The Dynamics of Small Bodies in the Solar System: A Major Key to Solar Systems Studies

620 Pages·1999·17.64 MB·English

by  E. Belbruno

The Dynamics of Small Bodies in the Solar System
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SeriesC:Mathematical andPhysicalSciences- Vol.522
The Dynamics of Small Bodies
in the Solar System
A Major Key to Solar System Studies
edited by
Bonnie A. Steves
Department ofMathematics,
GlasgowCaledonian University,
Glasgow, United Kingdom
and
Archie E. Roy
Department of Physics and Astronomy,
Universityof Glasgow,
Glasgow, United Kingdom
~.
'I
Springer-Science+Business Media, B.V.
Publishedincooperation withNATOScientific AffairsDivision
ProceedingsoftheNATOAdvanced Study Institute on
The DynamicsofSmallBodiesinthe SolarSystem: AMajorKeytoSolarSystem
Studies
Maratea, Italy
29June- 12July 1997
LibraryofCongressCataloging-in-Publication Data
The dyna.lcs of s.all bod'es In the solar syste. a .aJor key to
solar systeo studies I edIted by BonnIe A. Steves and ArchIe E. Roy.
p. c,. -- (NATO ASI sertes SerIes C, Mathe.atlcal and
physIcal scIences ; vol. 522)
·Proceedlngs of the NATO Advanced Study Instttute. held In Maratea
-Acquafredda. Italy. bet.een June 29 and July 12, 1997, entitled The
Oyna.lcs of S.alt BodIes tn the So'ar Systeo, a Major Key to Solar
Syste. Studles--Preface.
Includes Index.
1. Solar syste.--Congresses. 2. Asterolds--Congresses. 3. Few
-body proble~--Congresses. 4. Astrophys1cs--Congresses.
I. Steves, BonnIe A. II. Roy. A. E. (ArchIe E.). 1924-
III. The Oyna.lcs of S.all BodIes In the Solar Syste., a Major Key
to'Solar Syste. Studtes (1997 Acquafredda dl Maratea, Italy)
IV. Sertes, NATO ASI serIes. Sertes C, Mathe.atlcal and physical
scIences ; no. 522.
OB500.5.092 1999
523.5--dc21 98-31687
ISBN 978-90-481-5133-2 ISBN 978-94-015-9221-5 (eBook)
D0O01I 10.1007/978-94-015-9221-5
Printedonacid-freepaper
AllRightsReserved
© 1999 SpringerScience-Business MediaDordrecht
OriginallypublishedbyKluwerAcademicPublishersin1999.
Softcoverreprintofthehardcover1stedition1999
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical, including photo
copying, recording orby any information storage and retrieval system, without written
permissionfromthecopyright owner.
These Proceedings ofthe 1997 NATO Advanced Study
Institute held in Maratea, Italy
between June 29 and July 12
are dedicated to the
memory of
Professor Victor Szebehely
(1921 - 1997)
renowned celestial mechanician, cherished teacher and dearfriend.
