This paper presents the preliminary analysis of an in-orbit demonstration opportunity to test plu... more This paper presents the preliminary analysis of an in-orbit demonstration opportunity to test plume impingement as a viable means to change the attitude state of a space debris based on the Prisma and Picard missions. This technique has been proposed as part of the COBRA concept studied by ESA in collaboration with GMV, Politecnico di Milano and Thales-Alenia Space, as an active debris removal concept relying on the exhaust plume of a monopropellant chemical propulsion system as a means to impart momentum and ultimately modify the orbit of a space debris object in a contactless manner. The feasibility of the experiment is presented as well as its critical areas, no showstoppers are identified.
The paper presents different strategies to model the gravitational field in the vicinity of irreg... more The paper presents different strategies to model the gravitational field in the vicinity of irregular celestial bodies, such as asteroids and comets. The gravitational attraction of these irregular objects has been modeled, through accurate shape discretization, with a constant density polyhedron or an ensemble of point masses. In the latter case, an optimization algorithm to distribute the mass elements within the volume of the body has been developed. All the different modeling techniques are compared in order to highlight their advantages and drawbacks. In addition, an extensive analysis of the results is performed with the purpose to find the model that has an optimal balance between level of accuracy and required computational effort.
Recently, the development of dedicated numerical codes has pushed forward the study of N-body gra... more Recently, the development of dedicated numerical codes has pushed forward the study of N-body gravitational dynamics leading to better and wider understanding of processes involving the formation of natural bodies in the Solar System. A major branch includes the study of asteroid formation: evidence from recent studies and observations support the idea that small and medium size asteroids between 100 m and 100 km may be gravitational aggregates with no cohesive force other than gravity. This evidence implies that asteroid formation depends on gravitational interactions between different boulders and that asteroid aggregation processes can be naturally modeled with N-body numerical codes implementing gravitational interactions. This work presents a new implementation of a N-body numerical solver. The code is based on Chrono::Engine [1]. It handles the contact and collision of large numbers of complex-shaped objects, while simultaneously evaluating the effect of N to N gravitational interactions. A special case of study is considered, investigating the relative dynamics between the N bodies and highlighting favorable conditions for the formation of a stable gravitationally bound aggregate from a cloud of N boulders. The code is successfully validated for the case of study by comparing relevant results obtained for typical known dynamical scenarios. The outcome of the numerical simulations shows good agreement with theory and observation and suggests the ability of the developed code to predict natural aggregation phenomena.
One of the most important aspects when dealing with a Potentially Hazardous Object (PHO) is the a... more One of the most important aspects when dealing with a Potentially Hazardous Object (PHO) is the accurate determination of its dynamical state. In particular, the determination of orbital and rotational perturbations is important to propagate accurately the heliocentric orbital path of an asteroid or a comet, and to be more precise in the impact risk determination and related uncertainty containment. The paper discusses the analysis and study of the motion of an irregularly-shaped celestial body, with particular attention to its complex three-dimensional rotational dynamics: the rotation state, nutation and precession motions are considered while modelling. All perturbations, relevant to the case of study, are included in the dynamical model, from the classical to the more complex, such as the Solar Radiation Pressure (SRP), the third body gravitational effect (presence of the Sun), the YORP effect and the internal dissipation of energy. In addition, particular attention has been paid to accurately model the shape of the asteroid: simple spherical models demonstrated to possess low accuracy when the asteroid or the comet is not spherically shaped. Irregular shapes represent, indeed, one of the most important aspects to compute the disturbances affecting the dynamics of these objects. The study has been performed by considering different characteristic shapes for typical irregular bodies: from the quasispherical, to the dog-bone and the elongated shapes. The perturbations due to external sources are modelled numerically. The sources of disturbances are then ranked and different criteria to propagate rotational motion have been derived depending on the shape of the observed asteroid. Even if the simulation results have been verified on selected asteroids dynamics, the presented methods and approach apply to the dynamical propagation of any kind of asteroid or comet.
This paper presents a new environment to simulate close-proximity dynamics around rubble-pile ast... more This paper presents a new environment to simulate close-proximity dynamics around rubble-pile asteroids. The code provides methods for modeling the aster-oid's gravity field and surface through granular dynamics. It implements state-of-the-art techniques to model both gravity and contact interaction between particles: 1) mutual gravity as either direct N2 or Barnes-Hut GPU-parallel octree and 2) contact dynamics with a soft-body (force-based, smooth dynamics), hard-body (constraint-based, non-smooth dynamics), or hybrid (constraint-based with compliance and damping) approach. A very relevant feature of the code is its ability to handle complex-shaped rigid bodies and their full 6D motion. Examples of spacecraft close-proximity scenarios and their numerical simulations are shown.
