PHYSICS OF THE SOLAR SYSTEM

Cover: The solar system in many ways resembles a complex clockwork, in which subtle inter-actions produce unexpected results. The rational understanding and mathematical descriptionof the physical processes involved is the gist of our book and is well illustrated in the cover.On March 5, 1979 the Voyager 1 space probe imaged volcanic plumes on Io, one of the fourGalilean satellites of Jupiter (discovered by G. GALILEI in 1611); the picture we show, with onlyone, but impressive plume, has been obtained by the Galileo spacecraft in 1995 (and is availableat NASA’s node http:��www.jpl.nasa.gov�galileo�images�io). Io’s volcanism provides direct evi-dence that the satellite interior is extremely hot, and raises the question of the energy source ofthis surprising activity. On January 26, 1979 S.J. PEALE of the University of Santa Barbara (Cal-ifornia), P. C ASSEN and R.T. R EYNOLDS (both of the NASA Ames Research Center, California)submitted to Science a paper, “Melting of Io by Tidal Dissipation”, in which they specificallypredicted this volcanic activity. A special refereeing process was requested, and obtained fromthe editor, so that the paper could appear before the Voyager encounter; the paper was in factaccepted, and published on March 2, just three days before. A sample of the preparatory noteswas kindly provided by S.J. Peale and are shown in the cover. We thank him very much for hishelp.

Io is tidally deformed by Jupiter’s gravitational field into an oblate shape aligned with thedirection of the planet; this deformation locks the satellite in a synchronous state, in which therotation and the orbital periods are the same. But since the orbit is eccentric the tidal deformationchanges periodically and the ensuing friction heats its interior. The striking prediction by Pealeand his collaborators is based on three conditions: (i) the rate of tidal energy dissipation inducedby the orbital eccentricity can be calculated, (ii) the orbital eccentricity is maintained in spite ofthe dissipation, and (iii) the tidally deposited heat could not escape fast enough to keep Io cool.The dissipated heat, proportional to the square of the eccentricity, can be established in order ofmagnitude, as discussed at the end of Sec. 15.3; in the bottom of the cover Peale gives a rigorousformula. The triplet of Jupiter’s satellites Io, Europa and Ganymede (in the cover indicated withthe suffixes 1, 2 and 3) are locked in a peculiar three-body resonance first understood and studiedby P.S. L APLACE in 1805. The eccentricities of Io and Europa are maintained by the resonance atthe particular values shown in the first two formulas below the plot. In our book this resonanceis briefly described in Sec. 14.2, while the mechanism of resonant enhancement of eccentricity(and inclination in some cases) is introduced in Sec. 15.2. The rate of heat loss from a solidIo by solid state convection was shown to be less than the rate of deposition by tidal friction,so Io had to get hot and form a molten core. The formation of a fluid core increases the tidaldissipation in the remaining solid shell so the fluid core would grow in a runaway fashion. Asshown in Peale’s plots on the cover, the fluid core becomes a substantial part of the body of thesatellite in a time much shorter than the satellite lifetime.

ASTROPHYSICS ANDSPACE SCIENCE LIBRARY

VOLUME 293

EDITORIAL BOARD

Chairman

W.B. BURTON, National Radio Astronomy Observatory, Charlottesville, Virginia, U.S.A.(burton@starband.net); University of Leiden, The Netherlands (burton@strw.leidenuniv.nl)

Executive Committee

J. M. E. KUIJPERS, Faculty of Science, Nijmegen, The NetherlandsE. P. J. VAN DEN HEUVEL, Astronomical Institute, University of Amsterdam,

The NetherlandsH. VAN DER LAAN, Astronomical Institute, University of Utrecht,

The Netherlands

MEMBERS

I. APPENZELLER, Landessternwarte Heidelberg-Königstuhl, GermanyJ. N. BAHCALL, The Institute for Advanced Study, Princeton, U.S.A.

