This paper presents the design of solar-sail transfer trajectories to solar-sail displaced libration point orbits in the Earth- Moon system. The existence of families of solar-sail displaced libration point orbits in the Earth-Moon system has recently been demonstrated. These families originate from complementing the dynamics of the classical Earth-Moon circular restricted three-body problem with a solar-sail induced acceleration. Previous work has furthermore demonstrated the applicability of these orbits for high-latitude observation of the Earth and Moon. To not only demonstrate the existence and applicability of these orbits, but also their accessibility, this paper investigates the design of solar-sail transfers from Earth-bound parking orbits to a subset of these orbits. Initial guesses for the transfers are generated using reverse time propagation of the dynamics, where the control is provided by a locally optimal steering law. These initial guesses are subsequently used to initialize a 12th-order Gauss-Lobatto collocation method to satisfy a large number of constraints: departure from specific high Earth orbits, a minimum altitude with respect to the Earth and the Moon, and a maximum rotation rate of the solar sail. As an application of the developed methodology, this paper shows results for transferring two spacecraft to a constellation of displaced vertical Lyapunov orbits at the Earth-Moon L2 point. This constellation has been shown to provide continuous coverage of the lunar Aitken Basin and the lunar South Pole while maintaining a continuous line of sight with Earth. Sets of feasible trajectories for both spacecraft with identical launch conditions are produced in order for the constellation to be initiated using a single Soyuz launch. Such a Soyuz launch can deliver two 1160-kg spacecraft into the found transfer trajectories. One of the spacecraft subsequently requires a transfer time of 53.06 days to enter its constellation orbit, while the transfer of the other spacecraft takes 67.89 days. These results prove the accessibility of solar-sail displaced libration point orbits in the Earth-Moon system, thereby reaffirming the potential of solar-sail technology to enable novel scientific missions in the Earth-Moon system. @en

This paper presents the design of solar-sail transfer trajectories to solar-sail displaced libration point orbits in the Earth- Moon system. The existence of families of solar-sail displaced libration point orbits in the Earth-Moon system has recently been demonstrated. These families originate from complementing the dynamics of the classical Earth-Moon circular restricted three-body problem with a solar-sail induced acceleration. Previous work has furthermore demonstrated the applicability of these orbits for high-latitude observation of the Earth and Moon. To not only demonstrate the existence and applicability of these orbits, but also their accessibility, this paper investigates the design of solar-sail transfers from Earth-bound parking orbits to a subset of these orbits. Initial guesses for the transfers are generated using reverse time propagation of the dynamics, where the control is provided by a locally optimal steering law. These initial guesses are subsequently used to initialize a 12th-order Gauss-Lobatto collocation method to satisfy a large number of constraints: departure from specific high Earth orbits, a minimum altitude with respect to the Earth and the Moon, and a maximum rotation rate of the solar sail. As an application of the developed methodology, this paper shows results for transferring two spacecraft to a constellation of displaced vertical Lyapunov orbits at the Earth-Moon L2 point. This constellation has been shown to provide continuous coverage of the lunar Aitken Basin and the lunar South Pole while maintaining a continuous line of sight with Earth. Sets of feasible trajectories for both spacecraft with identical launch conditions are produced in order for the constellation to be initiated using a single Soyuz launch. Such a Soyuz launch can deliver two 1160-kg spacecraft into the found transfer trajectories. One of the spacecraft subsequently requires a transfer time of 53.06 days to enter its constellation orbit, while the transfer of the other spacecraft takes 67.89 days. These results prove the accessibility of solar-sail displaced libration point orbits in the Earth-Moon system, thereby reaffirming the potential of solar-sail technology to enable novel scientific missions in the Earth-Moon system. @en

