Configuration space and stability analysis of solar sail near-vertical earth-trailing orbits

Regions outside the reach of traditional propulsion systems or the ones that require significant propellant, may be reached by harnessing the solar radiation pressure and leveraging coupled dynamics to maneuver a sail-based spacecraft. Earth-trailing orbits have recently been investigated for getting a unique perspective of the Sun while maintaining the spacecraft in close proximity to Earth. Vertical orbits trailing the Earth exhibit the additional capability to view the Sun from above and below the ecliptic plane. In this work, families of sail-based orbits are explored for varying Earth-trailing angles and Z amplitudes in the Sun-Earth circular restricted three-body problem. Optimization is carried out to ensure that the non-traditional vertical orbits exhibit a constant pitch angle control history, as well as symmetry across the X-Y plane. The stability of the resulting orbit families is assessed using an extension of Flouquet theory to Differential Algebraic Equations. Results indicate that sail-based Earth-trailing vertical orbits can be more stable than traditional sub-L₁ sail-based vertical orbits.     

Dynamical analysis of a spinning solar sail

This paper discusses the orbit and attitude dynamics of a solar sail, and gives the sufficient conditions of a stable orbit and attitude coupled system. The stability of the coupled system is determined by the orbit stability and attitude stability. Based on the sufficient conditions, a spin-stabilized solar sail of cone configuration is proposed to evolve in the heliocentric displaced orbit. For this kind of configuration, the attitude is always stable by spinning itself. The orbit stability depends on the orbit parameters of the heliocentric displaced orbit, the ratio of the orbit radius to displaced distance and orbit angular velocity. If the center of mass and center of pressure overlap, it can be proved that the coupled system is stable when the orbit parameters are chosen in the stable region. When the center of mass and center of pressure offset exists, the stability of the coupled system can not be judged. A numerical example is given and the result shows that both the orbit and attitude are stable for the case.     

Status of solar sail technology within NASA

In the early 2000s, NASA made substantial progress in the development of solar sail propulsion systems for use in robotic science and exploration of the solar system. Two different 20-m solar sail systems were produced. NASA has successfully completed functional vacuum testing in their Glenn Research Center’s Space Power Facility at Plum Brook Station, Ohio. The sails were designed and developed by Alliant Techsystems Space Systems and L’Garde, respectively. The sail systems consist of a central structure with four deployable booms that support each sail. These sail designs are robust enough for deployment in a one-atmosphere, one-gravity environment and are scalable to much larger solar sails – perhaps as large as 150 m on a side. Computation modeling and analytical simulations were performed in order to assess the scalability of the technology to the larger sizes that are required to implement the first generation of missions using solar sails. Furthermore, life and space environmental effects testing of sail and component materials was also conducted.     

Application of a modified generalized sail model on a solar sail with wrinkles

In this paper, we present an analysis of effect of wrinkles on the solar sail performance. We describe different analytical, semi-analytical and numerical approaches to the calculation of general large-scale curvature of a solar sail as well as parameters of so-called wrinkled domains, and introduce the impact of such wrinkles on the thrust and torque of the solar sail. Finally, we present a model of an optically-orthotropic surface for such non-ideal sail, providing a connection with the Generalized Sail Model, and other solar sail thrust models.     

Solar sail optimal control with solar irradiance fluctuations

The optimization of a solar sail-based orbital transfer amounts to searching for the control law that minimizes the flight time. In this context, the optimal trajectory is usually determined assuming constant solar properties. However, the total solar irradiance undergoes both long-term (solar cycles) and short-term variations, and recent analyses have shown that this may have an impact on solar sailing for missions requiring an accurate thrust modulation. In this regard, the paper discusses a strategy to overcome such an issue by suitably adjusting the thrust vector in order to track a reference, optimal, transfer trajectory. In particular, the sail propulsive acceleration magnitude is modified by means of a set of electrochromic material panels, which change their optical properties on application of a suitable electric voltage. The proposed control law is validated with a set of numerical simulations that involve a classical Earth-Mars, orbit-to-orbit, heliocentric transfer.     