Periodicity of motion around the collinear libration point associated with the Elliptic Restricte... more Periodicity of motion around the collinear libration point associated with the Elliptic Restricted Three-Body Problem is studied. A survey of periodic solutions in the Circular Restricted Three-Body Problem is presented considering both Sun–Earth and Earth–Moon systems. Halo, Lyapunov and Vertical families around L1, L2 and L3 points are investigated, and their orbital period ranges through the entire family are reported. Resonant motions within the orbit families in the circular problem are identified and selected as suitable initial guess to find periodic orbits in the elliptic problem, which are targeted using a differential correction algorithm. Periodic solutions found are cataloged depending on the number of revolutions around libration points. Geometry, dynamical behavior and stability properties of single-revolution orbits are shown, as well as double-, triple- and quadruple-revolution solutions.
The close-proximity exploration of small celestial bodies of our Solar System is the current fron... more The close-proximity exploration of small celestial bodies of our Solar System is the current frontier of space exploration. Trajectory design and exploitation of the natural dynamics around such bodies represents a very challenging astrodynamics problem, due to their weak and highly chaotic gravitational environment. The paper discusses design solutions for the ballistic landing of a small and passive probe, released to land on the smaller of a binary asteroid couple. The work is focused on the Asteroid Impact Mission (AIM) case study, although the methods and analyses presented are general and applicable to any binary asteroid scenario. The binary system is modeled using a shape-based three-body problem and three-body solutions are investigated within the Didymos binary system. Manifold dynamics near libration points associated to the asteroid three-body system are exploited to find low-energy and high-success landing trajectories. The validity of implemented approach and solutions found are discussed and results in terms of success rate and landing dispersion are shown.
The design of formations of spacecraft in a three-body environment represents one of the most pro... more The design of formations of spacecraft in a three-body environment represents one of the most promising challenges for future space missions. Two or more cooperating spacecraft can greatly answer some very complex mission goals, not achievable by a single spacecraft. The dynamical properties of a low acceleration environment such as the vicinity of libration points associated to a three-body system, can be effectively exploited to design spacecraft configurations able of satisfying tight relative position and velocity requirements. This work studies the evolution of an uncontrolled formation orbiting in the proximity of periodic orbits about collinear libration points under the Circular and Elliptic Restricted Three-Body Problems. A three spacecraft triangularly-shaped formation is assumed as a representative geometry to be investigated. The study identifies initial configurations that provide good performance in terms of formation keeping, and investigates key parameters that control the relative dynamics between the spacecraft within the three-body system. Formation keeping performance is quantified by monitoring shape and size changes of the triangular formation. The analysis has been performed under five degrees of freedom to define the geometry, the orientation and the location of the triangle in the synodic rotating frame.
The development of dedicated numerical codes has recently pushed forward the study of N-body grav... more The development of dedicated numerical codes has recently pushed forward the study of N-body gravitational dynamics, leading to a better and wider understanding of processes involving the formation of natural bodies in the Solar System. A major branch includes the study of asteroid formation: evidence from recent studies and observations support the idea that small and medium size asteroids between 100 m and 100 km may be gravitational aggregates with no cohesive force other than gravity. This evidence implies that asteroid formation depends on gravitational interactions between different boulders and that asteroid aggregation processes can be naturally modeled with N-body numerical codes implementing gravitational interactions. This work presents a new implementation of an Nbody numerical solver. The code is based on Chrono::Engine (2006). It handles the contact and collision of large numbers of complex-shaped objects, while simultaneously evaluating the effect of N to N gravitational interactions. A special case of study is considered, investigating the relative dynamics between the N bodies and highlighting favorable conditions for the formation of a stable gravitationally bound aggregate from a cloud of N boulders. The code is successfully validated for the case of study by comparing relevant results obtained for typical known dynamical scenarios. The outcome of the numerical simulations shows good agreement with theory and observation, and suggests the ability of the developed code to predict natural aggregation phenomena.
The paper presents a strategy for trajectory design in the proximity of a binary asteroid pair. A... more The paper presents a strategy for trajectory design in the proximity of a binary asteroid pair. A novel patched approach has been used to design trajectories in the binary system, which is modeled by means of two different three-body systems. The model introduces some degrees of freedom with respect to a classical two-body approach and it is intended to model to higher accuracy the peculiar dynamical properties of such irregular and low gravity field bodies, while keeping the advantages of having a full analytical formulation and low computational cost required. The neighborhood of the asteroid couple is split into two regions of influence where two different three-body problems describe the dynamics of the spacecraft. These regions have been identified by introducing the concept of surface of equivalence (SOE), a three-dimensional surface that serves as boundary between the regions of influence of each dynamical model. A case of study is presented, in terms of potential scenario that may benefit of such an approach in solving its mission analysis. Cost-effective solutions to land a vehicle on the surface of a low gravity body are selected by generating Poincaré maps on the SOE, seeking intersections between stable and unstable manifolds of the two patched three-body systems.