This paper proposes the use of solar-sail technology currently under development at NASA Langley Research Center for a CubeSat rendezvous mission with asteroid 2016 HO3, a quasi-satellite of Earth. Time-optimal trajectories are sought for within a 2022 – 2023 launch window, starting from an assumed launcher ejection condition in the Earth-Moon system. The optimal control problem is solved through a particular implementation of a direct pseudo-spectral method for which initial guesses are generated through a relatively simple and straightforward genetic algorithm search on the optimal launch date and sail attitude. The results show that the trajectories take 2.16 – 4.21 years to complete, depending on the assumed solar-sail reflectance model and solar-sail technology. To assess the performance of solar-sail propulsion for this mission, the trajectory is also designed assuming the use of near-term solar electric propulsion. The resulting fuel-optimal trajectories take longer to complete than the solar-sail trajectories and require a propellant consumption that exceeds the expected propellant capacity onboard the CubeSat. This comparison demonstrates the superior performance of solar-sail technology for this mission. @en

This paper explores the capability of solar sails to transfer a probe from the displaced L1 and L2 libration points to the region of practical stability (RPS) around the triangular equilibrium points L4 and L5. If the sailcraft arrives inside the RPS with zero synodical velocity, it will remain there with no need for station keeping maneuvers. Moreover, the location of the RPS is ideal for space weather missions as the Sun can be observed from a dierent angle compared to spacecraft orbiting the L1 point. The solar sail unstable mani-folds of the displaced L1 and L2 points come close to these regions providing opportunities for natural transfer trajectories. By varying the solar sail orientation along the manifold, the dynamics are altered and simple transfer trajectories that reach the RPS with few sail maneuvers are enabled. However, these trajectories are not optimal from a transfer time perspective, but they are used in this paper as an initial guess in a direct optimization method to nd minimum-time transfers between the displaced L1 and L2 points and the RPS at L4 and L5.@en

This paper explores the existence of homo- and heteroclinic connections between solar-sail periodic orbits in the planar Earth-Moon circular restricted three-body problem. The existence of such connections has been demonstrated to great extent for the planar and spatial classical (no-solar sail) three-body problem, but remains unexplored for the inclusion of a solar-sail induced acceleration. Similar to the search for homo- and heteroclinic connections in the classical case, this paper uses the tools and techniques of dynamical systems theory, in particular trajectories along the unstable and stable manifolds, to generate these connections. However, due to the time dependency introduced by the solar-sail induced acceleration, common methods and techniques to find homo- and heteroclinic connections (e.g., using the Jacobi constant and applying spatial Poincaré sections) do not necessarily apply. The aim of this paper is therefore to gain an understanding of the extent to which these tools do apply, define new tools (e.g., solar-sail assisted manifolds, temporal Poincaré sections, and a genetic algorithm approach), and ultimately find the sought for homo- and heteroclinic connections. As a starting point of such an investigation, this paper focuses on the planar case, in particular on the search for homo- and heteroclinic connections between three specific solar-sail Lyapunov orbits (two at the L1 point and one at the L2 point) that all exist for the same near-term solar-sail technology. The results of the paper show that, by using a simple solar-sail steering law, where a piece-wise constant sail attitude is applied in the unstable and stable solar-sail manifold trajectories, homo- and heteroclinic connections exist for these three solar-sail Lyapunov orbits. The remaining errors on the position and velocity at linkage of the stable and unstable manifold trajectories are < 10 km and < 1 m/s. Future studies can apply the tools and techniques developed in this paper to extend the search for homo- and heteroclinic connections to other solar-sail Lyapunov orbits in the Earth-Moon system (e.g., for different solar-sail technology), to other planar solar-sail periodic orbits, and ultimately also to the spatial, three-dimensional case.@en

