Celestial Mechanics: The Waltz of the Planets

276 Pages·2007·8.119 MB·English

by  Professor Alessandra Celletti, Dr Ettore Perozzi (auth.)

Celestial Mechanics
The Waltz of the Planets
Alessandra Celletti and Ettore Perozzi
Celestial Mechanics
The Waltz of the Planets
Published in association with
<a Springer P^^^i^. Publishing RRAXIS
Chichester, UK
Professor Alessandra Celletti Dr Ettore Perozzi
Universita di Roma 'Tor Vergata' Telespazio
Rome Rome
Italy Italy
SPRINGER-PRAXIS BOOKS IN POPULAR ASTRONOMY
SUBJECT ADVISORY EDITOR: John Mason B.Sc, M.Sc, Ph.D.
ISBN 10: 0-387-30777-X Springer Berlin Heidelberg New York
ISBN 13: 978-0-387-30777-0 Springer Berlin Heidelberg New York
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Printed in Germany on acid-free paper
Table of contents
Foreword ix
Authors' preface xvi
Acknowledgements xvii
List of illustrations xix
1 AROUND AND AROUND 1
The importance of being Lucretius 1
Eccentric Kepler 4
Tyge the astrologer 9
Giants' shoulders 11
Perturbations 13
Drawing orbits 15
Neptune's karma 18
Planets on a diet 20
Gone with the tides 21
2 THREE BODIES AND NO SOLUTION 25
Celestial mechanics gets the blues 25
Lagrange in equilibrium 28
Periodic orbits 31
Mapping chaos 32
KAM and all that 35
Inside the rings of Saturn 38
A flash in the night 39
3 CELESTIAL WALTZ 43
Heavenly resonances 43
Commensurable motions 46
Greeks and Trojans 48
Famous affairs 51
The chance of chaos 53
Colombo's egg 54
vi Table of contents
4 COSMIC SPINNING TOPS 59
Spin and orbit 59
The dark side of the Moon 62
Tidal friction 65
Geostationary satellites 69
A portrait of Mercury 72
Tidy chaos 73
The obliquity of the planets 74
Raiders of the lost equinoxes 76
Is the land of Atlantis really lost? 78
Astronology 80
5 OUR CHAOTIC SOLAR SYSTEM 83
The ubiquity of chaos 83
Propagating orbits 86
Planets in numbers 88
The stability of the Solar System 91
Close encounters 94
Raining comets 97
The long journey of meteorites 99
Jurassic asteroids 103
6 SINGULARITIES, COLLISIONS AND THREATENING BODIES 107
From zero to infinity 107
Collisions in the Solar System 110
Astroblames 112
Near-Earth asteroids 115
Impact probability 120
Don't panic! 123
Mitigation 126
7 OF MOON AND MAN 129
The cycles of Selene 129
Acts of the Gods 133
Eclipsed by the Saros 136
Lunar theories 137
Holidays in Elatina 140
Moonshadows 141
Highways to the Moon 144
8 ROCK AROUND THE PLANETS 149
Space in flight 149
Orbiting the Earth 152
Space debris 155
The accessibility of celestial bodies 158
Table of contents vii
Going deep space 163
Highways to the planets 168
Last but not least 169
9 LORDS OF THE RINGS 173
Ringed worlds 173
Forbidden regions 178
Jovian halos 180
Sightseeing Saturn 181
Elliptic rings 182
Arcs in the sky 183
Once upon a ring 185
10 AT THE EDGE OF THE SOLAR SYSTEM 187
Beyond Pluto 187
Smiley and the others 190
Big Brothers are watching us 193
Chiron and the Centaurs 194
Planet X 197
11 ON THE ROAD TO EXOLIFE 199
Beyond the Solar System 199
Hunting for exoplanets 202
A Galactic zoo 206
Astrobiology 209
Back to the future 211
Appendix 1 Planetary data 215
Appendix 2 Planetary satellite data 217
Appendix 3 Space missions 221
Appendix 4 internet resources 227
Glossary 231
Bibliography 237
index 239
To my husband Enrico and to my mother Mirella
Alessandra Celletti
To Eugenia Pennylane and Emilia Pollyjean
Ettore Perozzi
Foreword
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. It is the story of how their
struggles ultimately prevailed against an entrenched and arrogant authority
which believed it and it alone knew what to have faith in and would persecute
and threaten (cf Galileo and his statement that the Earth orbited the Sun - did
he really say under his breath: eppur si niuove as he backed out?) and kill anyone
displaying even more heretical tendencies (cf Giordano Bruno and his concept
of the plurality of worlds). And it is the story how by the second half of the
nineteenth century the immense prestige to the international brotherhood -
and sisterhood - of scientists worldwide, won by their successes in pure science
and technology, almost turned many of them into a new set of priests who
were in danger of pronouncing that really before very long they would have
discovered all of nature's secrets. Life would then hold nothing but carrying
out experiments to add a few more figures to our measures of the fundamental
constants of nature such as the constant of gravitation. How wrong can you
be? Even then Einstein, Bohr, J.J.Thomson, and Rutherford, to mention only a
few, were waiting in the wings preparing by their researches in sub-atomic
X Foreword
physics to demolish the new establishment belief in the achievement of
absolute truth.
This new establishment contained a harder type of scientist. To them, the
long march of science had rescued much of the human race from tormented eras
of superstition and fear that produced the horrific deaths of millions of people
judged to be witches or religious heretics. The modern misuse of scientific and
technological discoveries by our greedy, feckless society is quite another matter,
a problem that must lead to disastrous worldwide consequences for humanity if
twenty-first century society fails to solve it and is fast running out of time in
which to do so.
The popular myth of a scientist is of a rational person who observes, notes,
produces a theory or hypothesis, and carefully sets up an experiment to verify or
to disprove that theory. If the result of the experiment supports the theory, the
