Author's preface
Stability, resonances and chaos
often sparkle as magic words in popular
and scientific literature to explain the evolution of an astonishingly
wide variety of complex systems, from weather forecasting to
large-scale economies. Yet their origin can be traced back to an
ancient discipline: Celestial Mechanics.
Born as a practical means to observe and predict the motion of the stars and planets celestial mechanics has accompanied the history of any developing civilization on Earth. Since the early astronomical observations of the ancient Chaldeans to the work of Henri Poincaré (whose intuitions on the ubiquity of chaos continue to be an enlightening source of inspiration), until the space age, the number of celestial objects either discovered or launched in space has grown steadily. To date, more than one hundred thousand asteroids have been catalogued, the passage of thousands of comets has been recorded, satellites and rings are busily orbiting around the outer planets and the still poorly known population of transneptunian objects extends far away into the outskirts of the Solar System.
The
widespread diffusion of
digital computers, the sharp increase in their performance and the
significant advances in dynamical system theory, have allowed to trace
the orbital motion of celestial bodies for a time span comparable to
the age of our planetary system: five billion years. In this timescale
the Solar System is alive with events involving the major planets as
well as the smaller bodies wandering among them.
On a larger scale, stellar systems and galaxies exhibit complex dynamical behaviors while the long-awaited discovery of extra-solar planets and their exotic orbital configurations is slowly bridging the gap between planetary science and astrophysics.
At the turn of the new millennium, humans have achieved routine access to near-Earth and interplanetary space. A cloud of artificial satellites for commercial, military and scientific purposes surrounds the Earth. Man-made celestial objects explore the Solar System, perform fundamental physics experiments and observe the Universe far from the disturbing presence of our planet. Their trajectories are confidently mastered by spaceflight dynamics.
It is out of the question then that stability, resonances and chaos are, more than ever, firmly back to Celestial Mechanics.
The idea of reporting what modern celestial mechanics look like to the public at large is somehow a logical consequence to the
organization of the CELMEC meetings,
aiming to gather together mathematicians, physicists, astronomers and
engineers in order to facilitate communication amongst people working
on celestial mechanics but belonging to different institutions
(Universities, Astronomical Observatories, Space Agencies and
Industries). The enthusiastic international participation, the variety
of topics discussed and their interrelations within apparently distant
fields of study caught us by surprise. The chaotic behavior of
planetary spin-axes influences the long-term stability of climate on
Earth which, in turn, bears strong implications for the birth of life
on our planet. The orbital evolution of asteroids, comets and meteors
gives to a catastrophic impact the blame for the sudden disappearance
of dinosaurs and estimates the actual hazard for humankind. Spaceflight
dynamics has quickly become a mature science, mapping the spaceways to
get around the Solar System in economy class and warning mankind from
polluting the skies with orbiting debris.
We are aware that Celestial Mechanics has a long-standing reputation for being a rather complicated science; but an essential part of its fascination is that it has always been an ideal testing ground for the most complex mathematical theories. Bearing this in mind, we have tried to exploit as far as possible the graphic visualization of the trajectories of the celestial bodies, thus minimising the use of analytical equations.
Historical highlights have been frequently introduced for keeping the attention alive as the circumstances of famous astronomical discoveries often follow the intriguing plots typical of spy stories. Images have been also widely used throughout the text: apart from the fascination of looking at alien worlds, the pictures sent by exploration missions have often shown the existence of unusual orbital configurations awaiting a dynamical explanation.
Our hope is to have succeeded in presenting Celestial Mechanics in a "user friendly" form to the non scientist, as well as to have stimulated the more skilled audience into making connections among the various fields of study which characterize the interdisciplinary nature of modern Celestial Mechanics.
Born as a practical means to observe and predict the motion of the stars and planets celestial mechanics has accompanied the history of any developing civilization on Earth. Since the early astronomical observations of the ancient Chaldeans to the work of Henri Poincaré (whose intuitions on the ubiquity of chaos continue to be an enlightening source of inspiration), until the space age, the number of celestial objects either discovered or launched in space has grown steadily. To date, more than one hundred thousand asteroids have been catalogued, the passage of thousands of comets has been recorded, satellites and rings are busily orbiting around the outer planets and the still poorly known population of transneptunian objects extends far away into the outskirts of the Solar System.
The
widespread diffusion of
digital computers, the sharp increase in their performance and the
significant advances in dynamical system theory, have allowed to trace
the orbital motion of celestial bodies for a time span comparable to
the age of our planetary system: five billion years. In this timescale
the Solar System is alive with events involving the major planets as
well as the smaller bodies wandering among them.On a larger scale, stellar systems and galaxies exhibit complex dynamical behaviors while the long-awaited discovery of extra-solar planets and their exotic orbital configurations is slowly bridging the gap between planetary science and astrophysics.
At the turn of the new millennium, humans have achieved routine access to near-Earth and interplanetary space. A cloud of artificial satellites for commercial, military and scientific purposes surrounds the Earth. Man-made celestial objects explore the Solar System, perform fundamental physics experiments and observe the Universe far from the disturbing presence of our planet. Their trajectories are confidently mastered by spaceflight dynamics.
It is out of the question then that stability, resonances and chaos are, more than ever, firmly back to Celestial Mechanics.
The idea of reporting what modern celestial mechanics look like to the public at large is somehow a logical consequence to the
organization of the CELMEC meetings,
aiming to gather together mathematicians, physicists, astronomers and
engineers in order to facilitate communication amongst people working
on celestial mechanics but belonging to different institutions
(Universities, Astronomical Observatories, Space Agencies and
Industries). The enthusiastic international participation, the variety
of topics discussed and their interrelations within apparently distant
fields of study caught us by surprise. The chaotic behavior of
planetary spin-axes influences the long-term stability of climate on
Earth which, in turn, bears strong implications for the birth of life
on our planet. The orbital evolution of asteroids, comets and meteors
gives to a catastrophic impact the blame for the sudden disappearance
of dinosaurs and estimates the actual hazard for humankind. Spaceflight
dynamics has quickly become a mature science, mapping the spaceways to
get around the Solar System in economy class and warning mankind from
polluting the skies with orbiting debris. We are aware that Celestial Mechanics has a long-standing reputation for being a rather complicated science; but an essential part of its fascination is that it has always been an ideal testing ground for the most complex mathematical theories. Bearing this in mind, we have tried to exploit as far as possible the graphic visualization of the trajectories of the celestial bodies, thus minimising the use of analytical equations.
Historical highlights have been frequently introduced for keeping the attention alive as the circumstances of famous astronomical discoveries often follow the intriguing plots typical of spy stories. Images have been also widely used throughout the text: apart from the fascination of looking at alien worlds, the pictures sent by exploration missions have often shown the existence of unusual orbital configurations awaiting a dynamical explanation.
Our hope is to have succeeded in presenting Celestial Mechanics in a "user friendly" form to the non scientist, as well as to have stimulated the more skilled audience into making connections among the various fields of study which characterize the interdisciplinary nature of modern Celestial Mechanics.
Roma,
30 May
2006 Alessandra Celletti & Ettore Perozzi