F. BERTOLA, Universitá di Padova, ItalyJ. P. CASSINELLI, University of Wisconsin, Madison, U.S.A.

C. J. CESARSKY, Centre d'Etudes de Saclay, Gif-sur-Yvette Cedex, FranceO. ENGVOLD, Institute of Theoretical Astrophysics, University of Oslo, Norway

R. McCRAY, University of Colorado, JILA, Boulder, U.S.A.P. G. MURDIN, Institute of Astronomy, Cambridge, U.K.

F. PACINI, Istituto Astronomia Arcetri, Firenze, ItalyV. RADHAKRISHNAN, Raman Research Institute, Bangalore, India

K. SATO, School of Science, The University of Tokyo, JapanF. H. SHU, University of California, Berkeley, U.S.A.

B. V. SOMOV, Astronomical Institute, Moscow State University, RussiaR. A. SUNYAEV, Space Research Institute, Moscow, Russia

Y. TANAKA, Institute of Space & Astronautical Science, Kanagawa, JapanS. TREMAINE, CITA, Princeton University, U.S.A.

N. O. WEISS, University of Cambridge, U.K.

PHYSICS OF THESOLAR SYSTEM

Dynamics and Evolution, Space Physics,and Spacetime Structure

by

BRUNO BERTOTTI

Department of Nuclear and Theoretical Physics,University of Pavia, Italy

PAOLO FARINELLA

Department of Astronomy,University of Trieste, Italy

and

DAVID VOKROUHLICKÝInstitute of Astronomy,

Charles University, Prague, Czech Republic

Springer-Science+Business Media, B.V.

A C.I.P. Catalogue record for this book is available from the Library of Congress.

Printed on acid-free paper

No part of this work may be reproduced, stored in a retrieval system, or transmittedin any form or by any means, electronic, mechanical, photocopying, microfilming, recording

or otherwise, without written permission from the Publisher, with the exceptionof any material supplied specifically for the purpose of being entered

and executed on a computer system, for exclusive use by the purchaser of the work.

All Rights Reserved

Originally published by in Kluwer Academic Publishers 2003+

ISBN 978-1-4020-1509-0 ISBN 978-94-010-0233-2 (eBook)

