Solar sailing is a propulsion method that takes advantage of solar radiation pressure to generate thrust. Although most of near-future solar-sail missions will fly in low Earth orbit, where planetary radiation pressure can be as large as 20% of solar radiation pressure, studies on the accelerations produced by the Earth’s albedo and blackbody radiation have only been conducted to a very limited first-order extent. This paper therefore provides a novel, detailed analytical model for these perturbing accelerations, valid for perfectly reflecting solar sails. The full derivation of the model is described, and a thorough analysis of the blackbody and albedo radiation pressure accelerations is conducted for different orbital conditions. Then, to determine the model’s accuracy, a comparison with the state of the art (the finite-disk radiation source model and a high-fidelity numerical model) is provided. Ultimately, different analyses to quantify the effect of planetary radiation pressure acceleration on the solar-sail maneuvering capabilities are presented, using NASA’s upcoming ACS3 mission as reference scenario. The results highlight the nonnegligible effect of uncontrolled planetary radiation pressure acceleration, which can reduce the sailcraft’s achievable altitude and inclination gains to 76 and 80%, respectively, of the gains obtained when planetary radiation pressure is not accounted for.@en

NASA’s ACS3 mission will be the first Earth-bound solar-sail mission to fly so-called calibration steering laws. These steering laws are designed to expose the sailcraft to a variety of dynamical conditions to isolate the effects of different parameters on the dynamics, thereby facilitating the estimation of these parameters. This paper presents the set of candidate calibration steering laws of ACS3, highlighting their operational challenges and impact on the estimation of the sail’s reflectivity and specularity. The results show that, for a conservative GPS position accuracy of 10 m, accurate estimation of the reflectivity and specularity with uncertainties in the order of 10−4 − 10−3 can be achieved by flying any of the proposed calibration laws. However, ACS3’s calibration steering laws were also found to introduce operational challenges that may hinder their implementation for extended periods of time. In particular, the decreased power generation capability of solar arrays was found to be the most severe operational challenge for two out of the five ACS3’s calibration laws analysed. @en

Solar sailing is a propulsion method that uses solar radiation pressure (SRP) as main source of thrust and is therefore particularly suited for heliocentric flight regimes. However, the vast majority of sailcraft launched to date have flown around Earth, as will those scheduled for launch in the near future. Around the Earth, the dynamics of a solar sail are affected by the presence of eclipses and additional sources of acceleration apart from SRP, in particular, atmospheric drag and the Earth’s planetary radiation pressure (PRP). These accelerations can reach magnitudes in the order of (or even larger than) the SRP acceleration and, therefore, they can potentially be exploited to manoeuvre more effectively around the Earth. Nevertheless, the majority of research conducted on Earth-bound solar sailing either neglects these accelerations or treats them as uncontrollable sources of perturbation. In light of this, this paper presents a high-fidelity trajectory optimisation method which is then used to thoroughly characterise the manoeuvring capabilities of solar sails in the near-Earth environment. The optimisation algorithm is designed to change any orbital element in a locally optimal manner while accounting for the SRP, PRP, aerodynamic, and gravitational accelerations. To tune the optimiser, a first-order analysis of the accelerations achievable by sailcraft in proximity of the Earth is discussed. Then, the optimisation algorithm is exploited to fully characterise the manoeuvring capabilities of Earth-bound solar sails, taking NASA’s recently-launched ACS3 solar-sail mission as a baseline. Specifically, different parametric analyses are conducted to determine ACS3’s orbit-raising and inclination-changing capabilities for a large set of orbits, solar activities, and sailcraft characteristics. The results of this study not only enhance the understanding of ACS3’s performance but also provide valuable insights for the mission design of future Earth-bound solar-sail missions for a variety of mission applications, such as active-debris removal and in-orbit servicing. @en