CONTENTS
Preface Xl
I. InMemory ofYictory Szebehely Xlii
K.Zare
SECTION ONE:Asteroids andTrans-Neptunian Objects
2. Introduction
E.Belbruno and LP.Williams
3. OnHigh-Eccentricity Small-Amplitude Asteroidal Librations
A.Simula, S.Ferraz-Mello andC. Giordano 7
4. A.Symplectic Mapping Approach forthe Study of
Stochasticity inThree Dimensional Asteroidal Resonances
F. Roigand S.Ferraz-Mcllo 13
5. Chaotic Diffusion inthe 2/1,3/2 and4/3 Jovian Resonances
D.Nesvomy and S.Ferraz-Mello 19
6. Onthe Similarities and Differences Between3/2 and
2/1Asteroidal Resonances
T.A.Mitchenko and S.Ferraz-Mello 25
7. A Study ofChaos intheAsteroid Belt
M.Sidlichovsky and D. Nesvorny 31
8. Hopping inthe Kuiper Beltand Significance ofthe 2:3 Resonance
E.Belbruno 37
9. The Solar System Beyond Neptune
J.P.Williams 51
10. Dynamical Study ofTrans-Neptunian Objects atthe 2:3 Resonance
1. hadjidcmetriou and K.G. Hadjifotinou 65
II. Superosculating Intermediate OrbitsandtheirApplication inthe
Problem of Investigation ofthe Motion ofAsteroids and Comets
VA. Shefer 71
12. TestsofGeneral Relativity using Small Bodies ofthe Solar System
C.Marchal 77
SECTIONTWO: Near Earth Objects
13. Introduction
K.Muinonen andA.Milani 93
14. Dynamics of Planet-Crossing Asteroids
A.Milani 95
viii
15. Asteroid and Comet Encounters with the Earth. Impact Hazard and
Collission Probability
K. Muinonen 127
16. Optimal Low-Thrust Interception and Deflection ofEarth
CrossingAsteroids
B.A.Conway 159
17. SecularResonances:Transport Mechanism to Earth-Crossing Orbits
p. Michel 171
18. Meteoroid Streams and MeteorShowers
I.p. Williams 179
19. Planetary Close Encounters:The Engine ofCometary
Orbital Evolution
G.B.Valsecchi 187
20. Galactic Perturbations inthe Motion ofComets
H.Pretka 197
SECTIONTHREE: Natural andArtificial Satellites
21. Introduction
CD.Murray 203
22. Orbits ofSaturn's Satellites:Some Aspects ofCommensur-
abilities and Periodic Orbits
P.l. Message 207
23. How Ideal isthe Mirnas-Tethys Resonance?
1.Probin 227
24. The Dynamics ofPlanetary Rings and Small Satellites
CD.Murray 233
25. Long-TermEvolution ofCoorbital Motion
1.Waldvogel 257
26. Stability ofPerturbed Coorbital Satellites
M.H.M. Morais and CD. Murray 277
27. Instability and Chaotic Motion for Some Fictitious Satellites of
Venusand Mars
T.Yokoyama 283
28. ApplicationsofaHigh OrderSecular PerturbationTheory.
The Uranian Satellites and Beyond
A.A.Christou and CD. Murray 289
29. Non-Integrability ofthe Motion ofa Point Mass around a Planet
of Arbitrary Schape
M.E.Sansaturio, IVigo-Aguiarand1.M. Ferrandiz 295
ix
30. Dynamicsof SatelliteswithMulti-DayPeriods
B.Erdi 303
31. TranslunarHaloOrbitsintheQuasibicircularProblem
M.A.AndreuandC. Sima 309
32. ProblemsConnectedwiththeRotationalDynamicsof
CelestialBodies
A.J.Maciejewski 315
33. ClosedFormExpressionsforSomeGravitationalPotentials.
Triangle, Rectangle, PyramidandPolyhedron.
