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Multiple gravity-assist (MGA) trajectory design requires the solution of a mixed-integer programming problem to find the best sequence among all possible combinations of candidate planets and dates for spacecraft maneuvers. Current approaches require computing times rising steeply with the number of control parameters, and they strongly rely on narrow search spaces. Moreover, the challenging multiobjective optimization needs to be tackled to appropriately inform the mission design with full extent of launch opportunities. This paper describes a methodology based upon a trajectory model to transcribe the mixed-integer space into a discrete graph made by grids of interconnected nodes. The model is based on Lambert arc grids obtained for a range of departure dates and flight times between two planets. A Tisserand-based criterion selects planets to pass by. Dynamic programming is extended to multiobjective optimization of MGA trajectories and used to explore the graph, guaranteeing Pareto optimality with only moderate computational effort. Robustness is ensured by evaluating the relationship between graph and mixed-integer spaces. Missions to Jupiter and Saturn alongside challenging comet sample return transfers involving long MGA sequences are discussed. These examples illustrate the robustness and efficiency of the proposed approach in capturing globally optimal solutions and wide Pareto fronts on complex search spaces.

Recent advancements in CubeSat technology unfold new mission ideas and the opportunity to lower the cost of space exploration. Ground operations costs for interplanetary CubeSats, however, still represent a challenge toward low-cost CubeSat missions: hence, certain levels of autonomy are desirable. The feasibility of autonomous asteroid flyby missions using CubeSats is assessed here, and an effective strategy for autonomous operations is proposed. The navigation strategy is composed of observations of the Sun, visible planets, and the target asteroid, whereas the guidance strategy is composed of two optimally timed trajectory correction maneuvers. A Monte Carlo analysis is performed to understand the flyby accuracies that can be achieved by autonomous CubeSats, in consideration of errors and uncertainties in a) departure conditions, b) propulsive maneuvers, c) observations, and d) asteroid ephemerides. Flyby accuracies better than ±100 km (3σ)" role>±100 km (3σ)±100 km (3σ) are found possible, and main limiting factors to autonomous missions are identified, namely a) on-board asteroid visibility time (Vlim≥11" role=>Vlim≥11Vlim≥11), b) ΔV" role=">ΔVΔV for correction maneuvers (>15 m/s>15 m/s), c) asteroid ephemeris uncertainty (

This paper proposes a novel description of the equations of motion for low-thrust trajectory design in the presence of a third-body perturbation. The framework is formulated using Gauss’ Variational Equations (GVE) with two distinct accelerations: the one produced by the electric engine and the disturbing term of the third-body effect, which is computed using the disturbing potential of the previously studied Keplerian Map. The presented GVE third-body (GVE-3B) framework allows for a simple and intuitive description of the low-thrust optimisation problem. It is accurate until very close to the sphere of influence of the perturbing body, and thus can be used to target trajectories in low-energy regimes. Together with the framework, this paper develops a methodology to generate low-energy first-guess solutions for low-thrust trajectories. Both the methodology and the framework are showcased in the design of two distinct missions: a rendezvous with asteroid 2017 SV19 during its next Earth encounter, after departing from the unstable invariant manifold of the L2" role="presentation" style="display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border-width: 0px; border-style: initial; position: relative;">L2 point in the Sun-Earth system, and the capture of asteroid 2018 AV2 to a stable invariant manifold of the same point

This paper suggests a new way of interpreting visual information perceived by visible cameras in the proximity of small celestial bodies. At close ranges, camera-based perception processes generally rely on computational constructs known as features. Our hypothesis is that trends in the quantity of available optical features can be correlated to variations in the angular distance from the source of illumination. Indeed, the discussed approach is based on treating properties related to these detected optical features as readings of a field - the perception fields of the title, assumed induced by the coupling of the environmental conditions and the state of the sensing device. The extreme spectrum of shapes, surface properties and gravity fields of small celestial bodies heavily affects visual proximity operational procedures. Therefore, self-contained ancillary tools providing context and an evaluation of estimators' performance while using the least number of priors are extremely significant in these conditions. This preliminary study presents an analysis of the occurrences of optical feature observed around two asteroids, 101955 Bennu and (8567) 1996 HW1 in visual data simulated within Blender, a computer graphics engine. The comparison of three different feature detectors showed distinctive trends in the distribution of the detected optical features, directly correlated to the spacecraft-target-Sun angle, confirming our hypothesis.