Solar-sail periodic orbits in the Earth–moon circular restricted three-body problem are proposed for continuous observation of the polar regions of the Earth and the moon. The existence of families of solar-sail periodic orbits in the Earth–moon system has previously been demonstrated by the authors and is expanded by introducing additional orbit families. Orbits for near-term solar-sail technology originate by maintaining the solar sail at a constant attitude with respect to the sun such that mission operations are greatly simplified. The results of this investigation include a constellation of two solar-sail L 2 L2 -vertical Lyapunov orbits that achieves continuous observation of both the lunar South Pole and the center of the Aitken Basin at a minimum elevation of 15 deg. At Earth, a set of two, clover-shaped orbits can provide continuous coverage of one of the Earth’s poles at a minimum elevation of 20 deg. Results generated in the Earth–moon circular restricted three-body model are easily transitioned to one that includes eccentricity effects and demonstrates that the orbits are feasible in realistic regimes.@en

The oscillating sail is a novel solar sail configuration where a triangular sail is released at a deflected angle with respect to the Sun-direction. As a result, the sail will conduct an undamped oscillating motion around the Sun-line due to the offset between the centre-of-pressure and centre-of-mass. In this paper, the resulting oscillatory motion of the acceleration vector is exploited to design new families of periodic orbits in the Earth-Moon circular restricted three-body system. In particular, the effect of adding an oscillating sail to the family of Lyapunov orbits at the L1- and L2-points as well as the family of distant retrograde orbits (DROs) is investigated. Because the solar sail Earth-Moon system is non-autonomous (due to the apparent orbital motion of the Sun), the sail’s oscillating period, the orbital period and the period of the Sun around the Earth-Moon system all need to be commensurable in order for the orbits to be repeatable over time. Using a differential correction technique, orbits that satisfy these constraints can be obtained and the results comprise new families of periodic orbits that are parameterised by the required sail performance. In addition to exploiting the oscillating sail for generating new orbit families, this paper also investigates its potential for orbital transfers. By combining a systematic search method with a local optimiser, oscillating sail parameters and orbital parameters can be obtained that enable transfers between classical Lyapunov orbits at the L1-point, connections between classical Lyapunov orbits at different Lagrange points as well as transfers between orbits within the family of classical DROs.@en

Solar sailing is an elegant form of space propulsion that reflects solar photons off a large membrane to produce thrust. Different sail configurations exist, including a traditional fixed polygonal flat sail and a heliogyro, which divides the membrane into a number of long, slender blades. The magnitude and direction of the resulting thrust depends on the sail’s attitude with respect to the sun (cone angle). At each cone angle, a fixed polygonal flat sail can only generate force constrained to a particular magnitude and direction, whereas the heliogyro can arbitrarily reduce the thrust magnitude through the additional control of pitching the blades. This gives the heliogyro more force control authority, which is exploited in this paper for orbital control of solar sail, sun–Earth, sub-L 1 halo orbits through a linear-quadratic regulator feedback controller. Two test cases are considered, quantifying either the maximum error in the injection state or the maximum delay in solar sail deployment due to deployment failure at injection from which the nominal orbit can still be recovered. This paper finds that the heliogyro can accommodate approximately an order of magnitude larger injection error than a fixed polygonal flat sail and a significantly larger sail deployment delay of up to 20.2 days in some cases.@en

A pole-sitter is a satellite that is stationed along the polar axis of the Earth, or any other planet, to generate a continuous, hemispherical view of the planet’s polar regions. In order to maintain such a vantage point, a low-thrust propulsion system is required to counterbalance the gravitational attraction of the planet and the Sun. Previous work has considered the use of solar electric propulsion (SEP) or a hybrid configuration of an SEP thruster and a solar sail to produce the required acceleration. By subsequently optimising the propellant consumption by the thruster, estimates of the mission performance in terms of the payload capacity and mission lifetime have been obtained. This paper builds on these results and aims at lifting the pole-sitter concept to the next level by extending the work both from a technical and conceptual perspective: from a technical perspective, this paper will further improve the mission performance by optimising the pole-sitter orbits for the payload capacity or mission lifetime instead of for the propellant consumption. The results show that, at Earth, this allows improvements in the order of 5-10 percent in terms of payload capacity and mission lifetime. Furthermore, on a conceptual level, this paper will, for the first time, investigate the possibility of so-called quasi-pole-sitter orbits. For quasi-pole-sitter orbits the requirement to be exactly on the polar axis is relaxed to allow some movement around the polar axis as long as continuous observation of the entire polar region at a desired minimum elevation angle is achieved. This ultimately enables solar sail-only pole-sitter orbits that are no longer limited in performance by the SEP propellant consumption. Finally, this paper extends all analyses to other inner Solar System planets, showing that Mars provides excellent conditions for a pole-sitter platform with its low mass and relatively far distance from the Sun. With this extension of the pole-sitter concept to other planets as well as considering, for the first time, the option of quasi-pole-sitter orbits, the concept is lifted to the next level, strengthening the feasibility and utility of these orbits for continuous planetary polar observation.@en

