cole g.h.a., woolfson m.w. planetary science, the science of planets around stars

PLANETARY SCIENCE

THE SCIENCE OF PLANETS AROUND STARS



PLANETARY SCIENCE

THE SCIENCE OF PLANETS AROUND STARS

George H A Cole
Department of Physics, University of Hull, UK

Michael M Woolfson
Department of Physics, University of York, UK

Institute of Physics Publishing
Bristol and Philadelphia


# IOP Publishing Ltd 2002
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Universities UK (UUK).
British Library Cataloguing-in-Publication Data
A catalogue record of this book is available from the British Library.
ISBN 0 7503 0815 X
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Typeset by Academic ‡ Technical, Bristol
Printed in the UK by Bookcraft, Midsomer Norton, Somerset


CONTENTS

INTRODUCTION

xix

A REVIEW OF THE SOLAR SYSTEM
1

THE UNITY OF THE UNIVERSE
1.1. Cosmic abundance of the chemical elements
1.2. Some examples
Problem 1

1
1
2
4

2

THE
2.1.
2.2.
2.3.
2.4.
2.5.
2.6.
2.7.

SUN AND OTHER STARS
The interstellar medium
Dense cool clouds
Stellar clusters
A scenario for formation of a galactic cluster
Main sequence stars and their evolution
Brown dwarfs
Stellar companions
Problem 2

6
6
6

8
10
12
12
12
15

3

THE
3.1.
3.2.
3.3.
3.4.

PLANETS
An overview of the planets
Orbital motions
Orbits of the planets
Planetary structuresÐgeneral considerations
3.4.1. Planetary magnetic ®elds
Problems 3

16
16
16
19
21
24
26

4

THE TERRESTRIAL PLANETS
4.1. Mercury
4.1.1. The surface of Mercury
4.1.2. Mercury's magnetic ®eld
4.1.3. Mercury summary

27
27
28
31
31
v


vi

Contents
4.2.

4.3

4.4.

5

Venus
4.2.1. The surface of Venus

4.2.2. The atmosphere of Venus
4.2.3. Venus and magnetism
4.2.4. Venus summary
The Earth
4.3.1. The shape of the Earth
4.3.2. Surface composition and age
4.3.3. Changing surface features
4.3.4. Surface plate structure
4.3.5. Heat ¯ow through the surface
4.3.6. Earthquakes
4.3.6.1. The crust
4.3.6.2. The mantle
4.3.6.3. The core
4.3.7. The Earth's atmosphere
4.3.8. The Earth's magnetic ®eld
4.3.9. Earth summary
Mars
4.4.1. The surface of Mars
4.4.1.1. The highlands
4.4.1.2. The plains
4.4.1.3. Volcanic regions
4.4.1.4. Channels and canyons
4.4.2. Consequences of early water
4.4.3. Later missions
4.4.4. The atmosphere of Mars
4.4.5. Magnetism and Mars
4.4.6. Mars summary
Problem 4

THE MAJOR

5.1. Jupiter
5.1.1.
5.1.2.
5.1.3.
5.1.4.
5.1.5.
5.2. Saturn
5.2.1.
5.2.2.
5.2.3.
5.2.4.
5.2.5.
5.3. Uranus
5.3.1.
5.3.2.
5.3.3.

PLANETS AND PLUTO
The internal structure of Jupiter
Heat generation in Jupiter
The atmosphere of Jupiter
Jupiter's magnetic ®eld
Jupiter summary
The internal structure of Saturn
Heat generation in Saturn
The atmosphere of Saturn
Saturn's magnetic ®eld
Saturn summary
The internal structure of Uranus
Heat generation in Uranus

The atmosphere of Uranus

32
32
35
38
38
38
39
39
41
41
46
49
51
52
52
52
53
54
54
54
55
57
58
60
62
62
65
66

66
67
68
68
68
70
72
73
74
74
75
75
75
76
77
78
78
78


Contents

5.4.

5.5.

5.3.4. The magnetic ®eld of Uranus
5.3.5. Uranus summary
Neptune
5.4.1. The internal structure of Neptune

5.4.2. Heat generation in Neptune
5.4.3. The atmosphere of Neptune
5.4.4. Neptune's magnetic ®eld
5.4.5. Neptune summary
Pluto
5.5.1. Physical characteristics of Pluto
5.5.2. Relationship with Charon
Problem 5

vii
79
79
80
80
81
81
81
82
82
83
83
84

6

THE MOON
6.1. The physical characteristics of the Moon
6.1.1. The distance, size and orbit of the Moon
6.2. Earth±Moon interactions
6.2.1. The diurnal tides