The problem of how to solar sail around planets remains nearly unexplored. Most of the existing body of knowledge focuses on scape trajectories or locally optimal controls, not providing much insight into the inherent physical characteristics of the transfer problem. In this work, we present the first comprehensive study of solar-sail transfers around planetary bodies by analysing the simplest conceivable transfer, the planar Circular-to-Circular (C2C) transfer. The C2C transfer spans for only one orbital revolution, constituting the building block of more complex multi-revolution trajectories. By patching together a series of C2C transfers, a feasible initial guess for trajectory optimisation algorithms can be generated. The optimised control law maximises the orbital radius within the C2C transfer. The radius change is used as performance metric. The results suggest that the domain of the control variables can be substantially reduced, effectively enhancing convergence of the optimal control solver, and significantly reducing computational time. Furthermore, a dimensional analysis shows that the C2C performance only depends on one parameter: the ratio of the sail’s characteristic acceleration over the local gravitational acceleration. The scaled nature of the results allows to easily compute the C2C performance for a wide range of mission scenarios around any planetary body, providing a new tool for early mission design.@en

Solar sailing is a propellantless propulsion method that exploits solar radiation pressure to generate thrust. In recent years, several solar sails have been launched into Earth-bound orbit to demonstrate this technology’s potential. Because planetary radiation pressure can reach magnitudes comparable to that of solar radiation pressure in proximity of the Earth, it cannot automatically be neglected in near-Earth solar-sail mission design studies. Nevertheless, its effect on the solar-sail dynamics has been investigated only to a very limited, first-order extent, and every study considered an “ideal” – i.e., perfectly reflecting – sail model. Although employing the ideal sail model proves useful for preliminary orbital analyses, its limited fidelity prevents more in-depth research into the near-Earth solar-sail dynamics and trajectory optimization. In light of this, this paper provides a new planetary radiation pressure acceleration model for optical solar sails. This model forms an extension of the “spherical” planetary radiation pressure acceleration model for ideal solar sails devised by Carzana et al. in Reference [1]. In the current paper, the underlying assumptions and full derivation of the newly devised optical model are presented. Subsequently, the accuracy of the optical model is analyzed through a comparison with the ideal model, using NASA’s upcoming ACS3 mission as reference scenario. @en

Solar sailing is a propulsion method which takes advantage of solar radiation pressure (SRP) as main source of thrust. However, around Earth, other sources also affect the solar-sail dynamics, including planetary radiation pressure (PRP) and atmospheric drag. In literature, the accelerations from SRP, PRP, and atmospheric drag are modeled using different theoretical and idealistic models, which make use of simplifying assumptions to describe the near-Earth dynamical environment, the sail’s geometry, and optical properties. Consequently, sailcraft in orbit experience accelerations different from the theoretically predicted ones. In order to quantify these discrepancies between the real and modeled solar-sail dynamics, a first definition and preliminary assessment of a set of calibration steering laws is provided in this paper. These steering laws allow to characterize the solar-sail acceleration at every sail orientation and to identify the contributions due to solar radiation pressure, planetary radiation pressure, and aerodynamic drag. The analyses presented make use of NASA’s upcoming ACS3 mission as baseline scenario and account for different possible orientations of its orbit. The results highlight the benefits and implementation challenges of each steering law and the impact that they have on the orbital elements, with particular focus on the orbital altitude. @en

This paper addresses the significance of uncertainty quantification in solar-sail missions, focusing on the uncertainties associated with the sail’s optical coefficients, structural deformation, and attitude profiles for missions in the Earth environment. Due to the relatively low technological maturity of solar-sailing systems, understanding and quantifying uncertainties is crucial for mission success and reliability. This paper employs the Gauss von Mises method for uncertainty propagation and stochastic integration of Ornstein-Uhlenbeck processes, which proved to be robust methodologies for quantifying and modelling uncertainties. The results show a significant impact of uncertainties in the optical coefficients on mission performance, exemplified by a 3-σ uncertainty of 7.5% on the increase in semi-major axis achieved during orbit raising maneuvers using the coefficient uncertainties of the NEA Scout mission. As another example, the analysis on attitude uncertainty demonstrates a 3% lower mean performance in terms of altitude gain compared to ideal control profiles. The research furthermore underscores the effectiveness of the Gauss von Mises method, offering great computational efficiency compared to Monte Carlo simulations. These findings highlight the necessity of considering uncertainty in solar-sail missions and provide valuable insights for improved mission planning, risk assessment, and decision-making. @en

