M.J. Heiligers
info
Please Note
<p>This page displays the records of the person named above and is not linked to a unique person identifier. This record may need to be merged to a profile.</p>
56 records found
1
The problem of how to optimally transfer between two planet-centered orbits using solar sails remains nearly unexplored. Most of the existing body of knowledge focuses on (blended) locally optimal control laws, often considers open-ended trajectories instead of orbital transfers, or tackles specific mission scenarios, leaving insight into the general transfer problem unexplored. In this work, we present the first step in the comprehensive study of optimal solar-sail transfers around planetary bodies by analyzing the simplest conceivable transfer, the planar circular-to-circular (C2C) transfer. The considered C2C transfer spans only one orbital revolution, which may constitute the future building block of more complex multi-revolution trajectories. The optimized control law maximizes the change in orbital radius within the C2C transfer, where the achieved radius change is used as the performance metric. The results show that the C2C performance (i.e., the ability of the solar sail to transfer) depends on the illumination conditions of the orbital plane and the ratio of the sail’s characteristic acceleration to the local gravitational acceleration. Maximum performance is achieved when the orbital plane is perpendicular to the Sun-planet line, where the transfer structure resembles that of a C2C transfer conducted with an ion drive. Furthermore, by using the ratio as the scaling parameter, the results presented in this paper allow 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.
...
The problem of how to optimally transfer between two planet-centered orbits using solar sails remains nearly unexplored. Most of the existing body of knowledge focuses on (blended) locally optimal control laws, often considers open-ended trajectories instead of orbital transfers, or tackles specific mission scenarios, leaving insight into the general transfer problem unexplored. In this work, we present the first step in the comprehensive study of optimal solar-sail transfers around planetary bodies by analyzing the simplest conceivable transfer, the planar circular-to-circular (C2C) transfer. The considered C2C transfer spans only one orbital revolution, which may constitute the future building block of more complex multi-revolution trajectories. The optimized control law maximizes the change in orbital radius within the C2C transfer, where the achieved radius change is used as the performance metric. The results show that the C2C performance (i.e., the ability of the solar sail to transfer) depends on the illumination conditions of the orbital plane and the ratio of the sail’s characteristic acceleration to the local gravitational acceleration. Maximum performance is achieved when the orbital plane is perpendicular to the Sun-planet line, where the transfer structure resembles that of a C2C transfer conducted with an ion drive. Furthermore, by using the ratio as the scaling parameter, the results presented in this paper allow 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.
Understanding of what is achievable with solar-sail technology around planetary bodies is in its infancy. The seemingly simple problem of transferring from one circular orbit to another circular orbit with a solar sail around a planet is yet to be fully characterized. This work aims to start filling that gap by analyzing the coplanar patched multirevolution circular-to-circular (PMC2C) transfer. The PMC2C transfer is a continuous sequence of single-revolution circular-to-circular (SC2C) transfers, where each SC2C transfer is optimized for the achieved radius change in one orbital revolution. Then, the radius change and transfer time of a PMC2C transfer is obtained as the aggregation of the individual SC2C increments. To generalize to all initial geometries, hundreds of PMC2C transfers must be computed, which is not feasible in practice. To bypass this problem, the so-called patched method is proposed. The patched method uses a semianalytical approach to estimate the radius change and the transfer time of the PMC2C transfers, effectively removing the need for numerical optimization. Dimensionless in nature, the patched method can be used for any sail design around any planet orbiting a star. With this tool, early mission design is greatly simplified; hundreds of trajectories can be analyzed in a matter of minutes. In addition, the generalized formulation reveals the best and worst orbital geometries and initial epochs to start a PMC2C transfer, improving general knowledge of how to “sail” around planets.
...