Influence of optical parameters on a solar sail motion

Detailed dynamic modeling of a solar sail requires recording of solar radiation pressure influence. A photon-solar sail is determined by the thrust value and the direction. We define the solar sail’s reflectivity depending on the film materials, the sail design and temperature, the thickness of multiple layers, and degradation factor, with a reasonable degree of accuracy. Thus, this work is devoted to the identification of optical characteristics of thin multilayer films in space flight conditions, i.e. to finding its reflectance, absorbance, and transmittance. In particular, the paper asks whether the solar sail simulates by a mathematical model of the optical characteristics of a multilayer epitaxial thin film. The temperature change effect and optical properties of solar sail degradation are considered as well. Solar sail flight from Earth to Mercury is designed as a simulation of the flight change in optical parameters.     

Analysis of the solar sail deformation based on the point cloud method

The deformation of the solar-sail membrane is an important factor for causing inaccuracies in the solar-sail missions. This paper describes the solar sail under deformation by using a new modelling technique based on point cloud and triangular mesh generation. Two types of deformation, stemming from wrinkling and billowing, are modelled. The changes in the solar radiation pressure force and the moment caused by deformation are calculated and compared to the ideal non-deformed case. The heliocentric spiral trajectory and the orbital angular momentum reversal trajectory are taken as examples to quantify the influence of the deformation from an orbit point of view. Additionally, point cloud simplification, based on the normal vector and bounding box, is utilized to simplify the original deformed-sail model. It involves a reasonable reduction and renewal of the points in the model considering the variation of surface curvature. The simplification and its modelling accuracy are numerically investigated as well as computational efficiency.     

Numerical techniques for generating and refining solar sail trajectories

Like all applications in trajectory design, the design of solar sail trajectories requires a transition from analytical models to numerically generated realizations of an orbit. In astrodynamics, three numerical strategies are often employed. Differential correctors (also known as shooting methods) are perhaps the most common techniques. Finite-difference methods and collocation schemes are also employed and are successful in generating trajectories with pseudo-continuous control histories. These three numerical techniques are employed here to generate periodic trajectories displaced below the Moon in a circular restricted three-body system. All these approaches reveal trajectory options within the design space for solar sail applications.     

Durability characterization of mechanical interfaces in solar sail membrane structures

The construction of a solar sail from commercially available metallized film presents several challenges. The solar sail membrane is made by seaming together precut lengths of ultrathin metallized polymer film into the required geometry. This assembled sail membrane is then folded into a small stowage volume prior to launch. The sail membranes must have additional features for connecting to rigid structural elements (e.g., sail booms) and must be electrically grounded to the spacecraft bus to prevent charge build up. Space durability of the material and mechanical interfaces of the sail membrane assemblies will be critical for the success of any solar sail mission. In this study, interfaces of polymer/metal joints in a representative solar sail membrane assembly were tested to ensure that the adhesive interfaces and the fastening grommets could withstand the temperature range and expected loads required for mission success. Various adhesion methods, such as surface treatment, commercial adhesives, and fastening systems, were experimentally tested in order to determine the most suitable method of construction.     

A torus-shaped solar sail accelerated via thermal desorption of coating

A torus-shaped sail consists of a reflective membrane attached to an inflatable torus-shaped rim. The sail’s deployment from its stowed configuration is initiated by introducing inflation pressure into the toroidal rim with an attached circular flat membrane coated by heat-sensitive materials that undergo thermal desorption (TD) from a solid to a gas phase. Our study of the deployment and acceleration of the sail is split into three steps: at a particular heliocentric distance a torus-shaped sail is deployed by a gas inflated into the toroidal rim and the membrane is kept flat by the pressure of the gas; under heating by solar radiation, the membrane coat undergoes TD and the sail is accelerated via TD of coating and solar radiation pressure (SRP); when TD ends, the sail utilizes thrust only from SRP. We study the stability of the torus-shaped sail and deflection and vibration of the flat membrane due to the acceleration by TD and SRP.     