The exploration of NEA (Near Earth Asteroids) is characterized by many problematics such as colli... more The exploration of NEA (Near Earth Asteroids) is characterized by many problematics such as collision risks, irregular gravity fields and, in case of binary systems, multibody gravity perturbations, whose negative effects on mission design could be mitigated by the exploitation of multiple spacecraft in formation, with lower weights, dimensions and costs. Nanosatellite fully meet these needs, however, the poor control capabilities, and the strict requirements on relative dynamics to ensure the same performances of a single heavy spacecraft, request an efficient strategy to determine the suitable trajectories in this chaotic environment. The paper proposes a simple technique, based on orbit sampling and local optimization, to define a set of suitable configurations for a two-nanosatellite formation. After a quick review on the orbits determination and combination in binary asteroid environments, and the presentation of the objectives derived from the conceptual mission AIM (Asteroid Impact Mission), the local optimization algorithm is explained, paying attention to the selection of the method and its modification to best adapt to the specific problem. Then, results are presented, showing the strength and weakness points of the overall procedure, for the definition of future improvements.
Over the past years significant evidence has shown that asteroids with dimensions exceeding few h... more Over the past years significant evidence has shown that asteroids with dimensions exceeding few hundreds of meters are gravitational aggregates of smaller bodies bound together only by gravitational forces. 1 The study of such complex bodies is motivated by the recent efforts by space agencies, trying to intercept or redirect near-Earth asteroids (DART, ARM missions), as well as the ever-expanding possibilities of reaching further objects such as Jupiter trojans. The development of models for orbital dynamics about gravitational aggregates, complex gravity fields around irregular objects and collisions between orbiters and asteroids is therefore required. This work presents a new modeling and implementation of a N-body numerical solver using a GPU-parallel Barnes-Hut implementation to evaluate the effects of gravitational interactions and the Chrono::Engine multi-physics simulation engine to simulate collisions between bodies and integrate the dynamics of the problem. 2 The code is successfully validated for different cases of study based on previous works by P. Michel and P. Tanga concerning collisional disruption and gravitational re-accumulation leading to formation of asteroid families in different energetic regimes and by comparing relevant results obtained for well-known dy-namical scenarios. 3–5 Results of numerical simulations show good agreement with established theories and observations and confirm the ability of the developed code to predict natural aggregation phenomena.
In the recent years, nanosatellites based missions are becoming of great interest in the space pr... more In the recent years, nanosatellites based missions are becoming of great interest in the space programs panorama, since they offer the possibility of a wider hardware distribution, costs reduction and losses mitigation in case of failures. A distribution of nanosatellites would also grant a wide coverage of the space region under study, allowing better mapping or sampling, together with an enhancement of communications thanks to a distributed links net. The achievement of these objectives requires, however, the distribution of the spacecraft to have peculiar configuration geometries or to satisfy particular constraints, therefore deep study on the formation flying strategies has to be conducted. With reference to the future mission AIDA (Asteroid Impact and Deflection Assessment) and the target binary asteroid system " Dydimos " , the present study shows results of the research on periodic orbits in the Circular Restricted Three Body Problem frame, applied to irregular gravitational fields generated by the asteroids, to provide a set of suitable trajectories to maintain a formation of nanosatellites. After a general overview on the algorithms and computational strategies adopted, various orbit families in the asteroids environment are shown, highlighting differences with their equivalent in the point masses model. Then, configurations of a two satellites formation are searched to maximize the shape maintenance while satisfying the mission requirements. Finally, suggestions of possible improvements of the research are given.
The Asteroid Impact & Deflection Assessment (AIDA) mission is an international collaboration of E... more The Asteroid Impact & Deflection Assessment (AIDA) mission is an international collaboration of ESA and NASA, with the primary goals to test the ability to perform a spacecraft impact on a near-Earth asteroid and to measure and characterize the deflection caused by the impact. The ESA-led Asteroid Impact Mission (AIM) is to be designed on a low-cost approach and to be launched in 2020. Its primary objective is to characterise the binary asteroid system 65803 Didymos (1996 GT) and then to assess the consequences of an impact from a NASA provided spacecraft named DART (Double Asteroid Redirection Test) on the secondary. Prior to the arrival of DART, AIM is planned to rendezvous with the asteroid system in mid-2022. On arrival, AIM would conduct observations that can be used to complement and prepare for the DART impact and perform technology demonstration. In addition, it is planned to release a number of CubeSat opportunity-payload and place the MASCOT-2 lander on the surface of the secondary asteroid. Further, a demonstration of deep space optical communications is planned. AIM is currently studied in the scope of a Phase B1 under ESA contract by two consortia, one of those being led by OHB System. This paper presents OHB " s current mission and asteroid operations strategy, addressing mission design and operational challenges. The tight schedule (launch in 2020) and the low cost approach for spacecraft design and operations are challenging, especially in context of the high complexity and performance requirements connected to deep space mission operations and navigation. Special focus is therefore placed on asteroid local operations, the planned payload operations, the deployment of MASCOT-2 to the surface of the secondary asteroid in the binary system, the navigation strategy of AIM, and how OHB plans to overcome the challenges posed by this unique mission scenario.