6.2.2. The e€ects of tides on the Earth±Moon system
6.3. Lunar and solar eclipses
6.3.1. Solar eclipses
6.3.2. Eclipses of the Moon
6.4. The lunar surface
6.4.1. The maria
6.4.2. The highlands
6.4.3. Breccias
6.4.4. Regolith: lunar soil
6.5. The interior of the Moon
6.5.1. Gravity measurements
6.5.2. Lunar seismicity
6.5.3. The interior structure of the Moon
6.5.4. Heat ¯ow and temperature measurements
6.6. Lunar magnetism
6.7. Some indications of lunar history
6.8. Moon summary
Problems 6

85
85
85
88
88
89
90
90
90
91
92

93
95
95
96
96
98
98
98
100
101
103
104

7

SATELLITES AND RINGS
7.1. Types of satellites
7.2. The satellites of Mars
7.3. The satellites of Jupiter
7.3.1. Io
7.3.2. Europa
7.3.3. Ganymede
7.3.4. Callisto
7.3.5. Commensurabilities of the Galilean satellites
7.3.6. The smaller satellites of Jupiter

105
105
105
107

107
109
110
111
112
113


viii

Contents
7.4.

7.5.
7.6.
7.7.
7.8.

7.9.

The satellites of Saturn
7.4.1. Titan and Hyperion
7.4.2. Mimas, Enceladus, Tethys, Dione and co-orbiting satellites
7.4.3. Rhea and Iapetus
7.4.4. Phoebe
7.4.5. Other small satellites
The satellites of Uranus
The satellites of Neptune
Pluto's satellite
Ring systems

7.8.1. The rings of Saturn
7.8.2. The rings of Uranus
7.8.3. The rings of Jupiter
7.8.4. The rings of Neptune
General observations
Problem 7

114
114
115
117
117
118
118
119
120
120
120
122
122
123
123
123

8

ASTEROIDS
8.1. General characteristics
8.2. Types of asteroid orbits
8.3. The distribution of asteroid orbitsÐKirkwood gaps

8.4. The compositions and possible origins of asteroids
Problem 8

124
124
126
127
128
131

9

COMETS
9.1. Types of comet orbit
9.2. The physical structure of comets
9.3. The Oort cloud
9.4. The Kuiper belt
Problems 9

132
132
135
139
142
143

10

METEORITES
10.1. Introduction

10.2. Stony meteorites
10.2.1. The systematics of chondritic meteorites
10.2.2. Achondrites
10.3. Stony irons
10.4. Iron meteorites
10.5. The ages of meteorites
10.6. Isotopic anomalies in meteorites
10.6.1. Oxygen in meteorites
10.6.2. Magnesium in meteorites
10.6.3. Neon in meteorites
10.6.4. Other isotopic anomalies
Problems 10

144
144
148
148
151
153
155
159
159
159
160
162
163
163

11

DUST IN THE SOLAR SYSTEM
11.1. Meteor showers

164
164


Contents

ix

11.2. Zodiacal light and gegenschein
11.3. Radiation pressure and the Poynting±Robertson e€ect
Problem 11
12

166
166
167

THEORIES OF THE ORIGIN AND EVOLUTION OF THE SOLAR SYSTEM
12.1. The coarse structure of the Solar System
12.2. The distribution of angular momentum
12.3. Other features of the Solar System
12.4. The Laplace nebula theory
12.4.1. Objections and diculties
12.5. The Jeans tidal theory
12.5.1. Objections and diculties
12.6. The Solar Nebula Theory
12.6.1. The transfer of angular momentum

12.6.2. The formation of planets
12.6.2.1. Settling of dust into the mean plane
12.6.2.2. Formation of planetesimals
12.6.2.3. Planets and cores from planetesimals
12.6.2.4. Gaseous envelopes
12.6.3. General comments
12.7. The capture theory
12.7.1. The basic scenario of the capture theory
12.7.2. Modelling the basic capture theory
12.7.3. Planetary orbits and satellites
12.7.4. General Comments
12.8. Ideas on the evolution of the Solar System
12.8.1. Precession of elliptical orbits
12.8.2. Near interactions between protoplanets
12.9. A planetary collision
12.9.1. The Earth and Venus
12.9.2. Asteroids, comets and meteorites
12.10. The origin of the Moon
12.10.1. Darwin's ®ssion hypothesis
12.10.2. Co-accretion of the Earth and the Moon
12.10.3. Capture of the Moon
12.10.4. A single impact theory
12.10.5. Capture in a collision scenario
12.11. Other bodies in the Solar System
12.11.1. Mars and Mercury
12.11.2. Neptune, Triton, Pluto and Charon
12.12. Isotopic anomalies in meteorites
12.13. General comments on a planetary collision
Problem 12

168
168
168
169
170
170
171
172
172
173
173
174
174
174
174
174
175
175
175
176
176
178
178
179
179
179
181
181
181
182

182
183
183
185
185
185
187
189
189

TOPICS
A
BASIC MINERALOGY
A.1. Types of rock

190
190


x

Contents
A.2.

A.3.

