A precise force model is of vital importance for dynamics and control of solar sails. Among various factors, deviations from the ideal flat sails, elastic deformations of the sails, are really important as most solar sails are large flexible membranes. In this study, the deformed sails are modeled as smooth curved surfaces and a general total force model (GTFM) for the deformed sails is proposed. Various simplified versions of this GTFM are also derived for the symmetric deformation cases. Furthermore, differences between the ideal force models and our precise GTFM are investigated. The numerical results demonstrate that both the previous ideal reflected model and flat optical model are not as satisfactory as claimed before, by contrast with the actual dynamics from the GTFM. Thus this work paves the way for sail craft's precise navigation where exact forces are needed.
In this paper a new phase space of hodograph method is adopted to investigate and better understand the two-dimensional angular momentum reversal(H-reversal) trajectories for high performance solar sails within a fixed cone angle.As the hodograph method and the H-reversal trajectory are not very common,both of them are briefly introduced.The relationship between them are constructed and addressed with a sample trajectory.How the phase space varies according to the sail quality and the fixed sail cone angle is also studied.Through variation of the phase space,the minimum sail lightness number can be obtained by solving a set of algebraic equations instead of a parameter optimization problem.For a given sail lightness number,there are three types of the two-dimensional possible heliocentric motion,including the spiral inward trajectories towards the Sun,the H-reversal trajectories and the directly outward escape trajectories.The boundaries that separate these different groups are easily determined by using the phase space.Finally,the method and procedures to achieve the feasible region of the H-reversal trajectory with required perihelion distance are presented in detail.
A solar collector system is a possible method using solar energy to deflect Earth-threatening near-Earth objects.We investigate the dynamics and control of a solar collector system including a main collector （MC） and secondary collector （SC）.The MC is used to collect the sunlight to its focal point,where the SC is placed and directs the collected light to an asteroid.Both the relative position and attitude of the two collectors should be accurately controlled to achieve the desired optical path.First,the dynamical equation of the relative motion of the two collectors in the vicinity of the asteroid is modeled.Secondly,the nonlinear sliding-mode method is employed to design a control law to achieve the desired configuration of the two collectors.Finally,the deflection capability of this solar collector system is compared with those of the gravitational tractor and solar sail gravitational tractor.The results show that the solar collector is much more efficient with respect to deflection capability.
Shen-Ping Gong,Jun-Feng Li and Yun-Feng Gao School of Aerospace,Tsinghua University,Beijing 100084,China
The fuel consumption associated with some interplanetary transfer trajectories using chemical propulsion is not affordable. A solar sail is a method of propulsion that does not consume fuel. Transfer time is one of the most pressing problems of solar sail transfer trajectory design. This paper investigates the time-optimal interplanetary transfer trajectories to a circular orbit of given inclination and radius. The optimal control law is derived from the principle of maximization. An indirect method is used to solve the optimal control problem by selecting values for the initial adjoint vari- ables, which are normalized within a unit sphere. The conditions for the existence of the time-optimal transfer are dependent on the lightness number of the sail and the inclination and radius of the target orbit. A numerical method is used to obtain the boundary values for the time-optimal transfer trajectories. For the cases where no time-optimal transfer trajectories exist, first-order necessary conditions of the optimal control are proposed to obtain feasible solutions. The results show that the transfer time decreases as the minimum distance from the Sun decreases during the transfer duration. For a solar sail with a small lightness number, the transfer time may be evaluated analytically for a three-phase transfer trajectory. The analytical results are compared with previous results and the associated numerical results. The transfer time of the numerical result here is smaller than the transfer time from previous results and is larger than the analytical result.
Advanced solar sailing has been an increasingly attractive propulsion system for highly non-Keplerian orbits.Three new applications of the orbital angular momentum reversal（H-reversal） trajectories using solar sails are presented：space observation,heliocentric orbit transfer and collision orbits with asteroids.A theoretical proof for the existence of double H-reversal trajectories（referred to as‘H2RTs’） is given,and the characteristics of the H2RTs are introduced before a discussion of the mission applications.A new family of H2RTs was obtained using a 3D dynamic model of the two-body frame.In a time-optimal control model,the minimum period H2RTs both inside and outside the ecliptic plane were examined using an ideal solar sail.Due to the quasi-heliostationary property at its two symmetrical aphelia,the H2RTs were deemed suitable for space observation.For the second application,the heliocentric transfer orbit was able to function as the time-optimal H-reversal trajectory,since its perihelion velocity is a circular or elliptic velocity.Such a transfer orbit can place the sailcraft into a clockwise orbit in the ecliptic plane,with a high inclination or displacement above or below the Sun.The third application of the H-reversal trajectory was simulated impacting an asteroid passing near Earth in a head-on collision.The collision point can be designed through selecting different perihelia or different launch windows.Sample orbits of each application were presented through numerical simulation.The results can serve as a reference for theoretical research and engineering design.
Xiang-Yuan Zeng Hexi Baoyin Jun-Feng Li Sheng-Ping Gong
Near Earth Asteroids have a possibility of impacting the Earth and always represent a threat. This paper proposes a way of changing the orbit of the asteroid to avoid an impact. A solar sail evolving in an H-reversal trajectory is utilized for asteroid deflection. Firstly, the dynamics of the solar sail and the characteristics of the H-reversal trajectory are analyzed. Then, the attitude of the solar sail is optimized to guide the sail to impact the target asteroid along an H-reversal trajectory. The impact velocity depends on two important parameters： the minimum solar distance along the trajectory and lightness number of the solar sail. A larger lightness number and a smaller solar distance lead to a higher impact velocity. Finally, the deflection capability of a solar sail impacting the asteroid along the H-reversal trajectory is discussed. The results show that a 10kg solar sail with a lead-time of one year can move Apophis out of a 600-m keyhole area in 2029 to eliminate the possibility of its resonant return in 2036.