The Asteroid Impact Mission (AIM) is an ESA mission whose goal is the exploration and study of bi... more The Asteroid Impact Mission (AIM) is an ESA mission whose goal is the exploration and study of binary asteroid 65803 Didymos. AIM is planned to be the first spacecraft to rendezvous with a binary asteroid: its mission objectives include the highly relevant scientific return of the exploration as well as innovative technological demonstrations. The paper presents some updates on the ongoing design of the mission. Each phase of the operative life of AIM spacecraft is detailed with information and results on the solutions adopted for Mission Analysis design and on the strategies to suitably operate payloads. The work presented in this paper has been performed by the authors under ESA contract within the phase A design of AIM mission.
The Asteroid Impact Mission (AIM) includes among its primary objectives the release of a lander (... more The Asteroid Impact Mission (AIM) includes among its primary objectives the release of a lander (MASCOT-2) on the surface of the smaller asteroid of binary couple 65803 Didy-mos. The work here presented is performed under ESA contract , in the frame of phase A mission design of AIM spacecraft. The paper focuses on the landing-related part of the design and presents the ongoing work concerning the release strategy adopted to fulfill mission design requirements. The dynamics of the spacecraft are modeled using the most up-to-date gravity model of Didymos system, based on shape models of the two asteroids. Descent trajectories are selected by exploiting manifold dynamics associated to the peculiar three-body environment in the proximity of Didymos.
The Asteroid Impact Mission (AIM) is a European mission aimed at the exploration of the binary as... more The Asteroid Impact Mission (AIM) is a European mission aimed at the exploration of the binary asteroid 65803 Didymos. Among its mission objectives, AIM is planned to release a small and passive probe, called MASCOT-2, to land on the smallest asteroid of the binary couple. The paper presents the modeling strategy adopted to support the design of MASCOT-2 release. The modeling assumptions regarding the dynamical environment of such binary asteroid are discussed. The gravity field around the couple is modeled using shape-based models of the asteroids. A suitable model of the asteroid's surface is used to properly simulate the local interaction between the probe and the soil at touch down. Uncertainties regarding the release accuracy are modeled and results related to the AIM scenario are presented in terms of successful landing probability and final position of the lander at rest.
This paper presents the preliminary analysis of an in-orbit demonstration opportunity to test plu... more This paper presents the preliminary analysis of an in-orbit demonstration opportunity to test plume impingement as a viable means to change the attitude state of a space debris based on the Prisma and Picard missions. This technique has been proposed as part of the COBRA concept studied by ESA in collaboration with GMV, Politecnico di Milano and Thales-Alenia Space, as an active debris removal concept relying on the exhaust plume of a monopropellant chemical propulsion system as a means to impart momentum and ultimately modify the orbit of a space debris object in a contactless manner. The feasibility of the experiment is presented as well as its critical areas, no showstoppers are identified.
The paper presents different strategies to model the gravitational field in the vicinity of irreg... more The paper presents different strategies to model the gravitational field in the vicinity of irregular celestial bodies, such as asteroids and comets. The gravitational attraction of these irregular objects has been modeled, through accurate shape discretization, with a constant density polyhedron or an ensemble of point masses. In the latter case, an optimization algorithm to distribute the mass elements within the volume of the body has been developed. All the different modeling techniques are compared in order to highlight their advantages and drawbacks. In addition, an extensive analysis of the results is performed with the purpose to find the model that has an optimal balance between level of accuracy and required computational effort.
Recently, the development of dedicated numerical codes has pushed forward the study of N-body gra... more Recently, the development of dedicated numerical codes has pushed forward the study of N-body gravitational dynamics leading to better and wider understanding of processes involving the formation of natural bodies in the Solar System. A major branch includes the study of asteroid formation: evidence from recent studies and observations support the idea that small and medium size asteroids between 100 m and 100 km may be gravitational aggregates with no cohesive force other than gravity. This evidence implies that asteroid formation depends on gravitational interactions between different boulders and that asteroid aggregation processes can be naturally modeled with N-body numerical codes implementing gravitational interactions. This work presents a new implementation of a N-body numerical solver. The code is based on Chrono::Engine [1]. It handles the contact and collision of large numbers of complex-shaped objects, while simultaneously evaluating the effect of N to N gravitational interactions. A special case of study is considered, investigating the relative dynamics between the N bodies and highlighting favorable conditions for the formation of a stable gravitationally bound aggregate from a cloud of N boulders. The code is successfully validated for the case of study by comparing relevant results obtained for typical known dynamical scenarios. The outcome of the numerical simulations shows good agreement with theory and observation and suggests the ability of the developed code to predict natural aggregation phenomena.