DOI 10.1007/ 978-94-010-0 -2233

© 2003 Springer Science+Business Media Dordrecht

Contents

Introd uction x

Useful physical quantities xv ii

I. DYNAMICAL PRINCIPLES I

1.1 Gravitation al equilibrium I

1.2 The equation of stare 6

1.3 Dynam ics of fl uids 9

1.4 Dynam ics of so lid bodies 12

1.5 Transport 16

1.6 Magnetoh ydrodynamics 2 1

1.7 Conservation of magnetism and vortic ity 25

1.8 Kinetic theory 28

2. THE GRAVITATIONAL FIELD OF AN ISOLATED BODY 35

2.1 Spherical harmonics 35

2.2 Harmonic representation of the gravi ty field 42

2.3 The gravity field of the Earth 46

2.4 Gravity fie lds of planetary bodies 54

3. PLANETARY ROTATION 63

3.1 Meas urements of time and distance 63

3.2 Frames of reference 67

3.3 Slowly rotating bodies 74

3.4' Equi librium shapes of bodies in fas t rotation 78

3.5 Rigid-body dynamics: free precession 82

v

VI PHYSICS OF THE SOLAR SYSTEM

3.6 • The rotation of the Eart h and its interi or structure 87

4. GRAVITATIONAL TORQUES AND TID ES 95

4.1 Lunisolar precession 95

4.2 Tidal potential 99

4.3 Tides in a non-rigid Earth 11I2

4.4 T idal harm onics 104

4.5 • Equi librium shape of satellites 11I8

5. THE INTERIOR OF THE EARTH 115

5.1 Seismic propagation 115

5.2 Internal structure of the Earth 120

5.3 Heat generation and flow 127

5.4 Tectonic motions 135

6. PLANETARY MAGNETISM 145

6.1 The main dipole field 146

6.2 Magnetic harmonics and anomalies 147

6.3 Secularchanges and reversals 152

6.4 • The generation of planetary magnetic fields 155

6.5 Planetary magneti c fie lds 161

7. ATMOSPHERES 169

7. 1 Structure of the atmosphere and cl imate variations 169

7.2 Planetary atmospheres 182

7.3 • Radiative transfer 186

7.4 Dynamics of atmospheres 19 1

7.5 Turbulence 198

8. UPPER ATMOSPHERES 21 I

8. 1 General properties 2118.2 Ionosphere 216

8.3 Wa ves in an electron plasma 220

8.4 Atmospheric refract ion 2258.5 Evolution of atmospheres 229

9. THE SUN AND THE SOLAR WIND 239

9.1 The Sun 239

9.2 The solar wind 247

COII/ell/s

9.3 The heliosphere

VII

252

10. MAGNETOSPHERES 261

10.1 The solar wind and the magnc tosphcre 261

10.2 Motion of charged particles in a strong magnetic field 268

10.3 Trapped particles 274

10.4 Magnetohydrodynamic waves 278

10.5 The bow shock 281

10.6 · Cosmic rays and the magnetosphere 284

10.7 Planetary magnetospheres 286

1I. TH E TWO· BODY PROBLEM 297

11.1 Reduction to a central force problem 297

11.2 Keplerian orbits 300

11.3 Bound orbits 302

11.4 Unbound orbits 307

12. PERTURBATION THEORY 3 1.1

12.1 Gauss perturba tion equat ions 313

12.2 Lugrangc pert urbation equations 319

12.3 Atmospheric drag 325

12.4 Oblateness of the prima ry 33 1

12.5 Approximation methods 333

13. THE THR EE-BODY PROBLEM 345

13.1 Equations of motion and the Jacobi constant 346

13.2 Lagrangian points and zero-velocity curves 349

13.3 Stability analysis and motion near the Lagrangian points 355

13.4 Hill' s problem 364

13.5 • Tisserund's criterion 371

14. THE PLANETARY SYSTEM 377

14.1 Planets 377

14.2 Satellites 382

14.3 Asteroids 391

14.4 Transneptunian objects and Centaurs 405

14.5 Comets 4 12

14.6 Interplanetary material and meteorites 422

Vllt PH YSICS OF THE SOLAR SYSTEM

14.7

14.8 •

Planetary rings and ci rcumplanetary dust

From planets to boulders

433

449

IS. DYNAMICAL EVOLUTIO N OF THE SOLAR SYSTEM 459

15.1 Secular perturbations and the stability of the solar system 459

15.2 * Resonances and chaotic behaviour 473

15.3 Tidal orbital evolution 487

15.4 Dynamics of small bodies 493

16. ORIGIN OF THE SOLAR SYSTEM 509

16.1 Mass and structure of the solar nebula 5 10

16.2 Growth of solid grains and formation of plancrcsimals 5 15

16.3 Formation of planetary embryos and accretion of terrestrialplanets 52 1

16.4 Formation of giant planets and satellites 526

16.5 Extrasolar planetary systems 537

17. RELATIVISTIC Ef'f'ECTS IN TH E SOLAR SYSTEM 557

17.1 The equivalence principle 558

17.2 Curvature of spacetime 563

17.3 The nature of gravitation 565

17.4 Weak fields and slow motion 569

17.5 Doppler effect 575

17.6 Relativistic dynamical effec ts 578

17.7 * Gravitcmagnetism 58 1

18. ARTIFICIAL SATELLITES 587

18.1 Launch 587

18.2 Spacecraft and their environment 591

18.3 Forces acting upon an artificial satellite 603

18.4 Space navigation 6 13

19. TELECOMMUNICATIONS 62 1

19.1 The power budget 621

19.2 Spectra 625

19.3 Noise 63 1

19.4 Phase and freq uency measurements 634

19.5 Propagation in a random medium 637

COII/ell/s

20. PRECISE MEASUREME NTS IN SPACE

20. 1 Planetary imaging20.2 Spaee astromc try

20.3 Laser tracking20.4 Testing relativity in space

20.5 Signals and data analysis

Index

IX

64 1

64 1

648

657

665674

687

x

Introduction

PHYSICS OF THE SOLAR SYSTEM