This paper investigates trajectories within the Alpha Centauri system to reach planet Proxima b. These trajectories come in the form of connections between the classical Lagrange points of Alpha-Centauri’s binary system (composed of the stars Alpha Centauri A and B, AC-A and AC-B) and the classical Lagrange points of the Alpha Centauri C (AC-C)/Proxima b system. These so-called heteroclinic connections are sought using a patched restricted three-body problem method. A genetic algorithm is applied to optimize the linkage conditions between the two three-body systems, focusing on minimizing the position, velocity, and time error at linkage. Four different futuristic, graphenebased sail configurations are used for the analyses: two sails with a reflective coating on only one side of the sail with lightness numbers equal to β = 100 and β = 1779, and two sails with a reflective coating on both sides (again, considering β = 100 and β = 1779). Results from the genetic algorithm show that, for example, a transfer from the L2-point in the AC-A/AC-B system to the L1-point in the AC-C/Proxima b system can be accomplished with a transfer time of 235 years for the one-sided graphene-based sail with β = 1779. @en

A planetary sunshade is a large, reflecting disk built to shield the Earth from a small fraction of solar irradiance and partly compensate global warming caused by greenhouse gas emissions. As a specific form of solar geoengineering, the sunshade is an emergency solution that would be implemented to prevent catastrophic climate change, while working towards the net-zero emission goal. In this paper, a dynamic sunshade is proposed. The motion of the sunshade is designed as a combination of static permanence at two equilibrium points above and below the ecliptic plane to shade the poles and a time-optimal transfer trajectory to connect these equilibrium points without overshading the tropical regions. Such a system is capable of not only reducing the global mean surface temperature anomaly, but also minimizing regional climate changes by tailoring the sunshade’s motion according to climate requirements, which is the primary goal of this work. A simplified climate model is used to evaluate the results of a given shading pattern, directly related to the sunshade’s trajectory. A dynamic sunshade with a radius of 1434 km and orbiting in the vicinity of the Sun-Earth L1 point is able to reduce the global mean surface temperature from 16.39˝C (scenario with 680 ppm of atmospheric CO2, double the amount with respect to the pre-industrial era) to 14.13˝C until equilibrium is reached. It also reduces the polar mean surface temperature (for latitudinal bands above 65˝) by more than 2˝C with respect to a scenario without sunshade and by 0.06˝C with respect to a static sunshade at the displaced L1 point. The optimal results are achieved when the sunshade is located at a distance equal to 30% of the Earth’s radius above and below the ecliptic plane. In addition, the transfers between the equilibrium points start respectively at day 56 and day 250, both measured from the 1st of January. @en

This work demonstrates the usability of differential dynamic programming (DDP) to obtain optimal Earth-centred solar-sail trajectories. The dynamical model is implemented as a two-body problem, augmented with an ideal solar-sail reflectance model and accounts for eclipses. The numerical performance of the optimisation algorithm is enhanced by integrating the sailcraft state in modified equinoctial elements and performing a Sundman transformation to change the independent variable from time to the true anomaly. The DDP algorithm is proven to be robust for trajectories extending up to 500 revolutions and, compared to known locally optimal steering laws, allows to obtain equally optimal solutions. The latter is demonstrated in this paper through a set of test cases that range from theoretical scenarios to realistic mission applications, including increasing the specific orbital energy of NASA’s upcoming ACS3 mission. Additionally, the algorithm's ability to cope with different optimisation settings, perturbing accelerations and constraints is demonstrated.@en