scientist has greater faith in his theory, especially if studies by other scientists,
replicating his experiment and its results take place and support his findings. If
the result disproves his theory, he without hesitation dutifully discards it or at
least modifies it. In this way the body of identified knowledge is expanded,
evolving in time to give us a more accurate picture of the world. Ah! If only it
were like that.
Most scientists are formidably expert in their own speciality, are extremely
knowledgeable in a wider region and, apart from hobbies, are often as ignorant in
everything else as anyone else. One might expect however that their scientific
training should give them some advantage in assessing the validity of anything
new brought to their attention. Nevertheless scientists are human too and the
modern generations are well aware that they live in a world of politicians,
propaganda and spindoctors, a world awash with a torrent of ephemeral frothy
and downright worthless media pap for people of limited attention, education
and capacity for rational thought. In their own speciality scientists know what
they and previous generations of researchers have found. Anything that
drastically threatens to challenge the fortress of their hard-won and repeatedly
tested and applied consensus of opinion is automatically suspect until supported
by replicable experiment. Indeed, the greater the threat, the more reluctant the
scientist will be to undertake the required experiments, especially if the person
putting forward the new idea is not a respected colleague. In the past, many
scientists have demonstrated a hostility to such challenges to seemingly well-
established natural laws in their speciality. It is no good the aggrieved pioneer
complaining that surely history has shown that the establishment has always
spurned or neglected the maverick, the unconventional and the innovator only
to accept his discoveries in the end. In this respect the wise words of Marx - not
Karl but Groucho! - are relevant.
'They said Galileo was mad when he claimed the Earth revolved round
the Sun - but it does. They said Wilbur and Orville Wright were out of
their minds when they said men could fly - but they did. They said
my uncle Waldorf was crazy - and he was as mad as a hatter!'
Foreword xi
In modern times there are also the ever-pressing factors of time and money. In
these days when funds for research are difficult to come by, there is enormous
pressure from many quarters on the scientist to ensure that his available time is
devoted to research projects that are 'respectable', grant-attractive and with
promise of acceptable, immediately applicable results, improving the status and
reputation of the institution that employs him or her.
In a real sense, all the above is relevant and comes within the science of
celestial mechanics. But it is far more than that. In space research it also involves
the design and control of the orbits and trajectories within the solar system of
the spacecraft we launch together with the ability to know what it requires in
rocket hardware to launch them. Some of its successes in this branch of celestial
mechanics, called astrodynamics or astronautics, have been the placing in
carefully tailored circum-Earth orbits of the hundreds of multi-purpose satellites
for communication. Earth surveillance, observation of the far reaches of the
universe; the missions to the Moon, Mercury, Venus, Mars, Jupiter, Saturn and
beyond; missions to comets and asteroids; the Mariner and Voyager missions and
the spectacularly successful Cassini-Huyghens mission to greatly enlarge our
knowledge of Saturn and its system of satellites, particularly Titan. The
astronautical dreams of Tsiolkovski, Hermann Oberth, Walter Hohmann and
Werner von Braun became reality.
But wait a minute. Where in the book are all the elegant mathematical
techniques in celestial mechanics such as Delaunay's lunar theory or Hamilto-
nian canonical equations, or general and special perturbation theories that have
been developed over the past three and a quarter centuries since Newton's day,
not only analytical but also computational especially after the invention and
development of high speed and capacity electronic computers? They are an
integral part, indeed a major part of celestial mechanics, in their detailed
mathematical display a very beautiful story of the dedicated and tireless
mathematicians who created them. And in Alessandra and Ettore's book these
techniques are conspicuous by their absence. Certainly Newton's law of
gravitation is given - twice, but where is everything else? Is this book rather
like Hamlet with no mention of the prince? Is it in fact reminiscent of the story
of the old Professor of Celestial Mechanics asked by an enthusiastic,
mathematically inclined but celestial mechanics ignorant student to explain to
him what celestial mechanics is all about.
Professor, cautiously: "You've heard of Newton's law of gravitation?"
Brightly: "Yes!"
"Well," even more cautiously, "celestial mechanics is all about Newton's
law of gravitation but you've got to know it very well."
Indeed you do.
I am of course being totally unfair to our authors. For they have planned their
approach to their task carefully, they have hit upon the precise way in which it
can be accomplished successfully, and in doing so they have identified correctly
the readers they wish to capture and keep. Whether they be scientists already