Understanding of what is achievable with solar-sail technology around planetary bodies is in its infancy. The seemingly simple problem of transferring from one circular orbit to another circular orbit with a solar sail around a planet is yet to be fully characterized. This work aims to start filling that gap by analyzing the coplanar patched multirevolution circular-to-circular (PMC2C) transfer. The PMC2C transfer is a continuous sequence of single-revolution circular-to-circular (SC2C) transfers, where each SC2C transfer is optimized for the achieved radius change in one orbital revolution. Then, the radius change and transfer time of a PMC2C transfer is obtained as the aggregation of the individual SC2C increments. To generalize to all initial geometries, hundreds of PMC2C transfers must be computed, which is not feasible in practice. To bypass this problem, the so-called patched method is proposed. The patched method uses a semianalytical approach to estimate the radius change and the transfer time of the PMC2C transfers, effectively removing the need for numerical optimization. Dimensionless in nature, the patched method can be used for any sail design around any planet orbiting a star. With this tool, early mission design is greatly simplified; hundreds of trajectories can be analyzed in a matter of minutes. In addition, the generalized formulation reveals the best and worst orbital geometries and initial epochs to start a PMC2C transfer, improving general knowledge of how to “sail” around planets.
NASA's ACS3 mission aims to be the first Earth-bound solar sail to execute calibration steering laws for in-orbit estimation of solar-sail acceleration parameters. To maximise the mission's scientific return, this study identifies the physical effects to include in the dynamical model, the solar-sail acceleration parameters observable from flight data, and the uncertainties to consider during the orbit determination process. The sensitivity of the solar-sail dynamics to perturbations, model uncertainties, and sail-attitude errors is investigated by 1) comparing a reference orbit with modified orbits, each altered in a single dynamical aspect, and 2) evaluating the accuracy of modified models in reconstructing the reference orbit through iterative initial state adjustments. For the one-sigma 10-meter observation noise level of the ACS3 mission and a seven-day arc, results indicate that higher-order lunar perturbations, planetary third-body effects, and relativistic corrections can be omitted from the dynamical model. Additionally, the geopotential expansion may be limited to degree and order 32. In contrast, the dynamics should include the effects of solid Earth tides, account for the instantaneous Sun-sailcraft distance in the solar radiation pressure model, and assume imperfect reflection from the sail surface in the solar and planetary radiation pressure models. Furthermore, the analysis reveals varying levels of observability for the sail optical coefficients, with frontside reflectivity and specularity showing the strongest influence on the solar-sail dynamics. Finally, systematic attitude errors and uncertainties in atmospheric density and accommodation coefficients are the most challenging factors to absorb through initial state adjustment, potentially complicating the estimation of solar-sail acceleration parameters.
...
NASA's ACS3 mission aims to be the first Earth-bound solar sail to execute calibration steering laws for in-orbit estimation of solar-sail acceleration parameters. To maximise the mission's scientific return, this study identifies the physical effects to include in the dynamical model, the solar-sail acceleration parameters observable from flight data, and the uncertainties to consider during the orbit determination process. The sensitivity of the solar-sail dynamics to perturbations, model uncertainties, and sail-attitude errors is investigated by 1) comparing a reference orbit with modified orbits, each altered in a single dynamical aspect, and 2) evaluating the accuracy of modified models in reconstructing the reference orbit through iterative initial state adjustments. For the one-sigma 10-meter observation noise level of the ACS3 mission and a seven-day arc, results indicate that higher-order lunar perturbations, planetary third-body effects, and relativistic corrections can be omitted from the dynamical model. Additionally, the geopotential expansion may be limited to degree and order 32. In contrast, the dynamics should include the effects of solid Earth tides, account for the instantaneous Sun-sailcraft distance in the solar radiation pressure model, and assume imperfect reflection from the sail surface in the solar and planetary radiation pressure models. Furthermore, the analysis reveals varying levels of observability for the sail optical coefficients, with frontside reflectivity and specularity showing the strongest influence on the solar-sail dynamics. Finally, systematic attitude errors and uncertainties in atmospheric density and accommodation coefficients are the most challenging factors to absorb through initial state adjustment, potentially complicating the estimation of solar-sail acceleration parameters.