Space exploration has seen a growing number of asteroid missions being launched; mostly due to their scientific interest, but also on account of the potential impact threat and prospective valuable resources of their targets. Landing safely on the surface of an asteroid is one of the main technical challenges before obtaining in-situ observations and ground-truth data. Given the asteroid's extremely weak gravitational field, purely ballistic descent trajectories become a suitable option to reach its surface. However, this is still a very risky operation due to the limited knowledge of the object's physical characteristics. Hence, deploying a small lander is often a more conservative option than endangering the mothercraft itself, and thus a simple CubeSat may provide a low cost solution for asteroid exploration. However, for a CubeSat system to be able to safely land on the surface of an asteroid, a sufficient dissipation of energy must naturally occur at touchdown, or else the resultant bouncing may lead to high uncertainties on the final landing location, or even yield an escape trajectory. This paper describes the result of ESA Academy's Drop Your Thesis! 2018 (DYT2018) programme. DYT2018 carried out a microgravity experiment, led by Land3U team from the Astronautics and Space Engineering Course at Cranfield University, to provide additional data on the engineering constraints relevant to land a CubeSat on the surface of an asteroid. The experiment was performed in ZARM's Drop Tower, located in Bremen, during two Drop campaigns in November 2018 and February 2019. A total of 7 drops were completed, each providing 4.74 s of microgravity under vacuum environment. The experiment measured the coefficient of restitution of a 1U mock-up, equipped with a 4-kg mass, touching down on the simulated asteroid surface with an average velocity of 150 mm/s. Three successful drops measured a coefficient of restitution of 0.26 ± 0.03.

CubeSat technology has recently attracted great interest from the scientific community, industry and space agencies, and represents today an exciting movement towards a more affordable and accessible space industry. In view of potential applications of CubeSat technology to small-body planetary exploration, this paper studies the feasibility of using autonomous CubeSats to flyby near-Earth asteroids. This work provides an overview of the current state of CubeSat technology and proposes a 3U CubeSat mission using primarily off-the-shelf components. The proposed mission considers a CubeSat is deployed by a larger spacecraft in a periodic orbit around the first (L1) or the second (L2) Sun-Earth Lagrange points (common destinations to observe the Sun and outer space), from where fuel-optimal impulsive trajectories are designed to flyby asteroids between 2019 and 2025. Navigation support and ground operations costs still represent a major challenge for interplanetary CubeSats. As such, Monte Carlo simulations are performed to determine the flyby accuracies that can be accomplished by a 3U CubeSat flying autonomously (i.e., using observations of the Sun during cruise and observations of the asteroid before the flyby to estimate its own trajectory, instead of using ground stations for navigation support). Asteroid flyby opportunities for an autonomous 3U CubeSat are identified between years 2019 and 2025. Flyby altitudes below 500 km are found possible with currently-available CubeSat components. Possible science payloads are also overviewed, and the potential scientific return of such a low-cost mission is discussed.

Remote sensing instrumentation onboard missions to asteroids is paramount to address many of the fundamental questions in modern planetary science. Yet in situ surface measurements provide the “ground truth” necessary to validate and enhance the science return of these missions. Nevertheless, because of the dynamical uncertainties associated with the environment near these objects, most missions spend long periods of times stationed afar. Small landers can be used much more daringly, however, and thus have already been identified as valuable assets for in situ exploration. This paper explores the potential for ballistic landing opportunities enabled by the natural dynamics found in binary asteroid systems. The dynamics near a binary asteroid are modeled by means of the circular restricted three-body problem, which provides a reasonable representation of a standard binary system. Natural landing trajectories are then sought that allow for a deployment from the exterior region and touchdown with minimum local-vertical velocity. The results show that, although landing on the main body of the system would require an effective landing system capable to dissipate excess of energy and avoid bouncing off the asteroid, the smaller companion offers the prospect of simple ballistic landing opportunities.

Fast development of CubeSat technology now enables the first interplanetary missions. The potential application of CubeSats to flyby near-Earth asteroids is explored in this paper in consideration of CubeSats' limited propulsive capabilities and systems constraints. Low-energy asteroid flyby trajectories are designed assuming a CubeSat is initially parked around to the Sun-Earth Lagrange points. High-impulse and low-thrust trajectories with realistic thrusting models are computed first in the Circular Restricted Three-Body Problem (CR3BP), and then in a high-fidelity ephemeris model. Analysis in the ephemeris model is used to confirm that trajectories computed in the CR3BP model also exist in a more realistic dynamical model, and to verify the validity of the results obtained in CR3BP analysis. A catalogue of asteroid flyby opportunities between years 2019 and 2030 is provided, with 80 m/s of available ΔV and departure from halo orbits around the first and second Sun-Earth Lagrange points (of similar size to those typically used by scientific missions). Results show that the CR3BP model can serve as an effective tool to identify reachable asteroids and can provide an initial estimation of the ΔV cost in the ephemeris model (with ±15 m/s accuracy). An impulsive maneuver model can also provide an accurate estimation of the ΔV requirement for a CubeSat equipped with a high-impulse thruster (with 4 m/s accuracy), even if its thrust magnitude is small and requires duty cycling; low-thrust ΔV requirements, however, may differ significantly from the impulsive results (±15 m/s)., Funding was provided by Cranfield University’s European Partnership Programme (2016–2017, United Kingdom).

