Homo- and Heteroclinic Connections in the Spatial Solar-Sail Earth-Moon Three-Body Problem

This paper explores the existence of homo- and heteroclinic connections between solar-sail periodic orbits in the Earth-Moon three-body problem. While such connections have been explored extensively in the classical system, the addition of a solar-sail induced acceleration introduces a time-dependency in the dynamics which prevents the use of traditional tools for reducing the dimensionality of the problem (e.g., the Jacobi constant and spatial Poincaré sections). This paper therefore explores the use of solar-sail assisted manifolds, temporal Poincaré sections, and a genetic algorithm approach to achieve the sought-after connections and apply the approach to a range of solar-sail periodic orbits.Astrodynamics & Space Mission

Homo- and Heteroclinic Connections in the Planar Solar-Sail Earth-Moon Three-Body Problem

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.Astrodynamics & Space Mission

Time-optimal solar sail heteroclinic-like connections for an Earth-Mars cycler

This paper investigates solar sail Earth-Mars cyclers, in particular cyclers between libration point orbits at the Earth-Moon L2 point and the Sun-Mars L1 point. In order to facilitate cyclers in as few Earth-Mars synodic periods as possible, the overall objective is to minimize the time of flight. These time-optimal cyclers are obtained by using a direct pseudospectral method and exploiting techniques from dynamical systems theory to obtain an initial guess. In particular, heteroclinic connections between the unstable and stable manifolds of the target libration point orbits at the Earth-Moon L2 point and the Sun-Mars L1 point are sought for. While such connections do not exist in the ballistic case, they can be achieved by complementing the dynamics with a solar sail and assuming a constant attitude of the sail with respect to the direction of sunlight. These trajectories are sub-optimal due to the assumed constant sail attitude as well as minor discontinuities in position and velocity at the linkage of the manifolds, which are overcome by transferring the initial guess to the direct pseudospectral optimal control solver. For near- to mid-term sails, results show time-optimal round-trip trajectories that span three synodic Earth-Mars periods, with a few months to one year stay times at the libration point orbits, depending on the time of departure within a five-month window. Through the propellant-less nature of solar sailing, these Earth-Mars cyclers can, in theory, be maintained indefinitely.Space Systems EgineeringAstrodynamics & Space Mission

Using solar-sail induced dynamics to increase the warning time for solar storms heading towards earth

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.Astrodynamics & Space Mission

Orbital Dynamics of an Oscillating Sail in the Earth-Moon System

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.Astrodynamics & Space Mission

Photon-Sail Trajectories Towards Exoplanet Proxima b

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.Astrodynamics & Space MissionsAerospace Engineerin

Coupled Roto-Translational Motion of the Heliogyro Applied to Earth-Mars Cyclers

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.Astrodynamics & Space Mission

Solar sail orbital motion about asteriods and binary asteroid systems

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.Astrodynamics & Space Mission

Mission analysis of space-based telescopes to detect impacting near-earth objects

Recognising the threat of near-Earth objects (NEOs) to life on Earth, many projects have been developed worldwide with the aim of detecting potential impactors, most of which are focused on ground-based surveys. However, _20% of the Earth-threatening NEOs are estimated to be approaching Earth from the day-side, and are thus very difficult to detect using ground surveys. Over the last decade, several space-based capabilities have emerged in an effort to discover and catalogue NEOs in order to better quantify their risk of impact, yet little research has gone into dealing with imminent-impacting NEOs. The aim of this paper is to design a space mission that places a telescope in-orbit in order to detect and provide warning for Earth-impacting NEOs down to 20m in size, by determining the performance of both a visible and an infrared (IR) space-based telescope used in two mission candidates. The first mission candidate consists of a halo orbit about the artificial equilibrium point sub-L1 of the Sun-Earth (SE) system, which is displaced with respect to the classical L1 point, along the SE direction towards the Sun, through the use of solar-sail propulsion. As second mission candidate, three vertical Lyapunov orbits about the libration points L3, L4 and L5 of the Sun-Venus system are considered. A trade-off between detection rates and warning times is conducted to determine the most suitable space-based NEO survey system. It is concluded that an IR space-based telescope placed at the SE solar-sail displaced L1 point is the best option because of the long warning times obtained and the beneficial contribution to existing ground-based NEO surveys. A preliminary mission analysis is also performed to determine a solar-sail propelled transfer trajectory to the SE sub-L1 region, assuming a ride-share launch on ESA’s Euclid mission.Astrodynamics & Space Mission

New solar-sail orbits for polar observation of the earth and moon

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.Accepted Author ManuscriptAstrodynamics & Space Mission