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.     

Economic assessment of high-thrust and solar-sail propulsion for near-earth asteroid mining

Asteroid mining has the potential to greatly reduce the cost of in-space manufacturing, production of propellant for space transportation and consumables for crewed spacecraft, compared to launching the required resources from the Earth’s deep gravity well. This paper discusses the top-level mission architecture and trajectory design for these resource-return missions, comparing high-thrust trajectories with continuous low-thrust solar-sail trajectories. The paper focuses on maximizing the economic Net Present Value, which takes the time-cost of finance into account and therefore balances the returned resource mass and mission duration. The different propulsion methods are compared in terms of maximum economic return and sets of attainable target asteroids. Results for transporting resources to geostationary orbit show that the orbital parameter hyperspace of suitable target asteroids is considerably larger for solar sails, allowing for more flexibility in selecting potential target asteroids. Also, results show that the Net Present Value that can be realized is larger when employing solar sailing instead of chemical propulsion. In addition, it is demonstrated that a higher Net Present Value can be realized when transporting volatiles to the Lunar Gateway instead of geostationary orbit. The paper provides one more step towards making commercial asteroid mining an economically viable reality by integrating trajectory design, propulsion technology and economic modelling.     

Sailing with solar and planetary radiation pressure

Literature on solar sailing has thus far mostly considered solar radiation pressure (SRP) as the only contribution to sail force. However, considering a sail in a planetary mission scenario, a new contribution can be added. Since the planet itself emits radiation, this generates a radial planetary radiation pressure (PRP) that is also exerted on the sail. Hence, this work studies the combined effects of both SRP and PRP on a sail for two case studies, i.e. Earth and Venus. In proximity of the Earth, the effect of PRP can be significant under specific conditions. Around Venus, instead, PRP is by far the dominating contribution. These combined effects have been studied for single- and double-sided reflective coating and including eclipse. Results show potential increase in the net acceleration and a change in the optimal attitude to maximise the acceleration in a given direction. Moreover, an increasing semi-major axis manoeuvre is shown with and without PRP, to quantify the difference on a real-case scenario.     

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.     

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.     

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.     

Paths not taken – The Gossamer roadmap’s other options

Highly efficient low-thrust propulsion is increasingly applied beyond commercial use, also in mainstream and flagship science missions, in combination with gravity assist propulsion. Another recent development is the growth of small spacecraft solutions, not in size but in numbers and individual capabilities.Just over ten years ago, the DLR-ESTEC Gossamer Roadmap to Solar Sailing was set up to guide technology developments towards a propellant-less and highly efficient class of spacecraft for solar system exploration and applications missions: small spacecraft solar sails designed for carefree handling and equipped with carried application modules.Soon, in three dedicated Gossamer Roadmap Science Working Groups it initiated studies of missions uniquely feasible with solar sails such as Displaced L₁ (DL1) space weather advance warning and monitoring, Solar Polar Orbiter (SPO) delivery to very high inclination heliocentric orbit, and multiple Near-Earth Asteroid (NEA) rendezvous (MNR). Together, they demonstrate the capability of near-term solar sails to achieve at least in the inner solar system almost any kind of heliocentric orbit within 10 years, from the Earth-co-orbital to the extremely inclined, eccentric and even retrograde. Noted as part of the MNR study, sail-propelled head-on retrograde kinetic impactors (RKI) go to this extreme to achieve the highest possible specific kinetic energy for the deflection of hazardous asteroids.At DLR, the experience gained in the development of deployable membrane structures leading up to the successful ground deployment test of a (20 m)², i.e., 20 m by 20 m square solar sail at DLR Cologne in 1999 was revitalized and directed towards a 3-step small spacecraft development line from as-soon-as-possible sail deployment demonstration (Gossamer-1) via in-flight evaluation of sail attitude control actuators (Gossamer-2) to an envisaged proving-the-principle flight in the Earth-Moon system (Gossamer-3). First, it turned the concept of solar sail deployment on its head by introducing four separable Boom Sail Deployment Units (BSDU) to be discarded after deployment, enabling lightweight 3-axis stabilized sailcraft. By 2015, this effort culminated in the ground-qualified technology of the DLR Gossamer-1 deployment demonstrator Engineering Qualification Model (EQM). For mission types using separable payloads, such as SPO, MNR and RKI, design concepts can be derived from the BSDU characteristic of DLR Gossamer solar sail technology which share elements with the separation systems of asteroid nanolanders like MASCOT. These nano-spacecraft are an ideal match for solar sails in micro-spacecraft format whose launch configurations are compatible with ESPA and ASAP secondary payload platforms.Like any roadmap, this one contained much more than the planned route from departure to destination and the much shorter distance actually travelled. It is full of lanes, narrow and wide, detours and shortcuts, options and decision branches. Some became the path taken on which we previously reported. More were explored along the originally planned path or as new sidings in search of better options when circumstance changed and the project had to take another turn. But none were dead ends, they just faced the inevitable changes when roadmaps face realities and they were no longer part of the road ahead. To us, they were valuable lessons learned or options up our sleeves. But for future sailors they may be on their road ahead.     

