Abstract
This paper proposes new quasi-periodic orbits around Earth–Moon collinear libration points using solar sails. By including the time-varying sail orientation in the linearized equations of motion for the circular restricted three-body problem (CR3BP), four types of quasi-periodic orbits (two types around L1 and two types around L2) were formulated. Among them, one type of orbit around L2 realizes a considerably small geometry variation while ensuring visibility from the Earth if (and only if) the sail acceleration due to solar radiation pressure is approximately of a certain magnitude, which is much smaller than that assumed in several previous studies. This means that only small solar sails can remain in the vicinity of L2 for a long time without propellant consumption. The orbits designed in the linearized CR3BP can be translated into nonlinear CR3BP and high-fidelity ephemeris models without losing geometrical characteristics. In this study, new quasi-periodic orbits are formulated, and their characteristics are discussed. Furthermore, their extendibility to higher-fidelity dynamic models was verified using numerical examples.
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Abbreviations
- a :
-
acceleration due to SRP (m/s2)
- A :
-
area of reflective surface (m2)
- B f :
-
Lambertian coefficient
- c :
-
speed of light (m/s)
- Ca, Cs, C d :
-
coefficients of optical properties
- CR3BP:
-
circular restricted three-body problem
- d S :
-
distance between the Sun and the Earth–Moon barycenter (km)
- D :
-
spacecraft-to-Sun distance (au)
- m :
-
spacecraft mass (kg)
- n :
-
unit vector normal to reflective surface
- r :
-
position (km)
- s :
-
unit vector directed from reflective surface to the Sun
- SRP:
-
solar radiation pressure
- S 0 :
-
solar constant (W/m2)
- t :
-
time (day)
- U :
-
effective potential in CR3BP
- θ, ϕ, ψ :
-
2–1–3 Euler angles (rad)
- Θ S :
-
phase angle for the Sun (rad)
- µ :
-
gravitational parameter
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Acknowledgements
This study was supported by the Japan Society for the Promotion of Science, KAKENHI Grant No. JP21K14345.
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Open access funding provided by Tokyo Institute of Technology.
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Toshihiro Chujo received his Ph.D. degree in engineering from the University of Tokyo, Japan, in 2017. He is currently an assistant professor at Tokyo Institute of Technology, Japan. His main research field includes astrodynamics, space mission design, and spacecraft system, especially for solar sails. E-mail: chujo.t.aa@m.titech.ac.jp
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Chujo, T. Quasi-periodic orbits of small solar sails with time-varying attitude around Earth–Moon libration points. Astrodyn 8, 161–174 (2024). https://doi.org/10.1007/s42064-023-0186-0
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DOI: https://doi.org/10.1007/s42064-023-0186-0