This book is a direct sequel to: B. Bcrtotri and P. Farinclla, "Physics of theEarth and the Solar System, Dynami cs and Evolution . Space Navigat ion. Spa­cc -Time Structure" (K luwcr Academi c Publishers, 1990). Near ly 15 years af­tcr its publication it became evident that the volume was in need of a newedition to keep up with the outstanding progress and the changing perspectivesin this fie ld. David Vokrouhlicky agreed to collaborate on the project and bethe third autho r. On March 25, 2000. afte r a tong illness and a heart tran splant.Paolo Farinella passed away. We then decided that. rather than aiming at asecond edition, it made more sense to rewrite the book anew. While its basiccon te nt and the structure of the chapters are the same , import ant new topicshave bee n added, including the extrasolar planetary systems, tran sneptunianobj ects . acc urate determination of reference frames and new space projec ts .Greater relevance has been given to scmiquantita rive disc ussions be fore intro­d ucing formal developmen ts: many figures have been added and updated andseveral errors correc ted . Mo re emphasis has given to the solar system, whereasgeophysical topics have been left at a less adv anced level. To mark this changethe slightly different title "Ph ysics of the Sol ar Sy ste m" wa s chosen.

We wish to dedicate this book to the mem ory of Paolo Fari nella. an out­stand ing scientist, an invaluable collaborator and a dear friend.

Bru no Bert ott i and David Vok rouhli ck y... ,Pavia and Prague. January 2003

In the so lar system, gra vita tion , [he main force for the b ind ing of largebodies and their dynamics. ha s the role of proragoni st. Classica l (i.e. , non­relativistic ) celestia l mechanics had , already at the cnd of the 19th century,reached an extraord inary deg ree of perfe ction, thank s especially to the Fren chand English schoo ls; new math ematical tools had been discovered, incl udingperturbation theory and the three-body problem, whi ch were subsequently de ­veloped in grea t detail and are now the standa rd basis for curren t work. Cc lcs­tial mechan ics has provided an excellent. and basically correc t, understandingof the dynami cs of the solar sys tem, allowing accurate predictions of the posi-

Introduction XI

tions of planetary bodies in the sky. The comparison and the agreement of thesetheories with painstaking telescope observations are a great success of modemscience.

Before the last World War, four different fields in the parallel area of geo­physics were developed mainly through intelligent and extensive collectionand interpretation of data: gravity anomalies, magnetic and ionospheric dis­turbances. meteorological and cl imatic observations. and seismic oscillations.Progress occurred through slow accumulation and change within the frame­work of long-established paradigms, according to the well known patterns of a"normal" science , but often without an underlying unifying theory. This pro­cess fa voured extreme specialization and the growth of closed scientific com­munities whose main purpose was the development and the application of aparticular experimental technique and {he recording of its results.

Following the Second World War, owing in part to the great progress madein military technology (in particular in radar and rockets), new and much moreexpensive experimental techniques were developed and put to scientific use.They include scientific spacecraft, radio telescopes, Synthetic Aperture Radar,radio and optica l interferometry, and solid state radiation detectors. They havenot only ushered the exploration of bodies in the solar system other than theEarth, but have also greatly increased the accuracy of re levant physical quan­tities. Laser ranging to the Moon and to Ea rth satellites now provides theirdistance to cm accuracy, or even less; coherent and vcry stable microwavebeams can now measure relative velocities in the solar system to accuraciesof !1mfs. Before the last World War, it was known that the Ncwronian pictureof (Euclidcan) space and (uniform) time was not adequate and needed to besupplemented with Relativity Theory (both Special and General); this theory,however, had essentially unobscrvablc consequences in the solar system. Atpresent this scenario is utterly inadequate and celestial mechanics must be setup in spacetime, taking into account the relevant relativistic corrections. Ourmodel of the world has changed, even for practical applications like the GlobalPositioning System.

The above-mentioned instrumental developments together with several pa­radigmatic changes in theoretical understanding have also led to a mergingbetween geophysical and solar system sciences. Indeed, the Earth is best un­derstood as ju st onc of the planers: this is surely the case with major gcopbys­ical developments, i.e ., plate structure, polar motion, the orig in of the dipolarmagnetic field (now understood with the dynamo theory) and global cl imatol­ogy, all of which arc relevant for the whole solar system. Magnetic fields inother planetary bodies, in particular in Jupiter's satellites, have been discov­ered. A recent, major cxample of this widening of horizons is the discoveryof exrrasolar planetary systems which seem to have properties different fromour own and may call for major revisions of our understanding of its formation

XII PHYSICS OF THE SOLAR SYSTEM

and evolution. T he or igin of life is still not understood: although the presentbiochemi cal and biophys ical processes leading to replication and evolution arcwell es tablished , the early origin and history of elementary organ isms and theneed for particu lar atmospheres and places (i.c .. near the hot vents on the bo t­tom of the oceans) is unknown . Thi s topi c is not add ressed in the book.