Hierarchical global search for fuel-optimal impulsive transfers between lunar libration orbits

The attention to the periodic orbit in the Earth-Moon restricted three-body system continues to grow due to its special environment and locations. This research investigates the feasibility of constructing fuel-optimal single and multiple impulse transfers between unstable periodic orbits at L₁ and L₂ points. Invariant manifolds, which could provide the appropriate initial trajectories for optimization, are analyzed deeply to enable previously unknown orbit options and potentially to reduce mission cost. A global search strategy based on comparing the orbital state of the unstable and stable manifolds, incorporated with low-thrust techniques, is performed to seek a suitable matching point for maneuver application. Then the sequential quadratic programming (SQP) is adopted to further optimize the velocity increment and obtain the single/multiple impulse optimal transfers. The associated constraint gradients are derived to achieve higher accuracy and rapidity of the algorithm. To highlight the effectivity of the transfer scheme, three-dimensional low-energy transfers between different types and spatial regions of performing single and multiple impulses are explored. The total Delta-V required varies between a few meters per second and tens of meters per second, and the related flight time is about several weeks, mainly depending on the energy of periodic orbits and the invariant manifold structure. The results obtained in this paper can provide a useful reference for the selection of escape and capture site along the manifolds, maneuver magnitude and transfer time.     

Integrated guidance and control for solar sail station-keeping with optical degradation

Current control approaches for solar sail station-keeping on libration point orbits have not considered the degradation of the sail’s optical properties. However, significant optical degradation could lead to poor station-keeping performance or even complete failure. This paper presents an integrated guidance and control strategy to address this problem by updating the reference orbit based on in situ estimation. An exponential optical degradation model is incorporated into the solar radiation acceleration model, and an on-line reference orbit update approach is incorporated into the station-keeping, coupled with an active disturbance rejection controller. The reflection coefficient is estimated on-line and the reference orbit is updated discretely when the optical properties have degraded by a prescribed amount. This strategy provides discrete updates to the reference orbits such that the perturbation due to the optical degradation is maintained within a small range. These smaller perturbations can be dealt with by the controller’s robustness and station-keeping can be sustained for long durations even in the presence of large optical degradation.     

Considerations in the design and deployment of flexible booms for a solar sail

The majority of solar sailing missions utilise semi-rigid boom technology but this places limits on the possible size of the sail. Practical large sails may be constructed using flexible booms on a spinning satellite. The dynamics of the deployment of long flexible booms are investigated and limiting parameters discussed. Deployment strategies are proposed utilising active deployment and a means of passive deployment which requires no direct control of the deployment process. Practical insights into the design, testing and use of a flexible boom solar sail deployment mechanism is presented based on small scale experimental testing, discussing aspects such as boom winding and balanced deployment. Three novel deployment mechanism design concepts are developed; two passive mechanisms using rotational damping to retard the boom deployment and one active concept takes advantage of the forces produced by the spinning nature of the satellite to develop a compact deployment mechanism.     

Influence of curved thin-film device on deformation of a solar sail

A spinning solar sail IKAROS’s membrane is estimated to unexpectedly deform into an inverted pyramid shape due to thin-film devices with curvature, such as thin-film solar cells and steering devices on the membrane. It is important to investigate the deformation caused by the curved thin-film devices and predict the sail shape because the out-of-plane deformation greatly affects solar radiation pressure (SRP) and SRP torque. The purpose of this paper is to clarify the relationship between the global shape and orientation and position of curved thin-film devices and to evaluate SRP torque on the global shape using finite element analysis. The global shape is evaluated based on the out-of-plane displacement and the SRP torque. When the curved thin-film devices make the membrane shrink in the circumferential, diagonal, and radial direction, the sail deforms into a pyramid shape, an inverted pyramid one, and a saddle one, respectively. The saddle shape is more desirable for solar sails than the inverted pyramid shape and the pyramid one from the viewpoint of shape stability to SRP and control of SRP torque in the normal direction of the sail (windmill torque). The position of the thin-film device tends to increase the absolute value of windmill torque when it is biased circumferentially from the petal central axis. The suggested design principles for the arrangement of thin-film devices is that the curved thin-film devices should be directed so that the sail shrinks in the radial direction in order to deform the sail into a saddle shape with high shape stability, and the position of the thin-film devices should be biased in the circumferential direction paying attention to the absolute value of windmill torque to determine the direction of windmill torque.     