This paper presents a three-dimensional semi-analytical formulation to model the third-body effect on a massless particle in the circular restricted three-body problem dynamical regime. The final expressions are obtained by means of the classical Lagrange planetary equations, by considering as small parameter of the perturbative approach the mass parameter of the system. The variations of the Keplerian orbital elements of the massless particle over one orbital period are computed as a function of the relative phasing between the massless particle and the secondary, and the overall behavior is described in terms of kick maps. Several applications to mission design are introduced, and the accuracy provided by the methodology is discussed on the basis of different initial conditions and physical systems.

The design of a space trajectory is strongly linked to the gravitational and non-gravitational environment and the dynamical frameworks required to model it. These dynamical models may range from low to high fidelity, with corresponding computational costs. This paper proposes a multifidelity approach for the computation of nearly resonant trajectories with the Earth. This framework is used to compute trajectories for the capture of near-Earth asteroids into libration point orbits of the Sun – Earth system. The transfer is first computed in a suitable low-fidelity model, the Keplerian map, and a multifidelity approach is subsequently used to refine the solution from an impulsive approximation into a low-thrust transfer in the circular restricted three-bodyproblem. The entire trajectory follows a nearly resonant motion with the Earth, lasting less than two synodic periods; starting when the retrieval spacecraft attaches itself to the asteroid, they will encounter the Earth twice, being captured into the target orbit at the end of the second encounter. A velocity change maneuver is carried out at the beginning of the motion, so that the first encounter with the Earth provides a gravitational perturbation resulting on a reduction of overall propellant costs of the transfer. The developed framework is very flexible in terms of the desired accuracy and allows for the low computational cost exploration of a vast number of possible trajectories. The obtained low-thrust transfers yield, for six asteroids, a much higher retrievable mass in comparison with direct capture trajectories, which do not undertake Earth-resonant encounters.

CASTAway is a mission concept to explore our Solar System's main asteroid belt. Asteroids and comets provide a window into the formation and evolution of our Solar System and the composition of these objects can be inferred from space-based remote sensing using spectroscopic techniques. Variations in composition across the asteroid populations provide a tracer for the dynamical evolution of the Solar System. The mission combines a long-range (point source) telescopic survey of over 10,000 objects, targeted close encounters with 10 to 20 asteroids and serendipitous searches to constrain the distribution of smaller (e.g. 10 m) size objects into a single concept. With a carefully targeted trajectory that loops through the asteroid belt, CASTAway would provide a comprehensive survey of the main belt at multiple scales. The scientific payload comprises a 50 cm diameter telescope that includes an integrated low-resolution (R = 30 to 100) spectrometer and visible context imager, a thermal (e.g. 6 to 16 microns) imager for use during the flybys, and modified star tracker cameras to detect small (approx. 10 m) asteroids. The CASTAway spacecraft and payload have high levels of technology readiness and are designed to fit within the programmatic and cost caps for a European Space Agency medium class mission, whilst delivering a significant increase in knowledge of our Solar System., 40 pages, accepted by Advances in Space Research October 2017

In response to the current interest in CubeSats and potential applications for planetary exploration, this work studies the feasibility of using autonomous CubeSats to flyby near-Earth asteroids. Considering the limited performance of current propulsion systems for CubeSats, low-energy (impulsive and low-thrust) trajectories are designed to encounter near-Earth asteroids in the medium-fidelity Circular Restricted Three-Body Problem, and their existence in a high-fidelity ephemeris model is also verified. The use of large ground antennas for deep-space communications might represent a major portion of CubeSat mission budgets, and thus the feasibility of performing optical navigation to autonomously estimate and correct the trajectory of the CubeSat is also evaluated through Monte Carlo simulations. Preliminary results show that approximately 4 asteroids per year could be reached by a 3U CubeSat if deployed around the first or second Sun-Earth Lagrange points. According to the limited performance of current CubeSat components, flyby altitudes of the order of 100–500 kilometers are determined possible using only observations of the Sun and of the target asteroid for autonomous navigation. Keywords: Interplanetary CubeSats; near-Earth asteroids; trajectory design; autonomous navigation