Th e new instruments are generally characte rized by the ir much greate r size,complexity and economic value; in this, as in other field s. we have see n a qual­itative transition from a "litt le" to a "big" scie nce, where experimental pro­grammes require long and often inflexible planning and large investments ofhuman resources and money. The outer space near the Earth is getting crowdedand the danger of collisions of spacecraft with artifi cial debris produced inlaunches and other space activities, both civilian and military, is relentlesslyincreasing. Furthermore, as far as we know, present military satellites do notcarry weapons: by tacit restraint space activities of all kinds are accepted andrespected by all nations; but, lacking international agrccmcms. this may notlast for ever and the safely of space activity may be endangered.

One must also recognize the great intellectual impact of space explorationwhich has shifted the boundary of unknown lands to natural satellites, planetsand interplanetary space. Now our machines can actually go out there andrepor t back; the magic spell of exploration, so well described in the story ofUlysses in Dante's Divino Conunedia (Inferno, Canro 26), is still with us. Thisfascination produces a convergence of wills and establishes and feeds well­organized scientific communities, commanding a large economic power.

."We now highlight some recent advances. By means of several experimental

techniques, the geopotential of the Earth is now known up to degree and or­der » 360, and further improvements and validations are possible with spacegradiomerers measuring the difference in gravitational acceleration. Accuratedescriptions of the gravity field of other solar system bodies, in particular ofthe Moon, Venus and Mars, are available. With multiple seismic arrays andbetter instrumentation. our knowledge of the interior of the Earth has muchimproved. in particular with the discovery of deviations from spherical sym­metry. especially at the boundary between eore and mantle, leading to a bctrcrunderstanding of convective motions and their consequences for long-wavesurfaec topography.

The spaee asrromcrric mission HIPPARCOS attained a level of accuracyof a milliarcsccond; other astromctric satellites will improve this accuracy bynearly three orders of magnitude, with major consequences for the search forextrasolar planetary systems and astrophysics. Routine monitoring of platemotions and Earth rotation is accomplished with several techniques, in partic-

Introduction X1I1

ular laser ranging to Earth spacecraft, Very Long Baseline Interferometry andthe Global Positioning System.

In 1994, the D/Shoemaker-Levy 9 comet in a close encounter with Jupiterbroke up into 2 1pieces; subsequently the fragments had a spectacular fall intothe planet At that time, the Galileo space probe was nearby, serendipitouslypositioned to observe the event. During its trip to Jupiter, Galileo had providedthe first close-up images of two asteroids, Gaspra and Ida, and discovered asmall moon of the latter. Tens of binary asteroidal systems (including severalin the transneptunian region) were discovered with ground-based observations.The most detailed investigation was obtained for Eros. where a probe landed inFebruary 200 1. Asteroids, both near the Earth and in the main belt, have alsobeen extensively observed with ground-based techniques, in particular radar,providing shape, physical properties, rotation and orbits of more than lOOob­jects. Evaluating and monitoring the risk of (potentially dangerous) impactswith the Earth is the objec t of several projects, including Spaccguard. A newpopulation of objects. hundreds of km in size, has been discovered beyondthe orbit of Neptune, in the zone called the Edgcworth-Kuipcr belt, providinga plausible source for the short-period comets; Pluto is now regarded as thelargest member of a vast population. rather than an individual small planet.Objects on transitory orbits, most likely escaping from the transneptunian beltand wandering in the zone of the large planets. have also been discovered.

In the early 1990's, the Magellan mission obtained high-resolution radarmaps of the surface of Venus that showed that a planer similar in size to theEarth has had a very different geological evolution. Several lunar missionshave unravelled long-standing puzzles of this most extensively known cosmicbody; in particular, the Lunar Prospector spacecraft detected a thin magneto­sphere. The Mars Pathfinder and the Mars Global Surveyor missions broughtabout significant advances in our understanding of Mars, in particular concern­ing the likelihood of vast water reservoirs in the geological past. The in situexploration of Mars, in particular with the Pathfinder mission which landed asmall vehicle on the planet in 1997, is in full swing today.