While SRP is often considered an undesirable effect, especially for missions to small bodies like asteroids and binary asteroid systems, this paper utilizes the SRP on a solar sail to generate artificial equilibrium points (AEPs) and displaced periodic orbits in these systems. While the solar sail dynamics for the single asteroid case are described using the Hill + SRP problem, those for the binary system are either described in the Hill four-body + SRP problem or the full bicircular + SRP problem. The results for the single asteroid case include solar sail acceleration contours to remain stationary with respect to the asteroid on either the Sun-lit or dark side of the asteroid and either in or above its orbital plane. Using a combination of analytical and numerical methods, i.e., the Lindstedt-Poincaré method and a differential corrector, orbits around these AEPs can be found. By switching to the Hill four-body problem and employing a direct multiple shooting method, these orbits can be extended to a binary system where the effect of the smaller asteroid is an oscillatory motion around the orbits found for the single asteroid case. Finally, by switching to the bi-circular + SRP problem, AEPs can once again be obtained, though their location becomes timedependent due to the changing direction of the Sun-vector. However, high above the binary system's orbital plane, the AEPs trace out a circular orbit that suggests the existence of so-called pole-sitter-like orbits. Using an analytical inverse method and a numerical differential corrector, the results indeed show families of solar sail periodic orbits above the binary system's orbital plane. Though all orbits, both in the single asteroid case and the binary system, are linearly unstable, they exist for near-term solar sail technology and for a simple steering law where the sail remains at a fixed attitude with respect to the Sun. These orbits therefore allow unique, geostationary-equivalent vantage points from where to monitor the asteroid(s) over extended periods of time.@en

Enable future missions Any mission to a DRO or halo orbit could benefit from the capability to transfer between these orbits Chemical propulsion could be used for these transfers, but at high propellant cost Fill gaps in knowledge A variety of transfers using SEP or solar sails have been studied for the Earth-Moon system Most results in literature study a single transfer This is a step toward understanding the wide array of types of transfers available in an N-body force model.@en

This paper proposes the use of solar sail periodic orbits in the Earth-Moon system for ob-servation of the high-latitudes of the Earth and Moon. At the Earth, the high-latitudes will be crucial in answering questions concerning global climate change, monitoring space weather events and ensuring sustainable development of these fragile regions. The polar regions of the Moon, especially the South Pole, are of great scientific interest as well as a potential destination for a future permanent lunar base. The existence of families of solar sail periodic orbits in the Earth-Moon system has previously been demonstrated by the authors and is expanded in this paper by introducing additional orbit families. The paper focuses in particular on orbits that are achievable with near-term solar sail technology and that originate by maintaining the solar sail at a constant attitude with respect to the Sun such that mission operations are greatly simplified. The results provide a set of constellations for continuous observation of the high-latitudes. For example, a constellation of two solar sail L2-displaced vertical Lyapunov orbits can achieve con-tinuous observation of both the lunar South Pole and the center of the Aitken Basin at a mini-mum elevation of 15 deg, while at the Earth, a set of two, so-called ‘clover-shaped’ orbits can provide continuous coverage of one of the Earth’s Poles at 20 deg minimum elevation. Transfer-ring these orbits to a higher-fidelity model, taking among others the eccentricity of the Moon into account, shows that these orbits still exist without any significant impact on their perfor-mance for high-latitude observation of the Earth and Moon.@en