Solar sailing exploits solar radiation pressure to generate propellantless thrust, enabling mission applications beyond the capabilities of conventional propulsion systems. Despite this potential, the lack of in-flight validation for solar-sail force models has limited confidence in applying solar sailing beyond technology demonstration missions. This study presents the first comprehensive investigation into the potential of solar-sail performance characterisation from flight data by applying a covariance-based estimation framework using simulated GNSS observations for NASA’s ACS3 mission.A set of calibration steering laws is proposed to facilitate the in-orbit estimation of the parameters governing the solar-sail acceleration. The study focuses on the sail frontside reflectivity and specularity, the optical coefficients exerting the strongest influence on the solar-sail dynamics. For each steering law, the covariance analysis quantifies the achievable estimation accuracy of these coefficients as a function of measurement noise, observation arc length, sampling rate, and ACS3 expected orbital evolution over the coming year. The operational feasibility of the calibration steering laws is also assessed through the evaluation of power budget, ground station communication, altitude maintenance, sail material degradation, and attitude rate limitations.For the 10-meter observation noise level expected in ACS3 telemetry, results indicate that a dedicated in-flight calibration can reduce the formal errors of the optical coefficients in the (Formula presented) to (Formula presented) range, an improvement of two to three orders of magnitude compared to pre-flight ground characterisation. When estimation performance is evaluated against operational constraints, the power budget is identified as the main limiting factor, and the fixed in-plane pointing steering law emerges as the most robust strategy, consistently delivering high-accuracy estimates while satisfying all operational constraints across diverse orbital geometries.
...
Solar sailing exploits solar radiation pressure to generate propellantless thrust, enabling mission applications beyond the capabilities of conventional propulsion systems. Despite this potential, the lack of in-flight validation for solar-sail force models has limited confidence in applying solar sailing beyond technology demonstration missions. This study presents the first comprehensive investigation into the potential of solar-sail performance characterisation from flight data by applying a covariance-based estimation framework using simulated GNSS observations for NASA’s ACS3 mission.A set of calibration steering laws is proposed to facilitate the in-orbit estimation of the parameters governing the solar-sail acceleration. The study focuses on the sail frontside reflectivity and specularity, the optical coefficients exerting the strongest influence on the solar-sail dynamics. For each steering law, the covariance analysis quantifies the achievable estimation accuracy of these coefficients as a function of measurement noise, observation arc length, sampling rate, and ACS3 expected orbital evolution over the coming year. The operational feasibility of the calibration steering laws is also assessed through the evaluation of power budget, ground station communication, altitude maintenance, sail material degradation, and attitude rate limitations.For the 10-meter observation noise level expected in ACS3 telemetry, results indicate that a dedicated in-flight calibration can reduce the formal errors of the optical coefficients in the (Formula presented) to (Formula presented) range, an improvement of two to three orders of magnitude compared to pre-flight ground characterisation. When estimation performance is evaluated against operational constraints, the power budget is identified as the main limiting factor, and the fixed in-plane pointing steering law emerges as the most robust strategy, consistently delivering high-accuracy estimates while satisfying all operational constraints across diverse orbital geometries.
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.
...
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.
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.
...
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.
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.
...
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.
Conference paper
(2024)
-
L. Carzana, A. Minervino Amodio, P.N.A.M. Visser, W. Keats Wilkie, M.J. Heiligers
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.
...
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.
Conference paper
(2023)
-
L. Carzana, W. Keats Wilkie, Andrew F. Heaton, Ben DIEDRICHc Diedrich, M.J. Heiligers
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.
...
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.
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.
...
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.
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.
...
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.
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.
...
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.
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.
...
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.
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.
...
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.
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.
...
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.
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.
...
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.
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.
...
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.
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.
...
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.