One of the most important aspects when dealing with a Potentially Hazardous Object (PHO) is the a... more One of the most important aspects when dealing with a Potentially Hazardous Object (PHO) is the accurate determination of its dynamical state. In particular, the determination of orbital and rotational perturbations is important to propagate accurately the heliocentric orbital path of an asteroid or a comet, and to be more precise in the impact risk determination and related uncertainty containment. The paper discusses the analysis and study of the motion of an irregularly-shaped celestial body, with particular attention to its complex three-dimensional rotational dynamics: the rotation state, nutation and precession motions are considered while modelling. All perturbations, relevant to the case of study, are included in the dynamical model, from the classical to the more complex, such as the Solar Radiation Pressure (SRP), the third body gravitational effect (presence of the Sun), the YORP effect and the internal dissipation of energy. In addition, particular attention has been paid to accurately model the shape of the asteroid: simple spherical models demonstrated to possess low accuracy when the asteroid or the comet is not spherically shaped. Irregular shapes represent, indeed, one of the most important aspects to compute the disturbances affecting the dynamics of these objects. The study has been performed by considering different characteristic shapes for typical irregular bodies: from the quasispherical, to the dog-bone and the elongated shapes. The perturbations due to external sources are modelled numerically. The sources of disturbances are then ranked and different criteria to propagate rotational motion have been derived depending on the shape of the observed asteroid. Even if the simulation results have been verified on selected asteroids dynamics, the presented methods and approach apply to the dynamical propagation of any kind of asteroid or comet.
This paper presents a new environment to simulate close-proximity dynamics around rubble-pile ast... more This paper presents a new environment to simulate close-proximity dynamics around rubble-pile asteroids. The code provides methods for modeling the aster-oid's gravity field and surface through granular dynamics. It implements state-of-the-art techniques to model both gravity and contact interaction between particles: 1) mutual gravity as either direct N2 or Barnes-Hut GPU-parallel octree and 2) contact dynamics with a soft-body (force-based, smooth dynamics), hard-body (constraint-based, non-smooth dynamics), or hybrid (constraint-based with compliance and damping) approach. A very relevant feature of the code is its ability to handle complex-shaped rigid bodies and their full 6D motion. Examples of spacecraft close-proximity scenarios and their numerical simulations are shown.
Periodicity of motion around the collinear libration point associated with the Elliptic Restricte... more Periodicity of motion around the collinear libration point associated with the Elliptic Restricted Three-Body Problem is studied. A survey of periodic solutions in the Circular Restricted Three-Body Problem is presented considering both Sun–Earth and Earth–Moon systems. Halo, Lyapunov and Vertical families around L1, L2 and L3 points are investigated, and their orbital period ranges through the entire family are reported. Resonant motions within the orbit families in the circular problem are identified and selected as suitable initial guess to find periodic orbits in the elliptic problem, which are targeted using a differential correction algorithm. Periodic solutions found are cataloged depending on the number of revolutions around libration points. Geometry, dynamical behavior and stability properties of single-revolution orbits are shown, as well as double-, triple- and quadruple-revolution solutions.
The close-proximity exploration of small celestial bodies of our Solar System is the current fron... more The close-proximity exploration of small celestial bodies of our Solar System is the current frontier of space exploration. Trajectory design and exploitation of the natural dynamics around such bodies represents a very challenging astrodynamics problem, due to their weak and highly chaotic gravitational environment. The paper discusses design solutions for the ballistic landing of a small and passive probe, released to land on the smaller of a binary asteroid couple. The work is focused on the Asteroid Impact Mission (AIM) case study, although the methods and analyses presented are general and applicable to any binary asteroid scenario. The binary system is modeled using a shape-based three-body problem and three-body solutions are investigated within the Didymos binary system. Manifold dynamics near libration points associated to the asteroid three-body system are exploited to find low-energy and high-success landing trajectories. The validity of implemented approach and solutions found are discussed and results in terms of success rate and landing dispersion are shown.
The design of formations of spacecraft in a three-body environment represents one of the most pro... more The design of formations of spacecraft in a three-body environment represents one of the most promising challenges for future space missions. Two or more cooperating spacecraft can greatly answer some very complex mission goals, not achievable by a single spacecraft. The dynamical properties of a low acceleration environment such as the vicinity of libration points associated to a three-body system, can be effectively exploited to design spacecraft configurations able of satisfying tight relative position and velocity requirements. This work studies the evolution of an uncontrolled formation orbiting in the proximity of periodic orbits about collinear libration points under the Circular and Elliptic Restricted Three-Body Problems. A three spacecraft triangularly-shaped formation is assumed as a representative geometry to be investigated. The study identifies initial configurations that provide good performance in terms of formation keeping, and investigates key parameters that control the relative dynamics between the spacecraft within the three-body system. Formation keeping performance is quantified by monitoring shape and size changes of the triangular formation. The analysis has been performed under five degrees of freedom to define the geometry, the orientation and the location of the triangle in the synodic rotating frame.