An increasing number of interplanetary missions are aiming at visiting asteroids and other small bodies, since these may provide clues to understand the formation and evolution of our Solar System. CubeSats allow a low-cost solution to land on these objects, as opposed to risking a much more expensive mothership. The weak gravitational field on these small bodies may also enable the possibility of simply dropping a CubeSat from afar (i.e. ballistic landing). However, ballistic landing of an unpowered spacecraft may be feasible solely within certain asteroid locations, and only if sufficient energy can be dissipated at touchdown. If such conditions are not met, the spacecraft will rebound off the surface. It is likely that the necessary energy dissipation may already occur naturally due to energy loss expected through the deformation of the regolith during touchdown. Indeed, previous low-velocity impact experiments in microgravity seem to indicate that this is exactly the case. However, data from past asteroid touchdowns, Hayabusa and Philae, indicate the contrary. This paper describes the development of an experiment which aims to bridge the aforementioned disagreement between mission data and microgravity experiment; to understand the behaviour of CubeSat landing on asteroids. The experiment will also test a novel damping system made by origami paper that should increase the dissipated energy at touchdown. The experiment will take place at the ZARM Drop Tower in Bremen in November 2018. With the constraint of 5 drops, the experiment will measure the coefficient of restitution during an available time window of 4.74 seconds of microgravity conditions. A 1UCubeSat mock-up will be used to represent a future asteroid lander. In order to mimic the landing of actual missions, the mock-up will have a mass of about 4 kg and it will be given a velocity of 15 cm/s with minimal rotation. This will be achieved by an automated spring-based release mechanism. An asteroid simulant, ESA03-A KM Bentonite Granules will be used to replicate an asteroid mechanical properties at the surface. This paper reviews the final design and the engineering challenges of the experiment.

In simple terms, an asteroid retrieval mission envisages a spacecraft that rendezvous with an asteroid, lassos it and hauls it back to the Earth's neighborhood. Speculative engineering studies for such an ambitious mission concept appeared in scientific literature at the beginning of the space age. This early work employed a two-body dynamical framework to estimate the Δv costs entailed with hauling an entire asteroid back to Earth. The concept however has experienced a revival in recent years, stimulated by the inclusion of a plan to retrieve a small asteroid in NASA's 2014 budget. This later batch of work is well aware of technological limitations, and thus envisages a much more level-headed space system, capable of delivering only the most minimal change of linear momentum to the asteroid. As a consequence, the design of retrieval trajectories has evolved into strategies to take full advantage of low energy transfer opportunities, which must carefully account for the simultaneous gravitational interactions of the Sun, Earth, and Moon. The paper reviews the published literature up to date, and provides a short literature survey on the historical evolution of the concept. This literature survey is particularly focused on the design of asteroid retrieval trajectories, and thus the paper provides a comprehensive account of: the endgame strategies considered so far, the different dynamical models and the trajectory design methodologies.

Small body missions can significantly benefit from deploying small landing systems onto the surface of the visited object. Despite the potential benefit that they may bring, deployments of landers in small body environments may entail significant mission design challenges. This paper thus addresses the potential of ballistic landing opportunities in binary asteroid moons from a mission design perspective, particularly focusing on reliability aspects of the trajectories. Two binaries that were previously identified as target bodies in several missions/proposals, Didymos and 1996 FG3, are considered in this paper. The dynamics near them are modeled by means of the Circular Restricted Three Body Problem (CR3BP), which provides a reasonable representation of a standard binary system. Natural landing trajectories that allow both minimum-velocity local-vertical touchdown and deployment from a safe distance are investigated. Coefficient of restitution values are used as a design parameter to compute the first touchdown speeds that ensure sufficient reliability of landing trajectories. A simple reliability index, which is derived via uncertainty ellipsoid from covariance analysis, is introduced to create a global reliability map across the asteroid surfaces. Assuming 3σ deployment errors on the order of 90 m and 2 cm/s, the results show that ballistic landing operations are likely to be successful for larger binary moons if the deployments target near equatorial regions within longitude range 320o–20°. It has also been shown that the deployments to smaller binary moons may require higher accuracy in navigation and deployment systems in their mothership, and/or closer deployment distances.

In recent years, space agencies have begun to seriously consider launching demonstration missions to test some of the asteroid orbital deflection technologies and methods that have been studied and discussed in the scientific literature. Consequently, several mission studies have already been carried out. This paper attempts to gain new insights into the target selection process by analyzing the orbital evolution of a large set of notional accessible asteroids that cover all types of Near Earth Object families. The evolution of their unperturbed orbits and their anthropogenically modified trajectories was compared, and a measure of the resilience of a given orbit to anthropogenic manipulation was taken (i.e., orbital innocuity). The results show that pruning criteria such as considering only Amor objects (i.e., non-Earth-crossers) reduce unnecessarily the population of potential suitable targets and that within large regions of Earth-crossing orbital space asteroids can be found that are both accessible and safe to manipulate from the standpoint of the Earth impact risk.