Solar sailing is a spacecraft propulsion method relying solely on solar radiation pressure to provide thrust and is therefore propellantless by nature. Although it represents a practical and promising propulsion system particularly suited for heliocentric flight regimes, the majority of sailcraft missions flown to date have remained Earth-bound and more Earth-bound missions are scheduled for the near future. However, the fundamental dynamics and trajectory optimization of a solar sail around the Earth have only been investigated to a limited extent, often neglecting the effect of non-negligible perturbations in the dynamics and the optimal control problem. Among these perturbations are the effect of eclipses, non-spherical gravity, and aerodynamic drag. Their magnitude can be comparable to, or even exceed that of solar radiation pressure and their effect on the solar-sail dynamics should be investigated to ensure the sailcraft's transfer capabilities and controllability. This article does so by including these perturbations in the dynamics and by considering aerodynamic drag in the optimal control problem. Using this formulation, it is shown that the optimal control problem is independent of the solar-sail loading parameter and that, by solving it, locally optimal steering laws can be derived to effectively change individual orbital elements. These newly derived steering laws form an extension to the laws found by McInnes for unperturbed solar-sail Earth-bound motion. By accounting for the perturbations in the derivation of the steering laws, it is possible to characterize how the perturbations affect the solar-sail maneuvering capabilities. This is quantified based on the established increase of the targeted orbital element. Furthermore, a range of different starting orbits will be considered to analyze the effects of perturbations in different orbital regimes. As demonstration of the real need for this investigation, NASA's Advanced Composite Solar Sail System (ACS3) mission will be considered as real-case scenario. This mission is scheduled for launch in mid-2022 and may benefit from the steering laws derived in this article to prove the maneuverability of solar sails in Earth orbit.

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Solar sailing is a flight-proven low-thrust propulsion technology with strong potential for innovative scientific missions. All previous solar-sail missions employed a solar-sail system design consisting of four triangular sail quadrants supported by deployable booms. As an alternative to such a fixed and flat sail-system design, this paper investigates the dynamics of the heliogyro. The heliogyro is a helicopter-like sail design that utilizes a set of long slender blades which are deployed and flattened by spin-induced tension and whose orientations can be individually controlled. The main advantages of such a design are the easier stowage and deployment, and potentially lower structural mass. Moreover, the individual blade orientation allows higher authority on the forces and moments produced by the sail, but at the same time complicates the heliogyro dynamics. The heliogyro’s translational and rotational motions are strongly coupled, with non-trivial relationships between the control inputs and the forces and moments produced by the sail. The purpose of this paper is to investigate for the first time the coupled roto-translational motion of the heliogyro. As tantalizing application, the paper analyzes the heliogyro’s performance for Earth-to-Mars stopover cycler trajectories, which could aid the exploration of Mars by providing recurrent propellant-less logistics links between Earth and Mars. Two numerical models to describe the heliogyro coupled roto-translational dynamics are derived; a spin-averaged and a non-averaged model. To design time-optimal heliogyro Earth-to-Mars stopover cycler trajectories, a multiple shooting algorithm is employed and the feasibility of the concept is demonstrated. The resulting trajectories are then compared to those of a traditional fixed-area and flat sail-system design, demonstrating that the heliogyro can perform similar trajectories as the traditional fixed-area and flat sailcraft, without the need of an additional system to control the sailcraft attitude. @en

Solar sailing is a propellantless propulsion method that takes advantage of solar radiation pressure to generate thrust. The last decades have seen the launch of several solar-sail missions to demonstrate the technology’s potential for space exploration and exploitation. Even more missions are scheduled for launch in the near future, including NASA’s ACS3 and NEA Scout missions and Gama’s Alpha sailcraft. Although most of these sailcraft have flown – or will fly – in LEO, where the planetary radiation pressure is strong (up to approximately 20% of the solar radiation pressure), studies on the perturbing accelerations produced by the Earth’s albedo and blackbody radiation have been conducted only to a very limited first-order extent. This paper therefore provides a novel, detailed analytical model for these perturbing accelerations, valid for double-sided perfectly reflecting solar sails. The underlying assumptions of the model are presented and its full derivation is described. A thorough analysis of the blackbody and albedo radiation pressure accelerations is conducted for a variety of orbital conditions and Sun-Earth-sail configurations. In order to quantify the accuracy of the model, a comparison with the state of the art (the finite-disk radiation source model) is provided. Ultimately, a variety of analyses to quantify the effect of Earth’s albedo and blackbody radiation on the maneuvering capabilities of solar sails are provided, using the orbit of the ACS3 mission as reference scenario. These analyses show that, for an orbit-raising steering law, losses in the altitude gain of 19.6% of the total gain are incurred over a 10-day orbit-raising period. Similarly, losses in the inclination gain of up to 25% of the total gain are observed when implementing an inclination-changing steering law. These results highlight the non-negligible effect of uncontrolled planetary radiation pressure acceleration on the maneuvering capabilities of solar sails in LEO. @en