A simple control law for reducing the effective characteristic acceleration of a solar sail

The direction and magnitude of a solar sail acceleration are strongly related. For this reason, once the characteristic acceleration has been fixed, it is not possible to modulate the acceleration in a particular direction. In this work, a semi-analytical switching control law is derived, enabling a solar sail to emulate a smaller effective characteristic acceleration (without changes in geometry or optical properties); by periodically changing the pitch (cone) angle of the sail, in average over time, the acceleration produced by the sail matches exactly (in both direction and magnitude) that of a “smaller” sail. The range in which this is possible is determined, and the limitations on this range due to the size difference is computed. The method is validated on optimal Earth-Mars trajectories.     

Shape optimization of a three-dimensional membrane-structured solar sail using an angular momentum unloading strategy

A shape of the satellite’s solar sail membrane is essential for unloading angular momentum in the three-axis stabilized attitude control system because the three-dimensional solar sail can receive solar radiation pressure from arbitrary directions. In this paper, the objective is the shape optimization of a three-dimensional membrane-structured solar sail using the angular momentum unloading strategy. We modelled and simulated the solar radiation pressure torque, for unloading angular momentum. Using the simulation system, since the unloading angular momentum rate is maximized, the shape of the three-dimensional solar sail was optimized using a Genetic algorithm and Sequential Quadratic Programming. The unloading velocity in the optimized shaped solar sail was greatly improved with respect to a conventional flat or pyramid solar sail.     

Dynamical evolution of high area-to-mass ratio debris released into GPS orbits

A large set of simulations, including all the relevant perturbations, was carried out to investigate the long-term dynamical evolution of fictitious high area-to-mass ratio (A/M) objects released, with a negligible velocity variation, in each of the six orbital planes used by Global Positioning System (GPS) satellites. As with similar objects discovered in near synchronous trajectories, long lifetime orbits, with mean motions of about 2 revolutions per day, were found possible for debris characterized by extremely high area-to-mass ratios. Often the lifetime exceeds 100 years up to A/M ∼ 45 m²/kg, decreasing rapidly to a few months above such a threshold. However, the details of the evolution, which are conditioned by the complex interplay of solar radiation pressure and geopotential plus luni-solar resonances, depend on the initial conditions. Different behaviors are thus possible. In any case, objects like those discovered in synchronous orbits, with A/M as high as 20–40 m²/kg, could also survive in this orbital regime, with semi-major axes close to the semi-synchronous values, with maximum eccentricities between 0.3 and 0.7, and with significant orbit pole precessions (faster and wider for increasing values of A/M), leading to inclinations between 30° and more than 90°.     

Long-term predictability of orbits around the geosynchronous altitude

For a family of simulated geostationary, geosynchronous and super-geostationary orbits we compute the indicator called MEGNO in order to find out which orbits are chaotic and the timescale of their exponential divergence. A symplectic integrator of the Wisdom–Holman type was used for this purpose, with an integration span of 40 years. The results indicate that chaotic orbits exist only at the separatrix between geostationary libration and circulation and that they are relatively rare. The super-geostationary region seems to be entirely regular and quasi-periodic on the timescale of few decades.     

Solar sail near the Sun: Point-like and extended models of radiation source

Some modifications of solar sail radiation pressure forces on a plate and on a sphere for use in the numerical simulation of ‘local-optimal’ (or ‘instantaneously optimal’) trajectories of a spacecraft with a solar sail are suggested. The force model development is chronologically reviewed, including its connection with solar sail surface reflective and thermal properties. The sail surface is considered as partly absorbing, partly reflective (specular and diffuse), partly transparent. Thermal balance is specified because the spacecraft moves from circular Earth orbit to near-Sun regions and thermal limitations on the sail film are taken into account. A spherical sail-balloon can be used in near-Sun regions for scientific research beginning with the solar-synchronous orbit and moving outward from the Sun. The Sun is considered not only as a point-like source of radiation but also as an extended source of radiation which is assumed to be consequently as a point-like source of radiation, a uniformly bright flat solar disc and uniformly bright solar sphere.