Mission analysis and performance comparison for an Advanced Solar Photon Thruster

The so-called “compound solar sail”, also known as “Solar Photon Thruster” (SPT), is a design concept, for which the two basic functions of the solar sail, namely light collection and thrust direction, are uncoupled. In this paper, we introduce a novel SPT concept, termed the Advanced Solar Photon Thruster (ASPT), which does not suffer from the simplified assumptions that have been made for the analysis of compound solar sails in previous studies. After having presented the equations that describe the force on the ASPT and after having performed a detailed design analysis, the performance of the ASPT with respect to the conventional flat solar sail (FSS) is investigated for three interplanetary mission scenarios: an Earth–Venus rendezvous, where the solar sail has to spiral towards the Sun, an Earth–Mars rendezvous, where the solar sail has to spiral away from the Sun, and an Earth-NEA rendezvous (to near-Earth asteroid 1996FG3), where a large change in orbital eccentricity is required. The investigated solar sails have realistic near-term characteristic accelerations between 0.1 and 0.2 mm/s². Our results show that an SPT is not superior to the flat solar sail unless very idealistic assumptions are made.     

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.     

Structural Analysis About a New Solar Sail

The article presents a structural analysis of a new space probe-solar sail. It was deployed successfully on ground. The loads for an outer space mission was introduced and expressed with equation. As a special state, the largest load around earth was used to analyze the model by the finite element method. Some results about strain and stress was obtained after setting some initial parameters. Compared to the results in the literature, the results presented here are significant.     

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.     

Attitude stability criteria of axisymmetric solar sail

Passive attitude stability criteria of a solar sail whose membrane surface is axisymmetric are studied in this paper under a general SRP model. This paper proves that arbitrary attitude equilibrium position can be designed through adjusting the deviation between the pressure center and the mass center of the sail. The linearized method is applied to inspect analytically the stability of the equilibrium point from two different points of views. The results show that the attitude stability depends on the membrane surface shape and area. The results of simulation with full dynamic equations confirm that the two stability criteria are effective in judging the attitude stability for axisymmetric solar sail. Several possible applications of the study are also mentioned.     

The interstellar heliopause probe technology reference study

The interstellar heliopause probe (IHP) is one of ESA’s technology reference studies (TRS). The TRS aim to focus the development of strategically important technologies of relevance to future science missions by studying technologically demanding and scientifically interesting missions that are currently not part of the science mission programme.

Equipped with a highly integrated payload suite (HIPS), the IHP will perform in situ exploration of the heliopause and the heliospheric interface. The HIPS, which is a standard element in all TRSs, miniaturize payloads through resource reduction by using miniaturized components and sensors, and by sharing common structures and payload functionality.

To achieve the scientific requirements of the mission, the spacecraft is to leave the heliosphere as close to the heliosphere nose as possible and reach a distance of 200 AU from the Sun within 25 years. This is possible by using a trajectory with two solar flybys and a solar sail with characteristic acceleration of 1.1 mm/s², which corresponds to a 245 × 245 m² solar sail and a sail thickness of 1–2 μm. The trajectory facilitates a modest sail design that could potentially be developed in a reasonable timeframe.