The development of dedicated numerical codes has recently pushed forward the study of N-body grav... more The development of dedicated numerical codes has recently pushed forward the study of N-body gravitational dynamics, leading to a better and wider understanding of processes involving the formation of natural bodies in the Solar System. A major branch includes the study of asteroid formation: evidence from recent studies and observations support the idea that small and medium size asteroids between 100 m and 100 km may be gravitational aggregates with no cohesive force other than gravity. This evidence implies that asteroid formation depends on gravitational interactions between different boulders and that asteroid aggregation processes can be naturally modeled with N-body numerical codes implementing gravitational interactions. This work presents a new implementation of an Nbody numerical solver. The code is based on Chrono::Engine (2006). It handles the contact and collision of large numbers of complex-shaped objects, while simultaneously evaluating the effect of N to N gravitational interactions. A special case of study is considered, investigating the relative dynamics between the N bodies and highlighting favorable conditions for the formation of a stable gravitationally bound aggregate from a cloud of N boulders. The code is successfully validated for the case of study by comparing relevant results obtained for typical known dynamical scenarios. The outcome of the numerical simulations shows good agreement with theory and observation, and suggests the ability of the developed code to predict natural aggregation phenomena.
The paper presents a strategy for trajectory design in the proximity of a binary asteroid pair. A... more The paper presents a strategy for trajectory design in the proximity of a binary asteroid pair. A novel patched approach has been used to design trajectories in the binary system, which is modeled by means of two different three-body systems. The model introduces some degrees of freedom with respect to a classical two-body approach and it is intended to model to higher accuracy the peculiar dynamical properties of such irregular and low gravity field bodies, while keeping the advantages of having a full analytical formulation and low computational cost required. The neighborhood of the asteroid couple is split into two regions of influence where two different three-body problems describe the dynamics of the spacecraft. These regions have been identified by introducing the concept of surface of equivalence (SOE), a three-dimensional surface that serves as boundary between the regions of influence of each dynamical model. A case of study is presented, in terms of potential scenario that may benefit of such an approach in solving its mission analysis. Cost-effective solutions to land a vehicle on the surface of a low gravity body are selected by generating Poincaré maps on the SOE, seeking intersections between stable and unstable manifolds of the two patched three-body systems.
The exploration of NEA (Near Earth Asteroids) is characterized by many problematics such as colli... more The exploration of NEA (Near Earth Asteroids) is characterized by many problematics such as collision risks, irregular gravity fields and, in case of binary systems, multibody gravity perturbations, whose negative effects on mission design could be mitigated by the exploitation of multiple spacecraft in formation, with lower weights, dimensions and costs. Nanosatellite fully meet these needs, however, the poor control capabilities, and the strict requirements on relative dynamics to ensure the same performances of a single heavy spacecraft, request an efficient strategy to determine the suitable trajectories in this chaotic environment. The paper proposes a simple technique, based on orbit sampling and local optimization, to define a set of suitable configurations for a two-nanosatellite formation. After a quick review on the orbits determination and combination in binary asteroid environments, and the presentation of the objectives derived from the conceptual mission AIM (Asteroid Impact Mission), the local optimization algorithm is explained, paying attention to the selection of the method and its modification to best adapt to the specific problem. Then, results are presented, showing the strength and weakness points of the overall procedure, for the definition of future improvements.
Over the past years significant evidence has shown that asteroids with dimensions exceeding few h... more Over the past years significant evidence has shown that asteroids with dimensions exceeding few hundreds of meters are gravitational aggregates of smaller bodies bound together only by gravitational forces. 1 The study of such complex bodies is motivated by the recent efforts by space agencies, trying to intercept or redirect near-Earth asteroids (DART, ARM missions), as well as the ever-expanding possibilities of reaching further objects such as Jupiter trojans. The development of models for orbital dynamics about gravitational aggregates, complex gravity fields around irregular objects and collisions between orbiters and asteroids is therefore required. This work presents a new modeling and implementation of a N-body numerical solver using a GPU-parallel Barnes-Hut implementation to evaluate the effects of gravitational interactions and the Chrono::Engine multi-physics simulation engine to simulate collisions between bodies and integrate the dynamics of the problem. 2 The code is successfully validated for different cases of study based on previous works by P. Michel and P. Tanga concerning collisional disruption and gravitational re-accumulation leading to formation of asteroid families in different energetic regimes and by comparing relevant results obtained for well-known dy-namical scenarios. 3–5 Results of numerical simulations show good agreement with established theories and observations and confirm the ability of the developed code to predict natural aggregation phenomena.