Solar sailing is a spacecraft propulsion method relying solely on solar radiation pressure to provide thrust and is therefore propellantless by nature. Although it represents a practical and promising propulsion system particularly suited for heliocentric flight regimes, near-term sailcraft missions will remain Earth-bound due to the current technology readiness level. This paper aims to show the suitability of solar sailing for planetocentric applications for future Earth-bound solar-sail missions. In Earth orbit, the sailcraft is subjected to perturbations absent or negligible in heliocentric flight, including the effect of eclipses, non-spherical gravity and aerodynamic drag. The magnitude of these perturbations can be comparable to, or even exceed that of solar radiation pressure and their effect on the solarsail dynamics should be investigated to ensure the sailcraft’s transfer capabilities and controllability. This paper does so by including the gravitational and aerodynamic perturbations in the optimal control problem. From this formulation, steering laws can be derived to optimally change individual orbital elements. These newly derived steering laws form an extension to the laws found by McInnes for unperturbed solar-sail Earth-bound motion. By accounting for the perturbations in the derivation of the steering laws, their effect can be exploited by the sailcraft to achieve orbits otherwise unreachable. The improved maneuverability will be quantified based on the established increase of the targeted orbital element. A range of different starting orbits will be considered to characterize how the perturbations affect the solar-sail maneuvering capabilities in different orbital regimes. As demonstration of the real need for this investigation, NASA’s Advanced Composite Solar Sail System (ACS3) mission will be considered as real-case scenario. This mission is scheduled for launch in mid-2022 and may benefit from the steering laws derived in this paper to proof the maneuverability of solar sails in Earth orbit. @en

The concept of a pole-sitter has been under investigation for many years, showing the capability of a low-thrust propulsion system to maintain a spacecraft at a static position along a planet's polar axis. From such a position, the spacecraft has a view of the planet's polar regions equivalent to that of the low- and mid-latitudes from geostationary orbit. Previous work has hinted at the existence of pole-sitters that would only require a solar sail to provide the necessary propulsive thrust if a slight deviation from a position exactly along the polar axis is allowed, without compromising on the continuous view of the planet's polar region (a so-called quasi-pole-sitter). This paper conducts a further in-depth analysis of these high-potential solar-sail-only quasi-pole-sitters and presents a full end-to-end trajectory design: from launch and transfer to orbit design and orbit control. The results are the next steppingstone towards strengthening the feasibility and utility of these orbits for continuous planetary polar observation.

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Coronal Mass Ejections (CMEs), commonly referred to as solar storms, that are on an Earth-intersecting trajectory, may lead to the breakdown of power grid transformers, the malfunctioning of Earth-orbiting spacecraft, and disruptions in navigation and communication systems, among many other effects. The financial impact of a solar storm is predicted to be in the order of trillions of euros and the probability of such an event occurring within the next decade is 12%. With society relying ever-more on technology, the impact of a solar storm is ever-increasing. It is therefore essential that operators of vital infrastructure are notified of an approaching storm in a timely manner such that they can take adequate measures to mitigate the impact. This paper investigates the use of solar-sail technology to increase the warning time for CMEs heading towards Earth. The warning time is proportional to the distance from the Earth to the spacecraft detecting the CME: a current warning time of 30 to 60 minutes is achieved by satellites at or near the Sun-Earth L1 point. By considering the actual shape of a CME, the continuous solar-sail acceleration from the solar sail can be used to find a periodic trajectory that travels further upstream of the CME-axis, thereby increasing the warning time with respect to current missions. Finding a periodic solar-sail trajectory can be regarded as an optimal control problem, which requires a near-feasible initial-guess trajectory. The latter is found by generating heteroclinic connections between artificial equilibrium points in the vicinity of the sub-L1 and sub-L5 point through the use of a genetic algorithm. The optimal control problem is solved with a direct pseudospectral method, resulting in four representative trajectories, each having specific (dis)advantages. Ultimately, with near-term solar-sail technology (a lightness number of 0.05), the most optimal trajectory increases the average and maximum warning time by a factor 20 and 30 with respect to current missions at L1, respectively, with a 90% probability that the spacecraft detects the CME. Finally, the paper investigated a set of sensitivity analyses (non-ideal sail properties and change in lightness number) to successfully prove the robustness of the methodology and the effect of assumptions made. @en