In 1996, the Galileo mission dropped a probe into Jupiter to explore itsionosphere and atmosphere. The Hubble Space Telescope provided images ofoutstanding resolution of small and/or faraway objects, like Pluto and otherrransncptunians. the asteroids Ccrcs and Vesta and the Jovian satellite 10. In1979, on the basis of dynamical considerations, voleanic activity was predictedfor la and subsequently observed with [he Voyager spacecraft. Since the be­ginning of the 1990's, the Ulysses spacecraft has been providing outstandingmeasurements of the hcliosphcrc, for the first time unravelling its complete,three-dimensional structure and its astonishing dynamics. In Octoher 1997. abig spacecraft - Cassini - was launched to explore the Sarumian system from2004 to 2008 and to release the Huygens probe into the opaque atmosphere of

XIV PHYSICS OF THE SOLAR SYSTEM

Titan. With ground instruments, it was discovered that Uranus and Neptunehave rings. Similarly, ground-based observations have recently allowed dis­covcry of many distant and irregular satellites of giant planets (34 of Jup iter,12 of Saturn and 5 of Uranus). Mercury and Pluro, the least explored planets,are the future targets of several new missions....

The subjec t maucr is developed starting from concrete objects; the rele­vant physical principles are in part discussed in Ch. I and then revisited ordeveloped as the need arises. Mathematical rigour, morpho logical derails anddescriptions of instrumentation are not a priority. Wc assume [hat the readeris acquain ted with undergraduate physics, in particular with dynamic s, clcctro­magnetism, Special Relativity, thermodynamics and statistical physics; startingfrom this basis the reader will hopefully be led up to [he threshold of currentresearch. In choosing the sequence of topics we have tried, when possible, tosatisfy the criterion of increasing difficulty; in many cases a substantial effortwas made to simplify and clarify the material. The earlier book has been thebasis of some courses of lectures, where its didactic structure, aimed at thequalitative and mathematical understanding of very rich and new physical pro­cesses, has been tested. Ch. 17 provides an introduction to General Relativitywith as little formalism as possible and to the extent required for the study ofthe solar system. Particular attention has been given to precise measurementsin space and the structure and evolution of the solar system; in the last Chapterwe discuss several interesting measurement techniques, with a focus on theirprinciples and the accuracy they can attain. The final Section in this Chapter isdevoted to noise and data analysis, a subtle topic that is so important in spaceexpe riments . A large amount of data can now be found on the Web, implying anew kind of organization of scientific work , from which this hook has largelyprofited.

Throughout the book we use the cgs system of units; Maxwell 's equationsare written in esu, non-rationalized units (see eqs. (1.70) and (1.71)). Boldsymbols denote Cartesian vectors. Sometim es, in a diadic notation. a sans serifand capital lette r denotes a tensor of second rank (e.g ., eg. (1.40» ; i = ~is the imaginary unit, but I is the orbital incl ination. To help the reader, wehave indicated with a star the more difficult Sections, which can be left out ina first reading. The problems at the end of each chapter are in no particularorder; they arc also starred to denote difficulty. At the end of eaeh chaptersome books and review articles arc listed for further reading. Here we quote afcw relevant general textbooks (in alphabetic order of authors):

• A.N. Cox (ed.), Alien' s Astrophysieal Quanti ties (4th edition), Springer­Verlag (2000);

Introduction

• W.K. Hartmann, Moons and Planets, Wadsworth (1983);

xv

• M. Hoskin (cd.), The General History of Astronomy, Vol. 2: Plan eta ryA \"rlVlIomY! 1V1n the Rena issance to the Rise ofAstrophysics (R. Talon andC. Wilson , eds.) Cambridge University Press (1995);

• W.M. Kuula. An Introduction to Planetary Physics, Wiley (1968);

• A. Morbidelli, Modem Celestial Mechanics: Aspects or Solar System Dy­namics, Taylor and Francis (2002):

• CD. Murray and S.F. Dermou. Solar System Dynamics, Cambridge Uni­versity Press (2000);

• I. de Paler and J.J. Lissuuer, Planetary Sciences, Cambridge UniversityPress (200 I);

• A.E. Ray, Orbital Motion, Hilger (1978);

• E O. Sracey, Physics of the Earth. Brookfield Press (1992);

• P.R. Wcissman, L.A. Mcl-addcn and T.V. Johnson (cds.). The Encyclopediaof the Solar System. Academic Press (1999).