This paper describes a robust methodology to design Earth-resonant asteroid capture trajectories leading to Libration Point Orbits (LPOs). These trajectories consider two impulsive manoeuvres; one occurring before the first Earth encounter and a final one that inserts the asteroid into a stable hyperbolic manifold trajectory leading to an LPO of the Sun-Earth system. The first manoeuvre is key to exploit the chaotic perturbative effects of the Earth and obtain important reductions on the cost of inserting the asteroid into a manifold trajectory. The perturbative effects caused by the Earth are here modelled by means of a Keplerian Map approximation, and these are a posteriori compared with the dynamics of the Circular Restricted Three-Body Problem. Savings in the order of 50% of total Δv are computed for four different asteroids.

This study is inspired by the Laplace orbit plane property of requiring minimal station-keeping and therefore its potential use for long-term geosynchronous synthetic aperture radar (GEOSAR) imaging. A set of GEOSAR user requirements is presented and analysed to identify significant mission requirements. Imaging geometry and power demand are assessed as a function of relative satellite speed (which is determined largely by choice of orbit inclination). Estimates of the cost of station-keeping as a function of orbit inclination and right ascension are presented to compare the benefits of different orbit choices. The conclusion is that the Laplace plane (and more generally, orbits with inclinations up to 15\degree) are attractive choices for GEOSAR.

Given a limited warning time, an asteroid impact mitigation campaign would hinge on uncertainty-based information consisting of remote observational data of the identified Earth-threatening object, general knowledge of near-Earth asteroids (NEAs), and engineering judgment Due to these ambiguities, the campaign credibility could be profoundly compromised. It is therefore imperative to comprehensively evaluate the inherent uncertainty in deflection and plan the campaign accordingly to ensure successful mitigation. This research demonstrates dual-deflection mitigation campaigns consisting of primary (instantaneous/quasi-instantaneous) and secondary (slow-push) deflection missions, where both deflection efficiency and campaign credibility are taken into account The results of the dual-deflection campaign analysis show that there are trade-offs between the competing aspects: the launch cost, mission duration, deflection distance, and the confidence in successful deflection. The design approach is found to be useful for multi-deflection campaign planning, allowing us to select the best possible combination of missions from a catalogue of campaign options, without compromising the campaign credibility.

During the early stages of NEO mitigation campaign planning, it is indispensable to characterise the hazardous object. However, exhaustive characterisation in close proximity to the object may not always be feasible when the lead time is in the order of a few years to a decade, hence causing uncertainty in its physical and compositional properties. This study aims to evaluate the reliability and robustness of different deflection methodologies subject to uncertainty in the asteroid composition. The Evidence Theory is used to quantify epistemic uncertainty in the asteroid properties. The kinetic impact, nuclear intercept, and the solar sublimation [mitigation approaches] are applied to a set of virtual Earth-threatening asteroids with different Keplerian elements, sizes (30–150 m), and mission lead times (5–18 years) with the goal of a minimum 2½ Earth-radii deviation distance. A typical S-type rubble pile configuration is used as the baseline asteroid composition for the study.

This paper examines the concept of a Sun-pointing elliptical Earth ring comprised of dust grains to offset global warming. A new family of non-Keplerian periodic orbits, under the effects of solar radiation pressure and the Earth's J(2) oblateness perturbation, is used to increase the lifetime of the passive cloud of particles and, thus, increase the efficiency of this geoengineering strategy. An analytical model is used to predict the orbit evolution of the dust ring due to solar-radiation pressure and the J(2) effect. The attenuation of the solar radiation can then be calculated from the ring model. In comparison to circular orbits, eccentric orbits yield a more stable environment for small grain sizes and therefore achieve higher efficiencies when the orbit decay of the material is considered. Moreover, the novel orbital dynamics experienced by high area-to-mass ratio objects, influenced by solar radiation pressure and the J(2) effect, ensure the ring will maintain a permanent heliotropic shape, with dust spending the largest portion of time on the Sun facing side of the orbit. It is envisaged that small dust grains can be released from a circular generator orbit with an initial impulse to enter an eccentric orbit with Sun-facing apogee. Finally, a lowest estimate of 1 x 10(12) kg of material is computed as the total mass required to offset the effects of global warming.