Our closest neighboring star system, Alpha Centauri, is located at “mere” 275,000 astronomical units (au) from Earth. Because of its “close proximity” to Earth, Alpha Centauri is often considered as the prime target for a future interstellar exploration mission [1]. It holds significant scientific importance for better understanding our sun, and stars in general, and for advancing our knowledge on the formation and evolution of the solar system [2]. Moreover, by visiting Alpha Centauri, Earth-like exoplanets may be discovered (in addition to the discovery of Proxima Centauri b in 2016 [3]). Voyager 1, our fastest and farthest spacecraft, 146 au from the sun at the time of writing, would take approximately 75,000 years to reach Alpha Centauri. Photon-sail propulsion could substantially reduce this travel time [4] even though it exclusively makes use of the radiation pressure from a star to drive the spacecraft forward [5]. This novel propulsion technology has made significant technological progress in recent years through JAXA’s IKAROS mission, NASA’s NanoSail-D2 mission, and the LightSail-1 and LightSail-2 missions by the Planetary Society. Continued technological advancement will be achieved through other proposed and scheduled missions such as NASA’s NEA Scout mission [6]. Proposals for using photon sails to reach targets far beyond our solar system are not new (see, e.g., Refs. [4,7]), and initiatives with clear goals of reaching Alpha Centauri within a generation are underway, e.g., the Breakthrough Starshot project.§ However, little is known about the dynamics of the photon sail once it arrives in the other star system, especially in a multistar system like Alpha Centauri. To date, the only works investigating these dynamics include Refs. [8,9]. Both articles focused on the dynamics in the binary-star system composed of the stars Alpha Centauri A and B, and investigated the possibility of decelerating the spacecraft after arrival, assuming a graphene-based sail covered with a highly reflective coating. The MIRA Collaboration focused on the computation of artificial equilibria (AE) in the same binary-star system, but for a photon-balloon spacecraft, before investigating capture and transfer trajectories for a photon-sail propelled spacecraft in the elliptical restricted three-body problem (ER3BP) [2,10].@en

In this paper, a new family of solar-sail periodic orbits with adequate properties for polar observation of the Earth and moon is developed under the simplified but nonautonomous dynamics of the solar-sail augmented Earth–moon circular restricted three-body problem. The novel orbits, termed “distant-circular orbits,” are found through differential correction and continuation and employ a simple sun-facing steering law for the solar sail. A basic coverage analysis shows that one of the distant-circular orbits is capable of providing continuous coverage of both the Earth’s and lunar north (or south) poles with just a single sailcraft at a minimum elevation angle of 14 deg and an average range of six Earth–moon distances. Moreover, simple transfer trajectories between orbits of the family are found, so that the sailcraft can switch between observing the northern and southern latitudes of the Earth and moon during a single mission. Subsequently, using multiple-shooting differential correction, all results are migrated to a higher-fidelity dynamic framework that considers, among others, the eccentricity of the moon’s orbit. The perturbations cause the periodicity of the orbits to break, turning them into seemingly quasi-periodic orbits, but it is shown that the coverage capabilities are maintained. Finally, an active control strategy is developed to counteract part of the perturbing effects such that, by appropriately steering the sail, the apparent quasi-periodicity of the orbits is enhanced and the deviation from the unperturbed orbits is reduced.

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