In this paper, an update to the results of studies being performed on this mission will be given and the current mission baseline and spacecraft design will be described. Furthermore, alternative solar sail systems and enabling technologies will be discussed.     

On-orbit verification of fuel-free attitude control system for spinning solar sail utilizing solar radiation pressure

This paper introduces a new attitude control system for a solar sail, which leverages solar radiation pressure. This novel system achieves completely fuel-free and oscillation-free attitude control of a flexible spinning solar sail. This system consists of thin-film-type devices that electrically control their optical parameters such as reflectivity to generate an imbalance in the solar radiation pressure applied to the edge of the sail. By using these devices, minute and continuous control torque can be applied to the sail to realize very stable and fuel-free attitude control of the large and flexible membrane. The control system was implemented as an optional attitude control system for small solar power sail demonstrator named IKAROS (Interplanetary Kite-craft Accelerated by Radiation Of the Sun). In-orbit attitude control experiments were conducted, and the performance of the controller was successfully verified in comparison with the ground-based analytical performance estimation.     

On the practical exploitation of perturbative effects in low Earth orbit for space debris mitigation

This paper presents the results of a numerical evaluation of the natural lifetime reduction in low Earth orbit, due to dynamical perturbations. The study considers two values for the area-to-mass ratio, a nominal ratio which resembles a typical value of spacecraft in orbit today, and an enhanced ratio which covers the surface augmentation. The results were obtained with two orbit propagators, one of a semi-analytical nature and the second one using non-averaged equations of motion. The simulations for both propagators were set up similarly to allow comparison. They both use the solar radiation pressure and the secular terms of the geopotential ($J_2,J_4$ and $J_6$). The atmospheric drag was turned on and off in both propagators to alternatively study the eccentricity build up and the residual lifetime. The non-averaging case also covers a validation with the full 6?×?6 geopotential. The results confirm the findings in previous publications, that is, the possibility for de-orbiting from altitudes above the residual atmosphere if a solar sail is deployed at the end-of-life, due to the combined effect of solar radiation pressure and the oblateness of the Earth. At near polar inclinations, shadowing effects can be exploited to the same end. The results obtained with the full, non-averaging propagator revealed additional de-orbiting corridors associated with solar radiation pressure which were not found by previous work on space debris mitigation. The results of both tools are compared for specific initial conditions. For nominal values of area-to-mass ratio, instead, it is confirmed that this resonance effect is negligible.The paper then puts the findings in the perspective of the current satellite catalogue. It identifies space missions which are currently close to a resonance corridor and shows the orbit evolution within the resonances with a significantly shorter residual orbital lifetime. The paper finishes with a discussion on the exploitation of these effects with regards to the long-term simulation of the space debris environment and a flux and collision probability comparison.     

Solar sails for perturbation relief: Application to asteroids

A major cause of spacecraft orbital variation comes from natural perturbations, which, in close proximity of a body, are dominated by its non-spherical nature. For small bodies, such as asteroids, these effects can be considerable, given their uneven (and uncertain) mass distribution. Solar sail technology is proposed to reduce or eliminate the net secular effects of the irregular gravity field on the orbit. Initially, a sensitivity analysis will be carried out on the system which will show high sensitivity to changes in initial conditions. This presents a challenge for optimisation methods which require an initial guess of the solution. As such, the Genetic Algorithm (GA) is proposed as the preferred optimisation method as this requires no initial guess from the user. A multi-objective optimisation is performed which aims to achieve a periodic orbit whilst also minimising the effort required by the sail to do so. Given the system sensitivity, the control law for one orbit is not necessarily applicable for any subsequent orbit. Therefore, a new method of updating the control law for subsequent orbits is presented, based on linearisation and use of a Control Transition Matrix (CTM). The techniques will later find application in a multiple asteroid rendezvous mission with a solar sail as the primary propulsion system.     

