Equilibrium attitude and stability of a spacecraft on a stationary orbit around an asteroid |
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| Institution: | 1. Beijing Aerospace Automatic Control Institute, Beijing 142402, China;2. National Key Laboratory of Science and Technology on Aerospace Intelligence Control, Beijing 142402, China;3. School of Automation, Beijing Institute of Technology, Beijing 100081, China;1. Distributed Space Systems Lab, Faculty of Aerospace Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel;2. School of Astronautics, Beihang University, Beijing 100191, China;1. Delft University of Technology, Delft, The Netherlands;2. Northwestern Polytechnical University, Xi’an, China;1. Department of Control Science and Engineering, Jilin University, Changchun 130012, China;2. Department of Control Engineering, Changchun University of Technology, Changchun 130012, China |
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| Abstract: | The stationary orbits around an asteroid, if exist, can be used for communication and navigation purposes just as around the Earth. The equilibrium attitude and stability of a rigid spacecraft on a stationary orbit around a uniformly-rotating asteroid are studied. The linearized equations of attitude motion are obtained under the small motion assumption. Then, the equilibrium attitude is determined in both cases of a general and a symmetrical spacecraft. Due to the higher-order inertia integrals of the spacecraft, the equilibrium attitude is slightly away from zero Euler angles. Then necessary conditions of stability of this conservative system are analyzed based on the linearized equations of motion. The effects of different parameters, including the harmonic coefficients C20 and C22 of the asteroid and higher-order inertia integrals of the spacecraft, on the stability are assessed and compared. Due to the significantly non-spherical shape and rapid rotation of the asteroid, the effects of the harmonic coefficients C20 and C22 are very significant, while effects of the third- and fourth-order inertia integrals of the spacecraft can be neglected. Considering a spacecraft on a stationary orbit around an example asteroid, we show that the classical stability domain predicted by the Beletskii–DeBra–Delp method on a circular orbit in a central gravity field is modified due to the non-spherical mass distribution of the asteroid. Our results are confirmed by a numerical simulation. |
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