Accepted: 2016-05-26, 資料番号: SA1160099000

This paper presents a novel method of space-based geoengineering which uses the mass of a captured near Earth asteroid to gravitationally anchor a cloud of unprocessed dust in the vicinity of the L1 position to reduce the level of solar insolation at Earth. It has subsequently been shown that a cloud contained within the zero-velocity curve of the largest near Earth asteroid, Ganymed, can lead to an insolation reduction of 6.58% on Earth, which is significantly larger than the 1.7% required to offset a 2 °C increase in mean global temperature. The masses of the next largest near Earth asteroids are found to be too small to achieve the required level of insolation reduction, however, they are significant enough to be used as part of a portfolio of geoengineering schemes.

In this paper a method of geoengineering is proposed involving clouds of dust placed in the vicinity of the L1 point as an alternative to the use of thin film reflectors. The aim of this scheme is to reduce the manufacturing requirement for space-based geoengineering. It has been concluded that the mass requirement for a cloud placed at the classical L1 point, to create an average solar insolation reduction of 1.7%, is 7.60 × 1010 kg yr−1 whilst a cloud placed at a displaced equilibrium point created by the inclusion of the effect of solar radiation pressure is 1.87 × 1010 kg yr−1. These mass ejection rates are considerably less than the mass required in other unprocessed dust cloud methods proposed and are comparable to thin film reflector geoengineering requirements. Importantly, unprocessed dust sourced in-situ is seen as an attractive scheme compared to highly engineered thin film reflectors. It is envisaged that the required mass of dust can be extracted from captured near Earth asteroids, whilst stabilised in the required position using the impulse provided by solar collectors or mass drivers used to eject material from the asteroid surface.

The asteroid and cometary impact hazard has long been recognised as an important issue requiring risk assessment and contingency planning. At the same time asteroids have also been acknowledged as possible sources of raw materials for future large-scale space engineering ventures. This paper explores possible synergies between these two apparently opposed views; planetary protection and space resource exploitation. In particular, the paper assumes a 5 tonne low-thrust spacecraft as a baseline for asteroid deflection and capture (or resource transport) missions. The system is assumed to land on the asteroid and provide a continuous thrust able to modify the orbit of the asteroid according to the mission objective. The paper analyses the capability of such a near-term system to provide both planetary protection and asteroid resources to Earth. Results show that a 5 tonne spacecraft could provide a high level of protection for modest impact hazards: airburst and local damage events (caused by 15–170 m diameter objects). At the same time, the same spacecraft could also be used to transport to bound Earth orbits significant quantities of material through judicious use of orbital dynamics and passively safe aero-capture manoeuvres or low energy ballistic capture. As will be shown, a 5 tonne low-thrust spacecraft could potentially transport between 12 and 350 times its own mass of asteroid resources by means of ballistic capture or aero-capture trajectories that pose very low dynamical pressures on the object.

The fascinating idea of shepherding asteroids for science and resource utilization is being considered as a credible concept in a not too distant future. Past studies identified asteroids which could be efficiently injected into manifolds which wind onto periodic orbits around collinear Lagrangian points of the Sun-Earth system. However, the trajectories are unstable, and errors in the capture maneuver would lead to complete mission failure, with potential danger of collision with the Earth, if uncontrolled. This paper investigates the controllability of some asteroids along the transfers and the periodic orbits, assuming the use of a solar-electric low-thrust system shepherding the asteroid. Firstly, an analytical approach is introduced to estimate the stability of the trajectories from a dynamical point of view; then, a numerical control scheme based on a linear quadratic regulator is proposed, where the gains are optimized for each trajectory through a genetic algorithm. A stochastic simulation with a Monte Carlo approach is used to account for different perturbed initial conditions and the epistemic uncertainty on the asteroid mass. Results show that only a small subset of the considered combinations of trajectories/asteroids are reliably controllable, and therefore controllability must be taken into account in the selection of potential targets.

In this paper, a method to capture near-Earth objects (NEOs) incorporating low-thrust propulsion into the invariant manifolds technique is investigated. Assuming that a tugboat-spacecraft is in a rendez-vous condition with the candidate asteroid, the aim is to take the joint spacecraft-asteroid system to a selected periodic orbit of the Sun-Earth restricted three-body system: the orbit can be either a libration point periodic orbit (LPO) or a distant prograde periodic orbit (DPO) around the Earth. In detail, low-thrust propulsion is used to bring the joint spacecraft-asteroid system from the initial condition to a point belonging to the stable manifold associated to the final periodic orbit: from here onward, thanks to the intrinsic dynamics of the physical model adopted, the flight is purely ballistic. Dedicated guided and capture sets are introduced to exploit the combined use of low-thrust propulsion with stable manifolds trajectories, aiming at defining feasible first guess solutions. Then, an optimal control problem is formulated to refine and improve them. This approach enables a new class of missions, whose solutions are not obtainable neither through the patched-conics method nor through the classic invariant manifolds technique.

