Alessandra Celletti – författare

I was delighted to be invited by my colleagues Alessandra Celletti and Ettore Perozzi to provide a foreword to their book, Celestial Mechanics: The Waltz of the Planets. Having known them for many years and long admired their work in the subject so many of us love and are fascinated by, 1 read with great attention and pleasure the text when it arrived. It is a formidable task they have set themselves, to provide a book that describes attempts by successive generations of astronomers from the dawn of history five millennia ago to observe, record and understand the phenomena of the heavens, particularly the intricate and perplexing behaviour of the planets. Sun and Moon. As naked eye astronomy became aided by the telescope and the photographic plate, and since the middle of the twentieth century, by instruments launched on spacecraft into circum- Earth orbit or to the Moon and planets and beyond, the discovery of new satellites, scores of them, and ring systems displaying new and initially perplexing behaviour also demanded explanations for that behaviour. It is also the inspiring story of science itself with special reference to how lonely individuals, impelled by curiosity and dedicated to seeking the truth, and nothing but the truth, about the fascinating phenomena of nature, ultimately became accepted as scientists, those players in the most successful endeavour ever engaged in by the human race.

I was delighted to be invited by my colleagues Alessandra Celletti and Ettore Perozzi to provide a foreword to their book, Celestial Mechanics: The Waltz of the Planets. Having known them for many years and long admired their work in the subject so many of us love and are fascinated by, 1 read with great attention and pleasure the text when it arrived. It is a formidable task they have set themselves, to provide a book that describes attempts by successive generations of astronomers from the dawn of history five millennia ago to observe, record and understand the phenomena of the heavens, particularly the intricate and perplexing behaviour of the planets. Sun and Moon. As naked eye astronomy became aided by the telescope and the photographic plate, and since the middle of the twentieth century, by instruments launched on spacecraft into circum- Earth orbit or to the Moon and planets and beyond, the discovery of new satellites, scores of them, and ring systems displaying new and initially perplexing behaviour also demanded explanations for that behaviour. It is also the inspiring story of science itself with special reference to how lonely individuals, impelled by curiosity and dedicated to seeking the truth, and nothing but the truth, about the fascinating phenomena of nature, ultimately became accepted as scientists, those players in the most successful endeavour ever engaged in by the human race.

The range of phenomena that manifest at all different time and length scales and the wide range of sizes of space objects, from minor bodies in the Solar System to exoplanets, and from dust particles to Jupiter-size bodies, require the development of dynamical modeling and analysis tools that can handle these different scales. This volume collects contributions given by distinguished scientists at the hybrid IAU Symposium 364. The methods in dynamics modeling of space objects have already reached a state of maturity, and their implementation provided a large number of important results pertaining to both the theory and their applications. The contributions cover the recent advances in the multi-scale dynamics of natural and artificial space objects from various perspectives, which will benefit graduate students and researchers working in the fields of celestial mechanics, astrodynamics, planetary sciences, applied mathematics and dynamical systems.

At the opening of the "Third Meeting on Celestial Mechanics - CELMEC III", strong sensations hit our minds. The conference (18-22 June 2001) was being held in Villa Mondragone, a beautiful complex of buildings and gardens located within the township of Monte Porzio Catone, on the hills surrounding Rome. A former papal residence, the building has been recently restored by the University of Rome "Tor Vergata" to host academic activities and events. The conference room is called "Salone degli Svizzeri": here, Gregory XIII, on February 24, 1582, gave its sanction to the reform of the Julian calendar and declared officially in use the calendar still adopted nowadays. The magnificent high walls and tall ceiling strongly resounded, giving to our voice a peculiar Vatican sound, which took us by surprise. May be - we thought - a distant echo of the very words of Gregory XIII proclaiming the modem calendar was still haunting the room. Around us, in the audience, many countries were represented, thus indicating that the idea of putting together the three "souls" of modem Celestial Mechanics - perturbation theories, solar and stellar system studies, spaceflight dynamic- had been successful. CELMEC III is in fact the latest of a series of meetings (the first two editions took place in 1993 and 1997 in L' Aquila, Italy) whose aim is to establish a common ground among people working in Celestial Mechanics, yet belonging to different institutions such as universities, astronomical observatories, research institutes, space agencies and industries.

The book provides the most recent advances of Celestial Mechanics, as provided by high-level scientists working in this field. It covers theoretical investigations as well as applications to concrete problems. Outstanding review papers are included in the book and they introduce the reader to leading subjects, like the variational approaches to find periodic orbits and the space debris polluting the circumterrestrial space.