AcknowledgementsThe revision for the new version was mostly done by B.B. and O.V.; chap­

ter 14 on the planetary system is mainly the work of D.V. Wc arc particu­larly grateful to M. Broz for his competent help with the editing, in particu­lar for all of the figures, which have been prepared with a special software.Z. Knczcvic helped us with the E>-TEX version of the book and suggested manyimprovement". A number of colleagues advised us regarding issues in partic­ular chapters; we would like to thank them (in alphabetic order): B. Bavas­sano (Ch. 10), J. Bicak (Ch. 17), W.E Bottke (Ch.14), S. Breirer (Ch. 12),L Ciufolini (Ch. 17). L Hubeny (Sec. 7.3), G. Laske (Sec. 5.2), F. Mignard(Sec. 20.2) and P. Tanga (Cb. 16).

XVI PHYSICS OF THE SOLAR SYSTEM

Poetic note: Ur tel's aria in Haydn '5 'The Creation '

Nun schwanden vor dern hei ligen StrahleDes schwarze n Dunkel s graulic he Schatten :Der erste Tag enstand.Verrwirru ng weic h. und Ordnung keimt ernpor.

Now vanish before the holy beamsThe gloo my shades of ancient night;The first of days appears.Now chaos ends . and order fair app ears.

These verses, and El . Haydn's ( 1732-1809) music, offer a beautiful expres­sion of the emergence of the o rde r and struc ture of the plane tary system fro mformless interstellar gas after the sudden formation of the Sun. The libret toof this Oratorio (in Ge rman) is the work of van Swieren; he translated for thispurpose an Engli sh text by Mr Lindl cy, based on Milt on 's Paradi se Lost. whic hhas been used here.

Use}I!1physical quantities

Useful physical quantities

(a) Fundam ental and defining co nstants (sec also http://physics .nist.govf)

XVII

arcscc I" = 4 .84S x 10-6 rad

mu s = 0.00 1"corresponds to 3.1 cm on the surface ofthe Earth

c = 2.998 X 1010 emjs = 2.998 x Ht m/svelocity of light

e = 4.80 3 x 10 ' lo esu = 1.602 x 10-1" Coulombmagnitud e of elec tron charge

,v 1.602 X 1O -J2erg = 1.602 x 10- 19 Joule = 11,600 Kenerg y and tempera ture assoc iated with I elect ron volt

G = 6 ,674 x 1O-~ dy ne cm2g-2 = 6.674 X 10- 11 :\ m! kg- 2

grav itational cons tant

" 6.6 26 X 1O- 2J erg s = 6.6 26 X IO- J-l J s

Planck constant

k = 1.38 1 X 10- 16 erg / K = 1.381 x 10- 23 J/K

Boltzmann cons tant

ly Y.46 x lO17 cm = 9 .46 x IO I ~ mlight year

Ill" = Y.l09 X 1O-2~ g = 9. IOY X 10- -11 kgelect run mass

IIIr = 1.673xIO- 11 g= I .673xIo--l7 kgproton mass

pi: = 3.086 X 1018 c m = 3.0S6 x 10' 6 m = 3.26 1yparsec

,I" = ../kT/( 4rr.e2n, )= 743 ";;'('~'~/~'~V7)/"( ,-,,-,~m"'J l cm = 7.43 x 10-) ,)tkT/eVl/(n, m·l ) m

De bye length

(T 21t ~e/152hJ = 5.67 x 10- 5 crg/(l;m2 s K-l)

= 5.67 x 10 K W/tm ' K-l)

