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Conference Paper

Coorbital restricted problem and its application in the design of the orbits of the LISA spacecraft

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Heinzel,  Gerhard
Laser Interferometry & Gravitational Wave Astronomy, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society;

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Rüdiger,  Albrecht
Laser Interferometry & Gravitational Wave Astronomy, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society;

Jennrich,  Oliver
Laser Interferometry & Gravitational Wave Astronomy, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society;

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Citation

Yi, Z., Li, G., Heinzel, G., Rüdiger, A., Jennrich, O., Wang, L., et al. (2008). Coorbital restricted problem and its application in the design of the orbits of the LISA spacecraft. International Journal of Modern Physics D, 17(7), 1005-1019.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-141E-C
Abstract
On the basis of many coorbital phenomena in astronomy and spacecraft motion, a dynamics model is proposed in this paper - treating the coorbital restricted problem together with method for obtaining a general approximate solution. The design of the LISA spacecraft orbits is a special 2+3 coorbital restricted problem. The problem is analyzed in two steps. First, the motion of the barycenter of the three spacecraft is analyzed, which is a planar coorbital restricted three-body problem. And an approximate analytical solution of the radius and the argument of the center is obtained consequently. Secondly, the configuration of the three spacecraft with minimum arm-length variation is analyzed. The motion of a single spacecraft is a near-planar coorbital restricted three-body problem, allowing approximate analytical solutions for the orbit radius and the argument of a spacecraft. Thus approximative expressions for the arm-length are given.