Any envisioned future for space exploration involves both a growth in large space structures and a human presence in space. Some possible examples of future space endeavours are large space solar power satellites, space tourism or more visionary human space settlements. This, of course, implies a much larger mass of material in-use in space, for both structural mass and life support. The traditional approach to deliver material into orbit has always been to overcome the Earth’s gravity well, which is, arguably, not the most effective means if we bear in mind that the energy cost to reach low Earth orbit (LEO) is already “half-way to anywhere”.[“Once you get to Earth orbit, you’re halfway to anywhere in the solar system."-Robert A. Heinlein].

Asteroids and comets are of strategic importance for science in an effort to understand the formation, evolution and composition of the Solar System. Near-Earth Objects (NEOs) are of particular interest because of their accessibility from Earth, but also because of their speculated wealth of material resources. The exploitation of these resources has long been discussed as a means to lower the cost of future space endeavours. In this paper, we consider the currently known NEO population and define a family of so-called Easily Retrievable Objects (EROs), objects that can be transported from accessible heliocentric orbits into the Earth's neighbourhood at affordable costs. The asteroid retrieval transfers are sought from the continuum of low energy transfers enabled by the dynamics of invariant manifolds; specifically, the retrieval transfers target planar, vertical Lyapunov and halo orbit families associated with the collinear equilibrium points of the Sun-Earth Circular Restricted Three Body problem. The judicious use of these dynamical features provides the best opportunity to find extremely low energy Earth transfers for asteroid material. A catalogue of asteroid retrieval candidates is then presented. Despite the highly incomplete census of very small asteroids, the ERO catalogue can already be populated with 12 different objects retrievable with less than 500 m/s of {\Delta}v. Moreover, the approach proposed represents a robust search and ranking methodology for future retrieval candidates that can be automatically applied to the growing survey of NEOs.

Most plausible futures for space exploration and exploitation require a large mass in Earth orbit. Delivering this mass requires overcoming the Earth's natural gravity well, which imposes a distinct obstacle to any future space venture. An alternative solution is to search for more accessible resources elsewhere. In particular, this paper examines the possibility of future utilisation of near Earth asteroid resources. The accessibility of asteroid material can be estimated by analysing the volume of Keplerian orbital element space from which Earth can be reached under a certain energy threshold and then by mapping this analysis onto an existing statistical near Earth objects (NEO) model. Earth is reached through orbital transfers defined by a series of impulsive manoeuvres and computed using the patched-conic approximation. The NEO model allows an estimation of the probability of finding an object that could be transferred with a given Δv budget. For the first time, a resource map provides a realistic assessment of the mass of material resources in near Earth space as a function of energy investment. The results show that there is a considerable mass of resources that can be accessed and exploited at relatively low levels of energy. More importantly, asteroid resources can be accessed with an entire spectrum of levels of energy, unlike other more massive bodies such as the Earth or Moon, which require a minimum energy threshold implicit in their gravity well. With this resource map, the total change of velocity required to capture an asteroid, or transfer its resources to Earth, can be estimated as a function of object size. Thus, realistic examples of asteroid resource utilisation can be provided.

Most future concepts for exploration and exploitation of space require a large initial mass in low Earth orbit. Delivering this mass requires overcoming Earth's natural gravity well, which imposes a distinct obstacle to space-faring. An alternative for future space progress is to search for resources in-situ among the near Earth asteroid population. This paper examines the scenario of future utilization of asteroid resources. The near Earth asteroid resources that could be transferred to a bound Earth orbit are determined by integrating the probability of finding asteroids inside the Keplerian orbital element space of the set of transfers with an specific energy smaller than a given threshold. Transfers are defined by a series of impulsive maneuvers and computed using the patched-conic approximation. The results show that even moderately low energy transfers enable access to a large mass of resources.

The consequences of the fragmentation of an Earth-threatening asteroid due to an attempted deflection are examined in this paper. The minimum required energy for a successful impulsive deflection of a threatening object is computed and compared to the energy required to break up a small size asteroid. The results show that the fragmentation of an asteroid that underwent an impulsive deflection, such as a kinetic impact or a nuclear explosion, is a very plausible event.Astatistical model is used to approximate the number and size of the fragments as well as the distribution of velocities at the instant after the deflection attempt takes place. This distribution of velocities is a function of the energy provided by the deflection attempt, whereas the number and size of the asteroidal fragments is a function of the size of the largest fragment. The model also takes into account the gravity forces that could lead to a reaggregation of the asteroid after fragmentation. The probability distribution of the pieces after the deflection is then propagated forward in time until the encounter with Earth. A probability damage factor (i.e., expected damage caused by a given size fragment multiplied by its impact probability) is then computed and analyzed for different plausible scenarios, characterized by different levels of deflection energies and lead times.