In the recent years, nanosatellites based missions are becoming of great interest in the space pr... more In the recent years, nanosatellites based missions are becoming of great interest in the space programs panorama, since they offer the possibility of a wider hardware distribution, costs reduction and losses mitigation in case of failures. A distribution of nanosatellites would also grant a wide coverage of the space region under study, allowing better mapping or sampling, together with an enhancement of communications thanks to a distributed links net. The achievement of these objectives requires, however, the distribution of the spacecraft to have peculiar configuration geometries or to satisfy particular constraints, therefore deep study on the formation flying strategies has to be conducted. With reference to the future mission AIDA (Asteroid Impact and Deflection Assessment) and the target binary asteroid system " Dydimos " , the present study shows results of the research on periodic orbits in the Circular Restricted Three Body Problem frame, applied to irregular gravitational fields generated by the asteroids, to provide a set of suitable trajectories to maintain a formation of nanosatellites. After a general overview on the algorithms and computational strategies adopted, various orbit families in the asteroids environment are shown, highlighting differences with their equivalent in the point masses model. Then, configurations of a two satellites formation are searched to maximize the shape maintenance while satisfying the mission requirements. Finally, suggestions of possible improvements of the research are given.
The Asteroid Impact & Deflection Assessment (AIDA) mission is an international collaboration of E... more The Asteroid Impact & Deflection Assessment (AIDA) mission is an international collaboration of ESA and NASA, with the primary goals to test the ability to perform a spacecraft impact on a near-Earth asteroid and to measure and characterize the deflection caused by the impact. The ESA-led Asteroid Impact Mission (AIM) is to be designed on a low-cost approach and to be launched in 2020. Its primary objective is to characterise the binary asteroid system 65803 Didymos (1996 GT) and then to assess the consequences of an impact from a NASA provided spacecraft named DART (Double Asteroid Redirection Test) on the secondary. Prior to the arrival of DART, AIM is planned to rendezvous with the asteroid system in mid-2022. On arrival, AIM would conduct observations that can be used to complement and prepare for the DART impact and perform technology demonstration. In addition, it is planned to release a number of CubeSat opportunity-payload and place the MASCOT-2 lander on the surface of the secondary asteroid. Further, a demonstration of deep space optical communications is planned. AIM is currently studied in the scope of a Phase B1 under ESA contract by two consortia, one of those being led by OHB System. This paper presents OHB " s current mission and asteroid operations strategy, addressing mission design and operational challenges. The tight schedule (launch in 2020) and the low cost approach for spacecraft design and operations are challenging, especially in context of the high complexity and performance requirements connected to deep space mission operations and navigation. Special focus is therefore placed on asteroid local operations, the planned payload operations, the deployment of MASCOT-2 to the surface of the secondary asteroid in the binary system, the navigation strategy of AIM, and how OHB plans to overcome the challenges posed by this unique mission scenario.
The Asteroid Impact Mission (AIM) is an ESA mission whose goal is the exploration and study of bi... more The Asteroid Impact Mission (AIM) is an ESA mission whose goal is the exploration and study of binary asteroid 65803 Didymos. AIM is planned to be the first spacecraft to rendezvous with a binary asteroid: its mission objectives include the highly relevant scientific return of the exploration as well as innovative technological demonstrations. The paper presents some updates on the ongoing design of the mission. Each phase of the operative life of AIM spacecraft is detailed with information and results on the solutions adopted for Mission Analysis design and on the strategies to suitably operate payloads. The work presented in this paper has been performed by the authors under ESA contract within the phase A design of AIM mission.
The Asteroid Impact Mission (AIM) includes among its primary objectives the release of a lander (... more The Asteroid Impact Mission (AIM) includes among its primary objectives the release of a lander (MASCOT-2) on the surface of the smaller asteroid of binary couple 65803 Didy-mos. The work here presented is performed under ESA contract , in the frame of phase A mission design of AIM spacecraft. The paper focuses on the landing-related part of the design and presents the ongoing work concerning the release strategy adopted to fulfill mission design requirements. The dynamics of the spacecraft are modeled using the most up-to-date gravity model of Didymos system, based on shape models of the two asteroids. Descent trajectories are selected by exploiting manifold dynamics associated to the peculiar three-body environment in the proximity of Didymos.
The Asteroid Impact Mission (AIM) is a European mission aimed at the exploration of the binary as... more The Asteroid Impact Mission (AIM) is a European mission aimed at the exploration of the binary asteroid 65803 Didymos. Among its mission objectives, AIM is planned to release a small and passive probe, called MASCOT-2, to land on the smallest asteroid of the binary couple. The paper presents the modeling strategy adopted to support the design of MASCOT-2 release. The modeling assumptions regarding the dynamical environment of such binary asteroid are discussed. The gravity field around the couple is modeled using shape-based models of the asteroids. A suitable model of the asteroid's surface is used to properly simulate the local interaction between the probe and the soil at touch down. Uncertainties regarding the release accuracy are modeled and results related to the AIM scenario are presented in terms of successful landing probability and final position of the lander at rest.