This book discusses the design of new space missions and their use for a better understanding of the dynamical behaviour of solar system bodies, which is an active field of astrodynamics. Space missions gather data and observations that enable new breakthroughs in our understanding of the origin, evolution and future of our solar system and Earth’s place within it. Covering topics such as satellite and space mission dynamics, celestial mechanics, spacecraft navigation, space exploration applications, artificial satellites, space debris, minor bodies, and tidal evolution, the book presents a collection of contributions given by internationally respected scientists at the summer school “Satellite Dynamics and Space Missions: Theory and Applications of Celestial Mechanics”, held in 2017 at San Martino al Cimino, Viterbo (Italy). This school aimed to teach the latest theories, tools and methods developed for satellite dynamics and space, and as such the book is a valuable resource for graduate students and researchers in the field of celestial mechanics and aerospace engineering.

This book discusses the design of new space missions and their use for a better understanding of the dynamical behaviour of solar system bodies, which is an active field of astrodynamics. Space missions gather data and observations that enable new breakthroughs in our understanding of the origin, evolution and future of our solar system and Earth’s place within it. Covering topics such as satellite and space mission dynamics, celestial mechanics, spacecraft navigation, space exploration applications, artificial satellites, space debris, minor bodies, and tidal evolution, the book presents a collection of contributions given by internationally respected scientists at the summer school “Satellite Dynamics and Space Missions: Theory and Applications of Celestial Mechanics”, held in 2017 at San Martino al Cimino, Viterbo (Italy). This school aimed to teach the latest theories, tools and methods developed for satellite dynamics and space, and as such the book is a valuable resource for graduate students and researchers in the field of celestial mechanics and aerospace engineering.

The book consists of the proceedings of the workshop "New Trends and Challenges in Optimization Theory Applied to Space Engineering", held in l'Aquila (Italy), and organized by the Gran Sasso Science Institute (GSSI), on December 13-15, 2023. The main purpose of the book is to provide an overview of the most important current topics concerning optimal control in space. Optimal control theory is an exciting research area, where both new theoretical approaches and application problems come into play. The “New Trends and Challenges in Optimization Theory Applied to Space Engineering” conference brought together influential academic researchers and experts from industry and government to build bridges between their respective groups. The topics of the conference panels are selected to include the most advanced areas of interest for space applications. In line with the mission of the Gran Sasso Tech Foundation, interdisciplinary dialogue is promoted between the sciences, and different experts are encouraged to work together to identify new problems and generate new solutions. Covering a wide range of space-related topics and challenges, this conference aims to lay the foundation for a long-term collaboration between different groups of experts. A broad overview of control theory applications in space is presented, highlighting the most recent aspects, both from a theoretical and practical point of view, in particular on the following topics: - manifold dynamics, trajectory design and related control aspects;- AI techniques in guidance control problems and space missions;- optimization techniques for constellations with applications to space operations;- multi-stage control problems for launch and landing problems;- optimal control problems in the presence of uncertain parameters;- improved sufficient and necessary conditions in optimal control problems for space problems. New methods, specific mathematical models, ad hoc algorithms and heuristics, innovative mission scenarios, and advances in classical control theory are presented.

The book consists of the proceedings of the workshop "e;New Trends and Challenges in Optimization Theory Applied to Space Engineering"e;, held in l'Aquila (Italy), and organized by the Gran Sasso Science Institute (GSSI), on December 13-15, 2023. The main purpose of the book is to provide an overview of the most important current topics concerning optimal control in space. Optimal control theory is an exciting research area, where both new theoretical approaches and application problems come into play. The "e;New Trends and Challenges in Optimization Theory Applied to Space Engineering"e; conference brought together influential academic researchers and experts from industry and government to build bridges between their respective groups. The topics of the conference panels are selected to include the most advanced areas of interest for space applications. In line with the mission of the Gran Sasso Tech Foundation, interdisciplinary dialogue is promoted between the sciences, and different experts are encouraged to work together to identify new problems and generate new solutions. Covering a wide range of space-related topics and challenges, this conference aims to lay the foundation for a long-term collaboration between different groups of experts. A broad overview of control theory applications in space is presented, highlighting the most recent aspects, both from a theoretical and practical point of view, in particular on the following topics: - manifold dynamics, trajectory design and related control aspects;- AI techniques in guidance control problems and space missions;- optimization techniques for constellations with applications to space operations;- multi-stage control problems for launch and landing problems;- optimal control problems in the presence of uncertain parameters;- improved sufficient and necessary conditions in optimal control problems for space problems. New methods, specific mathematical models, ad hoc algorithms and heuristics, innovative mission scenarios, and advances in classical control theory are presented.