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.     

27-day variation in solar-terrestrial parameters: Global characteristics and an origin based approach of the signals

The Earth and the near interplanetary medium are affected by the Sun in different ways. Those processes generated in the Sun that induce perturbations into the Magnetosphere-Ionosphere system are called geoeffective processes and show a wide range of temporal variations, like the 11-year solar cycle (long term variations), the variation of ～27?days (recurrent variations), solar storms enduring for some days, particle acceleration events lasting for some hours, etc.In this article, the periodicity of ～27?days associated with the solar synodic rotation period is investigated. The work is mainly focused on studying the resulting 27-day periodic signal in the magnetic activity, by the analysis of the horizontal component of the magnetic field registered on a set of 103 magnetic observatories distributed around the world. For this a new method to isolate the periodicity of interest has been developed consisting of two main steps: the first one consists of removing the linear trend corresponding to every calendar year from the data series, and the second one of removing from the resulting series a smoothed version of it obtained by applying a 30-day moving average. The result at the end of this process is a data series in which all the signal with periods larger than 30?days are canceled.The most important characteristics observed in the resulting signals are two main amplitude modulations: the first and most prominent related to the 11-year solar cycle and the second one with a semiannual pattern. In addition, the amplitude of the signal shows a dependence on the geomagnetic latitude of the observatory with a significant discontinuity at approx. ±60°.The processing scheme was also applied to other parameters that are widely used to characterize the energy transfer from the Sun to the Earth: F10.7 and Mg II indices and the ionospheric vertical total electron content (vTEC) were considered for radiative interactions; and the solar wind velocity for the non-radiative interactions between the solar wind and the magnetosphere. The 27-day signal obtained in the magnetic activity was compared with the signals found in the other parameters resulting in a series of cross-correlations curves with maximum correlation between 3 and 5?days of delays for the radiative and between 0 and 1?days of delay for the non-radiative parameters. This result supports the idea that the physical process responsible for the 27-day signal in the magnetic activity is related to the solar wind and not to the solar electromagnetic radiation.     

Influence of Earth’s shadowing effects on space debris stability

Solar radiation pressure affects the evolution of high area-to-mass geostationary space debris. In this work, we extend the stability study of Valk et al. (2009) by considering the influence of Earth’s shadows on the short- and long-term time evolutions of space debris. To assess the orbits stability, we use the Mean Exponential Growth factor of Nearby Orbits (MEGNO), which is an efficient numerical tool to distinguish between regular and chaotic behaviors. To reliably compute long-term space debris motion, we resort to the Global Symplectic Integrator (GSI) of Libert et al. (2011) which consists in the symplectic integration of both Hamiltonian equations of motion and variational equations. We show how to efficiently compute the MEGNO indicator in a complete symplectic framework, and we also discuss the choice of a symplectic integrator, since propagators adapted to the structure of the Hamiltonian equations of motion are not necessarily suited for the associated variational equations. The performances of our method are illustrated and validated through the study of the Arnold diffusion problem. We then analyze the effects of Earth’s shadows, using the adapted conical and cylindrical Earth’s shadowing models introduced by Hubaux et al. (2012) as the smooth shadow function deriving from these models can be easily included into the variational equations. Our stability study shows that Earth’s shadows greatly affect the global behaviour of space debris orbits by increasing the size of chaotic regions around the geostationary altitude. We also emphasize the differences in the results given by conical or cylindrical Earth’s shadowing models. Finally, such results are compared with a non-symplectic integration scheme.     

太阳帆飞行器轨道动力学分析

通过分析对轨道要素影响最大的加速度分量,使太阳帆总是位于光压力沿这个加速度方向的分量最大的方位。通过分析轨道要素调整时的相互影响关系,提出了同时修正多种轨道偏差的控制方案。对处于地球静止轨道上太阳帆飞行器的轨道调整进行了数值仿真。结果证明利用太阳光压力进行轨道调整是可行的,而且有利的太阳方位是进行快速有效的轨道调整的必要条件。