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Papers by Fabio Ferrari
some very complex mission goals, not achievable by a single spacecraft. The dynamical properties of a low acceleration environment such as the vicinity of libration points associated to a three-body system, can be effectively exploited to design spacecraft configurations able of satisfying tight relative position and velocity requirements. This work studies the evolution of an uncontrolled formation orbiting in the
proximity of periodic orbits about collinear libration points under the Circular and Elliptic Restricted Three-Body Problems. A three spacecraft triangularly-shaped formation is assumed as a representative geometry to be investigated. The study identifies initial configurations that provide good performance in terms of formation keeping, and investigates key parameters that control the relative dynamics between the spacecraft within the three-body system. Formation keeping performance is quantified by monitoring shape and size changes of the triangular formation. The analysis has been performed under five degrees of freedom to define the geometry, the orientation and the location of the triangle in the synodic rotating frame.
that asteroid aggregation processes can be naturally modeled with N-body numerical codes implementing gravitational interactions. This work presents a new implementation of an Nbody numerical solver. The code is based on Chrono::Engine (2006). It handles the contact and collision of large numbers of complex-shaped objects, while simultaneously evaluating the effect of N to N gravitational interactions. A special case of study is considered, investigating the relative dynamics between the N bodies and highlighting favorable conditions for the formation of a stable gravitationally bound aggregate from a cloud of N boulders. The
code is successfully validated for the case of study by comparing relevant results obtained for typical known dynamical scenarios. The outcome of the numerical simulations shows good agreement with theory and observation, and suggests the ability of the developed code
to predict natural aggregation phenomena.
to model to higher accuracy the peculiar dynamical properties of such irregular and low gravity field bodies, while keeping the advantages of having a full analytical formulation and low computational cost required. The neighborhood of the asteroid couple is split into two regions of influence where two different three-body problems describe the dynamics of the spacecraft. These regions have been identified by introducing the concept of surface of equivalence (SOE), a three-dimensional surface that serves as boundary between the regions
of influence of each dynamical model. A case of study is presented, in terms of potential scenario that may benefit of such an approach in solving its mission analysis. Cost-effective solutions to land a vehicle on the surface of a low gravity body are selected by generating Poincaré maps on the SOE, seeking intersections between stable and unstable manifolds of the two patched three-body systems.
some very complex mission goals, not achievable by a single spacecraft. The dynamical properties of a low acceleration environment such as the vicinity of libration points associated to a three-body system, can be effectively exploited to design spacecraft configurations able of satisfying tight relative position and velocity requirements. This work studies the evolution of an uncontrolled formation orbiting in the
proximity of periodic orbits about collinear libration points under the Circular and Elliptic Restricted Three-Body Problems. A three spacecraft triangularly-shaped formation is assumed as a representative geometry to be investigated. The study identifies initial configurations that provide good performance in terms of formation keeping, and investigates key parameters that control the relative dynamics between the spacecraft within the three-body system. Formation keeping performance is quantified by monitoring shape and size changes of the triangular formation. The analysis has been performed under five degrees of freedom to define the geometry, the orientation and the location of the triangle in the synodic rotating frame.
that asteroid aggregation processes can be naturally modeled with N-body numerical codes implementing gravitational interactions. This work presents a new implementation of an Nbody numerical solver. The code is based on Chrono::Engine (2006). It handles the contact and collision of large numbers of complex-shaped objects, while simultaneously evaluating the effect of N to N gravitational interactions. A special case of study is considered, investigating the relative dynamics between the N bodies and highlighting favorable conditions for the formation of a stable gravitationally bound aggregate from a cloud of N boulders. The
code is successfully validated for the case of study by comparing relevant results obtained for typical known dynamical scenarios. The outcome of the numerical simulations shows good agreement with theory and observation, and suggests the ability of the developed code
to predict natural aggregation phenomena.
to model to higher accuracy the peculiar dynamical properties of such irregular and low gravity field bodies, while keeping the advantages of having a full analytical formulation and low computational cost required. The neighborhood of the asteroid couple is split into two regions of influence where two different three-body problems describe the dynamics of the spacecraft. These regions have been identified by introducing the concept of surface of equivalence (SOE), a three-dimensional surface that serves as boundary between the regions
of influence of each dynamical model. A case of study is presented, in terms of potential scenario that may benefit of such an approach in solving its mission analysis. Cost-effective solutions to land a vehicle on the surface of a low gravity body are selected by generating Poincaré maps on the SOE, seeking intersections between stable and unstable manifolds of the two patched three-body systems.