The spacecraft mission to asteroids is one of hot spots in the deep space exploration presently. The attitude dynamics of the spacecraft around the asteroids is a fundament problem in the mission. Meantime, the modern spacecrafts often have flexible appendages.

  In this work, we investigate the attitude stability of a spacecraft with two flexible solar arrays on a stationary orbit subjected to the fourth-order gravity gradient torque, in which the effect of the second order and degree harmonics C₂₀ and C₂₂ of the asteroids is considered emphatically. The sufficient conditions of attitude stability of the spacecraft are derived. The results obtained are generalized and encompass some special cases. The attitude stability domains determined by the sufficient conditions are analyzed in depth.

  It is found that the attitude stability domains of the spacecraft with two flexible solar arrays are evidently different when the solar arrays are installed in different directions (see Fig. 1); the effect of the harmonics C₂₀ and C₂₂ of the asteroids always has the significant  influence on the attitude stability domains of the spacecrafts with flexible appendages moving on stationary orbits; in the certain case, the effect of the harmonics C₂₀ and C₂₂ of the asteroids has no influence on the attitude stability domains of the rigid spacecrafts moving on stationary orbits, i.e. the attitude stability domains determined with and without C₂₀ and C₂₂ are the same and both the classical Lagrange regions (the asteroids 4769 Castalia and 25143 Itokawa just belong to this kind of asteroid), but in the other cases, the effect of the harmonics C₂₀ and C₂₂ of the asteroids has also the significant influence on the attitude stability domains of the rigid spacecrafts moving on stationary orbits; whether the harmonics C₂₀ and C₂₂ of the asteroids are considered or not, the effect of flexible appendages decreases the attitude stability domains.

（By with for ZHANG Mingjiang）

Fig.1 The attitude stability domains (shadow areas) of the spacecraft with three different configurations moving on stationary orbits around the asteroids 4769 Castalia and 25143 Itokawa 

The work by M.J. Zhang, C.Y. Zhao has been published in Astrophysics and Space Science. Please see the link for more details: http://link.springer.com/article/10.1007/s10509-014-1863-5