets of equations to predict and understand relative motion between satellites in a cluster, trying to improve Hill’s equations by inclusion of Earth oblateness effects. Actually, most of these studies were devoted to formation control, rather than orbital configuration design. In this paper, the authors present an analytical model which allows a time-explicit representation of relative motion on the basis of orbital parameters’ differences between satellites. In this way, it is possible to easily understand relations between orbital parameters and relative kinematics. In particular, first a new set of equations is developed, which generalizes, in the context of unperturbed dynamics, previous results. Two different sets of equations are derived, referring to the case of one of the satellites on a circular orbit, or both satellites on low eccentricity orbits, respectively. Then, these equations are improved by incorporating J2 secular effects, without changing the line of reasoning followed in their derivation. Numerical simulations have been performed in order to show how accurately can the new equations predict the relative motion. In particular, modeling errors are evaluated by calculating approximate and exact (non linear) solution, and achievable accuracy performance is compared with that of other linear models. Achieved results show that the new equations are able to capture J2 secular effects with a good approximation on an acceptable timescale, with respect to design requirements.
An analytical model to design satellite formations taking into account J2 effects / Fasano, Giancarmine; M., D’Errico. - ELETTRONICO. - (2005), pp. 1-12. (Intervento presentato al convegno XVIII Congresso nazionale AIDAA tenutosi a Volterra nel Settembre 2005).
An analytical model to design satellite formations taking into account J2 effects
FASANO, GIANCARMINE;
2005
Abstract
In the latest years there has been a growing interest in satellite formation flight and distributed satellite systems, in the context of such missions as space-based radar or interferometry. For example, different strategies and configurations have been proposed to complement SAR constellations with along-track and cross-track interferometry, and mission analyses have been carried out in the framework of several on-going projects. This recent flurry of research lead to the development of several sets of equations to predict and understand relative motion between satellites in a cluster, trying to improve Hill’s equations by inclusion of Earth oblateness effects. Actually, most of these studies were devoted to formation control, rather than orbital configuration design. In this paper, the authors present an analytical model which allows a time-explicit representation of relative motion on the basis of orbital parameters’ differences between satellites. In this way, it is possible to easily understand relations between orbital parameters and relative kinematics. In particular, first a new set of equations is developed, which generalizes, in the context of unperturbed dynamics, previous results. Two different sets of equations are derived, referring to the case of one of the satellites on a circular orbit, or both satellites on low eccentricity orbits, respectively. Then, these equations are improved by incorporating J2 secular effects, without changing the line of reasoning followed in their derivation. Numerical simulations have been performed in order to show how accurately can the new equations predict the relative motion. In particular, modeling errors are evaluated by calculating approximate and exact (non linear) solution, and achievable accuracy performance is compared with that of other linear models. Achieved results show that the new equations are able to capture J2 secular effects with a good approximation on an acceptable timescale, with respect to design requirements.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