Stefun-Bohzmann constant

XVItl PH YSICS OF THE SOLAR SYSTEM

(V p ../4 ....111'2/ 111, = 5.64 x Itr "Il em" rad/ s = 56.4 VII m] rad/splasma frequency

n., = eH/m,I' = 1.76 x 102 (B/ nT) rad/s = 1.76 x 1011 (B ml/weber) radfselec tron cyclot ron frequency

(b) Quantifies related to spec ific objects

AV = 1.496 X 101.1 cm = 1.496 x lOl l mAstronomical Unit (mean heliocent ric distance of the Earth)

H 55 krrt/s/Mrx:(with an uncertainty of "" 15%)Hubble constant

J, = (C - Al/M,.R; = 0.0010 8.26oblarcncss coefficien t of the Earth

1.0 3.845 x 10'1.1 erg/ s = 3.1l45 x JO'6 J/ssolar luminosi ty

Mo = 1.988 x IOn g = 1.988 X 1O ~! kgsolar mass

Ill., 1.41l km = 2.2 x ro- Rosolar gravitational radius

M. = 5.91.2 X 1027 g = 5.91.2 X 102~ kgEarth mass

Ill.. = O.44 l;m = 6.97 x 10- 10 ~

Earth gravitational radius

M, = 317.9 M<J> = M-'"/I047.35Jupite r mass

". = 1.991 X 10" raJ/smean motion of the Earth

R. = 6.371 x I(J'I cm = 6.371 x Hr mmean Earth rad ius

R~ = 6.958 X lO ll) cm = 6.958 x 1(J'l mmean solar radius

0« = ";2G M<fJ /J4 = 11.2 krrt/sescape velocity from the Earth

y = 3.15 x lO'sa year

Use}I!1physical quantities

f = 23b 26'21 "obliquity of the ecl iptic for 12000,0

Fu = 1.3()(i x 10"ergcm-2 s-1 = 1.366 x 10" J m-2 s- 'solar constant (so lar radiation [lux et 1 AV)

w. = (7.2921 X 10-5 - 1.4 X 10-14 T) rad/ ssiderea l angu lar velocity of the Earth and its secular decrease (T in y);

Up, = 50.29 1" Iy = 7.726 X 10.12 radl slunivolur precession constant

(c) Uni ts of power and flux

XIX

Luminositlcs, powers and power tluxcs arc given in egs units {sometimes in Watts (107 erg/s)and W/m 2 ). Teleco mmunica tion engin eers commonly measure ratios of powers in a logarithmicscale, wi th the quantity

1',IO xlog ,o - ,

P,whose unit is the decibel (dB) (Sec. 19 .1).

For luminosity, or brightness, astronomers use the co ncept of magn itude . also based on alogarithmic scale; here is a brief summary. The apparent magnitude m of a star (wi th tota l fluxF ) relative to a refere nce star (w ith total flux F* and magnitudc 111 * ) is

rm - m . = - 2.5 Ioglo F~ .

To roughly describe the colou r of a star and 10 account for the instrum ental bandwidt h, ma g ­

nitude s obtained with standardize d filter; and a restricted passband are also used; the mos tpopular referen ce in the optical reg ime is the Johnson-Morgan -Cousins system (UBV RI; seehttp://obswww .unige.ch/gcpd!sys tcm.hlml).

Name of the fi lterU ultraviolet

B blueV visualR redI infrared

Passband (nm)

300 420360 560460 700530 950700 - 1150

Effective wavele ngth (nm)365445550660SOS

The ahsolmc magnitude M of a star is its eppure nt magnitude at the distance of 10 pc. Since theflux decreases with the dist ance r as I !r,

rm - M = 5 Iog w - - .

10 ",

The absulu te magn itude of a star of luminosity L and the absolute magnitude of the Sun arerela ted by

LM - MC) = - 2.5 Iog,o - .

[ '0

The origin of the magnitude sys tem is chose n so that a star with lum inosity L = 3.055x 10-'5erg/shas the zero abso lute (bolomctric j magn itude.

xx PHYSICS OF THE SOLAR SYSTEM

Due to the obvious reasons, for planets and minor objects in the Solar system the absolutemagnitu de (he nceforth denoted H) is referred to a di stan ce of I All from the Earth and the Sunand a zer ophase angle u.e., at oppositio n).