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Astrodynamics 2024, 8(1): 121-134 https://doi.org/10.1007/s42064-023-0180-6
Research Article | Issue | Published: 08 February 2024

How are multiple satellites seen from the ground? Relative apparent motion and formation stabilization

Show Author's Information Kenta Nakajima( ),  Yasuhiro Yoshimura,  Hongru Chen,  Toshiya Hanada
Department of Aeronautics and Astronautics, Kyushu University, 744 Motooka Nishi-ku, Fukuoka 819-0395, Japan
Keywords:
relative motion, astrodynamics, formation flying, stabilization, multi-apparent motions, space advertisement
Cite this article:
Nakajima K, Yoshimura Y, Chen H, et al. How are multiple satellites seen from the ground? Relative apparent motion and formation stabilization. Astrodynamics, 2024, 8(1): 121-134. https://doi.org/10.1007/s42064-023-0180-6
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Abstract Full text About this article

This paper answers how multiple satellites are seen from the ground. This question is inspired by space-advertising, a public exhibition in the night sky using a dot matrix of satellites that are bright enough to be seen by the naked eye. Thus, it is important for space advertisement that the specific dot matrix is seen. Moreover, the stability of the dot matrix during a visible span is very valuable. To stabilize the dot matrix, this study formulates an apparent position of a dot from a representative dot seen from the ground. The formulation, linear functions of a set of relative orbital elements, reveals the appearance of the dot matrix. The proposed relative variable in the formulation drives the instability of the dot matrix, thereby revealing an initial stable configuration of deputies from a chief. The arbitrary dot matrix designed using the configuration is stable even at low elevations without orbital control during the visible span.


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About this article

How are multiple satellites seen from the ground? Relative apparent motion and formation stabilization

Show Author's information Kenta Nakajima( ), Yasuhiro Yoshimura, Hongru Chen, Toshiya Hanada
Department of Aeronautics and Astronautics, Kyushu University, 744 Motooka Nishi-ku, Fukuoka 819-0395, Japan

Abstract

This paper answers how multiple satellites are seen from the ground. This question is inspired by space-advertising, a public exhibition in the night sky using a dot matrix of satellites that are bright enough to be seen by the naked eye. Thus, it is important for space advertisement that the specific dot matrix is seen. Moreover, the stability of the dot matrix during a visible span is very valuable. To stabilize the dot matrix, this study formulates an apparent position of a dot from a representative dot seen from the ground. The formulation, linear functions of a set of relative orbital elements, reveals the appearance of the dot matrix. The proposed relative variable in the formulation drives the instability of the dot matrix, thereby revealing an initial stable configuration of deputies from a chief. The arbitrary dot matrix designed using the configuration is stable even at low elevations without orbital control during the visible span.

Keywords: relative motion, astrodynamics, formation flying, stabilization, multi-apparent motions, space advertisement

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Publication history
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Acknowledgements

Publication history

Received: 23 June 2023
Accepted: 30 August 2023
Published: 08 February 2024
Issue date: March 2024

Copyright

© Tsinghua University Press

Acknowledgements

The authors would like to acknowledge Mr. Kazunobu Takahashi, a graduate student at Kyushu University, Japan, for his useful advice on this study and writing.

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