R.A.Broucke 321
34. OrbitalElementsofa SatelliteMovinginthe Potentialofa
HemisphericalShell
B.ZafiropoulosandCh.Stavliotis 341
SECTION FOUR: FewBodySystems
35. Introduction
A.E.Royand B.A.Steves 349
36. SomeSpecialSolutionsoftheFour-BodyProblem.
B.A.Steves,A.E.RoyandM.Bell 351
37. SomeEqualMassFour-BodyEquilibriumConfigurations:
LinearStabilityAnalysis
1.Gomatam,B.A.StevesandA.E.Roy 373
38. The Finite-TimeStabilityMethodAppliedto PlanetsofBinaryStars
B.A.Steves,A.D.BarnettandA.E.Roy 379
39. DynamicsandStabilityofThree-BodySystems
R.MardlingandS.Aarseth 385
40. NewNumerical MethodforNon-ConservativeSystems
T.A. Taidakova and N.N.Gor'Kavyi 393
41. TidalFrictioninTripleSystems:AMeansof ProducingClose
StellarandPlanetaryOrbits
L.G.KiselevaandP.P.Eggleton 399
42. SpecialVersion oftheThree-BodyProblem
K.GozdziewskiandA.J.Maciejewski 407
43. Bifurcationsinthe MassRatioofthePlanarIsosceles
Three-Body Problem
S.ChesleyandK.Zare 413
x
SECTION FIVE: Studies of Dynamical Systems
44. Introduction
G.Contopoulos and R.Dvorak 425
45. Dynamical Spectra
G.Contopoulos and N.Voglis 429
46. Angular Dynamical Spectra and theirApplications
C. Efthymiopoulos, N.Voglisand G.Contopoulos 455
47. WeakChaos and Diffusion in Hamiltonian Systems.From
Nekhoroshev to Kirkwood
C. Froeschle and E. Lega 463
48. On the Relationship between Local Lyapunov Characteristic Numbers,
Largest Eigenvalues and Maximum Stretching Parameters
C. Froeschle, E.Lohingerand E. Lega 503
49. "Stickiness" in Dynamical Systems
R.Dvorak 509
50. Distribution ofPeriodic Orbits in 2-D Hamiltonian Systems
E.Grousouzakouand G.Contopoulos 535
51. The Many Faces ofDynamical Instability I:The definition of
"Chaos" and the (In)equivalence ofDifferent Indicators
P. Cipriani and M.Di Sari 545
52. The Many Faces ofDynamical Instability II:The Sources
"Chaos" in Dynamical Systems
M.Di Bari and P.Cipriani 55I
53. Scale Relativity inthe Solar System. A Review and Prospects
R.P.Hermann 557
54. Possible Cosmological Origin ofCounterrotating Galaxies
M.Harsoula and N.Voglis 565
55. Gylden-like Systems and DEF-Mappings
1.Aparicio and L. Floria 575
56. Uniform Development ofaTR-Transformation to Generalized
Universal Variables
L. Flor{a 581
EPILOGUE: The,Shape ofThings to Come
57. Future Planetary Missions
A.A. Christou 587
Participantsand Speakers 595
Subjectand AuthorIndexes 603
PREFACE
The reader willfind in this volume the Proceedings of the NATO Advanced Study
InstituteheldinMaratea-Acquafredda,Italy,betweenJune29andJuly12, 1997,entitledTHE
DYNAMICS OF SMALL BODIES IN THE SOLAR SYSTEM: A MAJOR KEY TO
SOLAR SYSTEM STUDIES.
This AdvancedStudy Institute wasthe latest inthe 'Cortina' series of NATO ASI's
begun in the early 1970's firstly under the directorship of Professor Victor Szebehely and
subsequently under ProfessorArchie Roy. All,except the latest, were heldat the Antonelli
Institute, Cortina d'Ampezzo, Italy. Manyof those now active inthe fieldmade their first
international contacts at these Institutes. The Institutes bring together many of the
brightest of our young people working in dynamical astronomy, celestial mechanics and
space science, enabling them to obtain an up-to-date synoptic view of their subjects
delivered bylecturers of highinternational reputation. The proceedingsfromtheseinstitutes
have been well-receivedinthe internationalcommunityof research workers inthe disciplines
studied.
The present instituteincluded15seriesof lecturesgivenbyinvitedspeakersand some
45 presentations made by the other participants. The majority of these contributions are
includedintheseproceedings.
The theme of thelatest ASIintheseries, viz.TheDynamics ofSmall Bodies in the
Solar System: Amajor keyto solarsystem studies was chosen because of the widespread
recognition that the small natural bodies of the solar system bear an importance in solar
system studies faroutweighingtheirsizeandmassrelative totheplanets. The study of the
nature and dynamics of asteroids, comets, meteor streams, natural satellites and ring
systems currently provides a wealth of information concerning the history and dynamical
evolutionof thesolar system as a whole. Such objectsalso provide excellent test-beds for
thestudy ofresonance andchaos.
It has become clear that the evidence of the bombardment of planet Earth by
cometsand asteroids with thesubsequentextinction ofaproportionof livingspecies isnot
only a topic of historical interest for the astronomer, biologist, botanist and geologist, but
is also an ongoing process that must be addressed by any scientist responsible for the
survival of terrestrial civilisation. The spectacularbombardmentofJupiterin 1995 by the
fragments ofComet Shoemaker-Levy underlines the necessity of international support for
operations such as Spaceguard for finding, listing and assessing all Earth orbit crossing
asteroids andcometswithin theSolar System.
xi