A heliogyro is a solar sail concept that divides the solar sail membrane into a number of long, slender blades of film extended from a central hub, maintained in a flat state through spin-induced tension. The heliogyro can redirect and scale the solar radiation pressure (SRP) force and can achieve attitude control by twisting the blades, similar to a helicopter rotor. Different pitch profiles exist, including pitching the blades in a collective, cyclic or combined collective and cyclic manner. While the forward mapping, i.e., computing the SRP force and moment generated by the heliogyro for a given pitch profile, is straightforward, the inverse of the problem is much more complex. However, this inverse problem (finding the blades’ pitch that results in a desired SRP force and/or moment) is crucial for heliogyro mission design and operations. This paper therefore solves the inverse problem numerically: first, only for a desired SRP force or SRP moment and subsequently for the fully coupled inverse problem. The developed methods are subsequently applied to track a reference trajectory that corrects for injection errors into a solar sail Sun-Earth sub-L1 halo orbit. I. Introduction@en

This paper presents families of libration point orbits in the Earth-Moon system that originate from complementing the classical circular restricted three-body problem with a solar sail. Through the use of a differential correction scheme in combination with a continuation on the solar sail induced acceleration, families of Lyapunov, halo, vertical Lyapunov, Earth-centred, and distant retrograde orbits are created. As the solar sail circular restricted three-body problem is non-autonomous, a constraint defined within the differential correction scheme ensures that all orbits are periodic with the Sun’s motion around the Earth-Moon system. The continuation method then starts from a classical libration point orbit with a suitable period and increases the solar sail acceleration magnitude to obtain families of orbits that are parametrised by this acceleration. Furthermore, different solar sail steering laws are considered (both in-plane and out-of-plane, and either fixed in the synodic frame or fixed with respect to the direction of Sunlight), adding to the wealth of families of solar sail enabled libration point orbits presented. Finally, the linear stability properties of the generated orbits are investigated to assess the need for active orbital control. It is shown that the solar sail induced acceleration can have a positive effect on the stability of some orbit families, especially those at the L₂ point, but that it most often (further) destabilises the orbit. Active control will therefore be needed to ensure long-term survivability of these orbits.

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Solar sailing is an elegant form of space propulsion that reflects solar photons to produce thrust. Different sail configurations exist, including a traditional flat sail (either square- or disc-shaped) and a heliogyro, which divides the sail membrane into a number of long, slender blades, analogous to a helicopter rotor. The magnitude and direction of the induced thrust force depends on the sail’s attitude with respect to the Sun, i.e. on the cone angle. At each cone angle, a flat sail can only generate force of particular magnitude and direction, while this paper demonstrates that a heliogyro can arbitrarily reduce the magnitude of the thrust vector through the additional control of pitching the blades. This gives the heliogyro more force control authority, which is exploited in this paper for orbital control. A linear-quadratic regulator feedback controller is used to quantify the maximum error in the injection state vector of a solar sail Sun-Earth sub-L1 halo orbit from which the nominal orbit can still be recovered. The conclusion is that approximately an order of magnitude larger error in position and velocity can be accommodated, demonstrating superior capabilities of the heliogyro over a flat sail for orbital control.@en

Solar sailing has great potential for a range of high-energy and long duration mis-sions in the Sun-Earth system. This paper extends this potential to the non-autonomous Earth-Moon system through the use of a differential correction scheme, and by selecting suitable in-plane and out-of-plane sail steering laws to develop new families of solar sail libration point orbits that are periodic with the Sun’s motion around the Earth-Moon system. New orbits include those that bifur-cate from the natural Lyapunov, halo and eight-shaped orbit families at the first and second Lagrange points. The potential of these orbits is demonstrated by con-sidering the performance of a subset of orbits for high-latitude Earth observations, lunar far-side communications, and lunar South Pole coverage.@en