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Astrodynamics

Article Title

Analysis of equilibria in the doubly synchronous binary asteroid systems concerned with non-spherical shape

Keywords

doubly synchronous, binary asteroid, equilibria, non-spherical shape, stability

Abstract

This paper investigates the equilibria and their stabilities in the doubly synchronous binaryasteroid systems, which are modelled as the two tri-axial ellipsoids with various shapeand system parameters. Particularly, the influences of shape and system parameters onequilibria are discussed analytically. Firstly, the geometrical models of doubly synchronousbinary asteroid systems are established. The dual second degree and order gravity field isemployed to approximate the gravitational potential of the system. Six shape and systemparameters are defined. Then, based on the linearized perturbation equations, the explicitexpressions of the offsets of equilibria in doubly synchronous systems are derived, whichclearly illustrate the relationship between the distribution of equilibria and the variations ofshape parameters. Further, the approximate expressions are applied to estimate the offsetsof equilibria due to parameter errors, respectively. Finally, in order to have a better insightinto the equilibriaum structure, the stabilities of equilibria under different system parametersare investigated. In particular, critical regions of triangular equilibria are calculated andthe role of the relative distance on the stability is discussed in detail. This study couldprovide a preliminary analysis of equilibria for the mission design in doubly synchronousbinary asteroid systems.

Publisher

Tsinghua University Press

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