The fragmentation of an Earth threatening asteroid as a result of a hazard mitigation mission is examined in\ud this paper. The minimum required energy for a successful impulsive deflection of a threatening object is\ud computed and compared with the energy required to break-up a small size asteroid. The fragmentation of an asteroid that underwent an impulsive deflection such as a kinetic impact or a nuclear explosion is a very plausible outcome in the light of this work. Thus a model describing the stochastic evolution of the cloud of fragments is described. The stochasticity of the fragmentation is given by a Gaussian probability distribution that\ud describes the initial relative velocities of each fragment of the asteroid, while the size distribution is expressed\ud through a power law function. The fragmentation model is applied to Apophis as illustrative example. If a barely\ud catastrophic disruption (i.e. the largest fragment is half the size the original asteroid) occurs 10 to 20 years prior\ud to the Earth encounter only a reduction from 50% to 80% of the potential damage is achieve for the Apophis test\ud case.

Geosynchronous synthetic aperture radar (GEO SAR) promises novel imaging capabilities which complement low Earth orbit missions. Many configurations for GEO SAR have been studied (e.g. monostatic, bistatic, multistatic): this study considers use of Laplace plane orbits which potentially offer longer lifetimes. In the Laplace orbit plane gravitational perturbations cancel out which reduces orbit maintenance costs. Choosing a GEO Laplace plane orbit defines the semimajor axis, inclination (about 7.4°.) and right ascension: the mission designer is only free to choose eccentricity and argument of perigee. Velocity relative to Earth is moderately fast (~400 m s-1) so integration times needed are minutes to 10s of minutes for resolution of 10 - 50 m. Squint viewing supports more versatile coverage. The study proposes a baseline mission concept. Lifetime for a single satellite can be extended beyond the conventional 15 yr for geostationary comsats, and the optimal lifetime is probably in the range 20-30 yr. Advantages of the concept include (a) long lifetime and feasibility with current technology, (b) improved area coverage, and less demanding technology relative to quasi-geostationary GEO SAR, and (c) lower power and smaller antenna than high inclination GEO SAR.

In this paper a method to retrieve asteroids incorporating low-thrust propulsion into the invariant manifolds technique is investigated. Assuming that a tugboat-spacecraft is in a rendez-vous condition with the candidate Near Earth Object (NEO), the aim is to take the joint spacecraft-asteroid system to selected periodic orbits of the Earth–Moon restricted three-body system: the orbits can be either libration point periodic orbits (LPOs) or distant periodic orbits around the Moon, both prograde (DPOs) and retrograde (DROs). In detail, low-thrust propulsion is used to bring the joint spacecraft-asteroid system from the initial condition to a point belonging to the stable manifold associated to the final periodic orbit: from here onward, thanks to the intrinsic dynamics of the physical model adopted, the flight is purely ballistic. The idea is to couple together the Sun–Earth and the Earth–Moon models following the ”patched restricted three-body problems approximation”, therefore allowing the spacecraft-asteroid system to fly along the interplanetary manifold trajectories, explicitly exploiting the hyperbolic transit orbits flying by L1 and L2. Dedicated capture sets are introduced to exploit the combined use of low-thrust propulsion with stable manifolds trajectories, aiming at defining feasible first guess solutions. An optimal control problem is then formulated to refine them. This approach enables a new class of missions, whose solutions are not obtainable neither through the patched-conics method nor through the classic invariant manifolds technique.

Asteroid surface science provides the necessary “ground-truth” to validate and enhance remote sensing from orbiting spacecraft. Yet, due to uncertainties associated with the dynamical environment near asteroids, it is generally prudent for the main spacecraft to remain at a safe distance. Instead, small landers could be used much more daringly. This paper explores the potential for ballistic landing opportunities in binary asteroid systems. The dynamics near a binary asteroid are modelled by means of the Circular Restricted Three Body Problem, which provides a reasonable representation of a standard binary system. Natural landing trajectories are sought that allow for deployment from safe distances and touchdown with minimum local-vertical velocity. The necessary coefficient of restitution to ensure a successful landing and the effects of navigation and deployment errors are also analysed. Assuming deployment errors in the order of 10 meters and 1 cm/s (1-sigma), the results show that ballistic descent landing operations are likely to be successful if targeting near equatorial regions with longitude within 320o to 20o in the secondary of the binary system.