This book is devoted to the presentation and discussion of some models of relevance in Celestial Mechanics and Astrodynamics. The motions of celestial bodies, either natural or artificial, are governed by conservative forces, like the gravitational attraction that preserve the total energy and by dissipative forces, like the tidal torque, Stokes drag, and the Poynting-Robertson effect. The basic idea of this book is to describe in each chapter a model in the conservative setting, providing its main features, and then to extend the model by including dissipative forces. In fact, the dynamics of many objects of the Solar system is well described, in a first approximation, by a conservative model; however, in the long term, dissipative effects may play a relevant role, for example, in shaping the dynamics and affecting the evolutionary history of the Solar system. Motivated by this observation, in this book, different models are presented and their main features are described in the conservative setting, but dissipative contributions, pertinent to the model, are added as well, which may lead to a completely different dynamics on long time scales. Conservative systems have a larger variety of motions, e.g., the dynamics can take place on rotational tori, librational motions, periodic orbits, and chaotic trajectories. On the contrary, dissipative systems admit a less rich dynamics, since the dissipation forces the motion to take place on a few attractors, e.g., rotational tori, periodic orbits or strange attractors. Besides, dissipative systems often need extra parameters to compensate for the loss of energy and to allow the dynamics to take place on non-trivial attractors.The book is addressed to graduate students and researchers interested in models of Celestial Mechanics and Astrodynamics.

This book is devoted to the presentation and discussion of some models of relevance in Celestial Mechanics and Astrodynamics. The motions of celestial bodies, either natural or artificial, are governed by conservative forces, like the gravitational attraction that preserve the total energy and by dissipative forces, like the tidal torque, Stokes drag, and the Poynting-Robertson effect. The basic idea of this book is to describe in each chapter a model in the conservative setting, providing its main features, and then to extend the model by including dissipative forces. In fact, the dynamics of many objects of the Solar system is well described, in a first approximation, by a conservative model; however, in the long term, dissipative effects may play a relevant role, for example, in shaping the dynamics and affecting the evolutionary history of the Solar system. Motivated by this observation, in this book, different models are presented and their main features are described in the conservative setting, but dissipative contributions, pertinent to the model, are added as well, which may lead to a completely different dynamics on long time scales. Conservative systems have a larger variety of motions, e.g., the dynamics can take place on rotational tori, librational motions, periodic orbits, and chaotic trajectories. On the contrary, dissipative systems admit a less rich dynamics, since the dissipation forces the motion to take place on a few attractors, e.g., rotational tori, periodic orbits or strange attractors. Besides, dissipative systems often need extra parameters to compensate for the loss of energy and to allow the dynamics to take place on non-trivial attractors.The book is addressed to graduate students and researchers interested in models of Celestial Mechanics and Astrodynamics.

In 2013 several scientific activities have been devoted to mathematical researches for the study of planet Earth. The current volume presents a selection of the highly topical issues presented at the workshop “Mathematical Models and Methods for Planet Earth”, held in Roma (Italy), in May 2013. The fields of interest span from impacts of dangerous asteroids to the safeguard from space debris, from climatic changes to monitoring geological events, from the study of tumor growth to sociological problems. In all these fields the mathematical studies play a relevant role as a tool for the analysis of specific topics and as an ingredient of multidisciplinary problems. To investigate these problems we will see many different mathematical tools at work: just to mention some, stochastic processes, PDE, normal forms, chaos theory.

In 2013 several scientific activities have been devoted to mathematical researches for the study of planet Earth. The current volume presents a selection of the highly topical issues presented at the workshop “Mathematical Models and Methods for Planet Earth”, held in Roma (Italy), in May 2013. The fields of interest span from impacts of dangerous asteroids to the safeguard from space debris, from climatic changes to monitoring geological events, from the study of tumor growth to sociological problems. In all these fields the mathematical studies play a relevant role as a tool for the analysis of specific topics and as an ingredient of multidisciplinary problems. To investigate these problems we will see many different mathematical tools at work: just to mention some, stochastic processes, PDE, normal forms, chaos theory.

In 2013 several scientific activities have been devoted to mathematical researches for the study of planet Earth. The current volume presents a selection of the highly topical issues presented at the workshop “Mathematical Models and Methods for Planet Earth”, held in Roma (Italy), in May 2013. The fields of interest span from impacts of dangerous asteroids to the safeguard from space debris, from climatic changes to monitoring geological events, from the study of tumor growth to sociological problems. In all these fields the mathematical studies play a relevant role as a tool for the analysis of specific topics and as an ingredient of multidisciplinary problems. To investigate these problems we will see many different mathematical tools at work: just to mention some, stochastic processes, PDE, normal forms, chaos theory.

The last decades have marked the beginning of a new era in Celestial Mech- ics. The challenges came from several di?erent directions. The stability theory of nearly-integrable systems (a class of problems which includes many models of - lestial Mechanics) pro?ted from the breakthrough represented by the Kolmogorov- Arnold-Moser theory, which also provides tools for determining explicitly the - rameter values allowing for stability. A con?nement of the actions for exponential times was guaranteed by Nekhoroshev's theorem, which gives much information about the geography of the resonances. Performing ever-faster computer simu- tionsallowedustohavedeeperinsightsintomanyquestionsofDynamicalSystems, most notably chaos theory. In this context several techniques have been developed to distinguish between ordered and chaotic behaviors. Modern tools for computing spacecraft trajectories made possible the realization of many space missions, es- cially the interplanetary tours, which gave a new shape to the solar system with a lot of new satellites and small bodies.Finally, the improvement of observational techniques allowed us to make two revolutions in the sky: the solar system does not end with Pluto, but it extends to the Kuiper belt, and the solar system is not unique, but the universe has plenty of extrasolar planetary systems. Cookingalltheseingredientstogetherwiththeclassicaltheoriesdevelopedfrom the 17th to the 19th centuries, one obtains themodern Celestial Mechanics.

The last decades have marked the beginning of a new era in Celestial Mech- ics. The challenges came from several di?erent directions. The stability theory of nearly-integrable systems (a class of problems which includes many models of - lestial Mechanics) pro?ted from the breakthrough represented by the Kolmogorov- Arnold-Moser theory, which also provides tools for determining explicitly the - rameter values allowing for stability. A con?nement of the actions for exponential times was guaranteed by Nekhoroshev's theorem, which gives much information about the geography of the resonances. Performing ever-faster computer simu- tionsallowedustohavedeeperinsightsintomanyquestionsofDynamicalSystems, most notably chaos theory. In this context several techniques have been developed to distinguish between ordered and chaotic behaviors. Modern tools for computing spacecraft trajectories made possible the realization of many space missions, es- cially the interplanetary tours, which gave a new shape to the solar system with a lot of new satellites and small bodies.Finally, the improvement of observational techniques allowed us to make two revolutions in the sky: the solar system does not end with Pluto, but it extends to the Kuiper belt, and the solar system is not unique, but the universe has plenty of extrasolar planetary systems. Cookingalltheseingredientstogetherwiththeclassicaltheoriesdevelopedfrom the 17th to the 19th centuries, one obtains themodern Celestial Mechanics.

This book is intended to diffuse original research results interesting people working in Celestial Mechanics in both theory and applications. Theoretical investigators will find several results on Hamiltonian Dynamics, periodic Orbits, Chaos Diagnostic and Perturbations Theory. Applications cover several directions of research starting with those related to space exploration (mission design and space research) to those related to astronomy (extrasolar planets, asteroids, Near Earth asteroids). Since this book carries original results, it is unique and complements similar books and journals. Some of the subjects have great media appeal: the risk of impact of space debris on the Space Station, the possibility of fly-by missions to asteroids approaching dangerously to our planet, the study of the orbits of these objects, etc. Appealing for a large audience among scientists are the subjects related to Chaos and Order as well as those centered on the study of the dynamics of exoplanets (extrasolar planets). The appeal of the more theoretical papers lies in the fact that they make a tour on the state-of-the-art of several classical problems.

The book provides the most recent advances of Celestial Mechanics, as provided by high-level scientists working in this field. It covers theoretical investigations as well as applications to concrete problems. Outstanding review papers are included in the book and they introduce the reader to leading subjects, like the variational approaches to find periodic orbits and the space debris polluting the circumterrestrial space.