Types of minerals
A.2.1. Silicates
A.2.2. Carbonates
A.2.3. Oxides

A.2.4. Other minerals
Rock composition and formation
A.3.1. Igneous rocks
A.3.2. Sedimentary rocks
A.3.3. Metamorphic rocks
A.3.3.1. Thermal metamorphism
A.3.3.2. Pressure metamorphism
A.3.3.3. Regional metamorphism
Problems A

191
192
193
193
194
194
194
196
198
199
199
200
200

B

GEOCHRONOLOGYÐRADIOACTIVE DATING
B.1. Comments on atomic structure
B.1.1. Nuclear structure
B.1.2. The emissions

B.2. The laws governing radioactive decay
B.2.1. The physical principles
B.2.2. A simple age measurement
B.2.3. Decay in a radioactive chain
B.2.4. Bifurcated decay
B.2.5. Age determination: the closure temperature
B.2.6. The isochron diagram
B.2.6.1. Rubidium 3 strontium
B.2.6.2. Samarium 3 neodymium
B.2.6.3. Rhenium 3 osmium : lutetium 3 hafnium
B.2.6.4. Uranium 3 lead
B.2.6.5. Thorium 3 lead
B.2.6.6. Potassium 3 argon
B.2.7. The concordant diagram
B.3. Using nuclear reactors
B.3.1. Argon±argon dating
B.3.2. Fission-track dating
Problems B

202
202
202
203
204
204
205
205
206
206
208

208
210
210
210
211
211
211
213
213
214
215

C

THE VIRIAL THEOREM
Problems C

216
217

D

THE JEANS CRITICAL MASS
D.1. An application of the Virial Theorem
D.2. From condensations to condensed bodies
Problem D

218
218
220

221

E

FREE-FALL COLLAPSE
Problem E

222
224


Contents

xi

F

THE EVOLUTION OF PROTOSTARS
F.1. The Hertzsprung±Russell diagram
F.2. The evolution of a protostar
Problems F

225
225
227
229

G

THE

G.1.
G.2.
G.3.
G.4.
G.5.
G.6.

230
230
231
232
232
232
234
234

H

ENERGY PRODUCTION IN STARS
H.1. Proton±proton (p-p) reactionsÐa classical view
H.2. A quantum-mechanical description
H.2.1. The distribution of proton relative energies
H.2.2. The rate of making close approaches
H.2.3. The tunnelling probability
H.2.4. The cross-section factor
H.2.5. The energy generation function
H.3. Nuclear reaction chains in the Sun
Problem H

235

235
236
237
238
238
239
239
240
242

I

EVOLUTION OF STARS AWAY FROM THE MAIN SEQUENCE
I.1.
An overview of the evolutionary path
I.2.
Hydrogen-shell burning
I.3.
Helium ignition and helium core burning
I.4.
Hydrogen and helium shell burning
I.5.
The evolution of higher mass stars
I.6.
Final comments
Problem I

243
243
245

246
247
248
250
250

J

THE
J.1.
J.2.
J.3.
J.4.

251
251
251
253
254
255

K

PLANETS AROUND OTHER STARS
K.1. Planets around neutron stars
K.2. E€ects of companions on the central star
K.3. Finding the speed and mass of the planet
K.4. The preliminary results of observations
K.4.1. Mass distributions
K.4.2. Characteristics of orbits

EQUILIBRIUM OF STARS ON THE MAIN SEQUENCE
Conditions for modelling a main-sequence star
The pressure gradient
The included-mass gradient
The luminosity gradient
The temperature gradient
Making models of stars
Problem G

CHANDRASEKHAR LIMIT, NEUTRON STARS AND BLACK HOLES
Some basic quantum mechanics principles
Degeneracy and white dwarf stars
Relativistic considerations
Neutron stars and black holes
Problems J

256
256
256
257
260
260
262


xii

Contents
K.5.

K.6.
K.7.
K.8.

The constitution of the companions
Atmospheres
Possibilities of conditions for life
A ®nal comment
Problem K

263
263
263
264
264

L

SOLAR-SYSTEM STUDIES TO THE BEGINNING OF THE SEVENTEENTH
CENTURY
L.1. Views of the ancient world
L.2. Nicolaus Copernicus
L.3. Tycho Brahe
L.4. Johannes Kepler
L.4.1. Kepler's determination of orbital shapes
L.5. Galileo Galilei
Problems L

265
265

268
268
269
270
273
275

M

NEWTON, KEPLER'S LAWS AND SOLAR-SYSTEM DYNAMICS
M.1. Isaac Newton, Kepler and the inverse-square law
M.2. General orbits
M.3. Kepler's laws from the inverse-square-law force
M.4. Establishing a Solar-System distance scale
M.5. The dynamics of elliptical orbits
M.6. Some special orbital situations
M.6.1. Parabolic paths of projectiles
M.6.2. Transfer orbits between planets
Problems M

276
276
277
279
281
281
284
284
286
287

N

THE FORMATION OF COMMENSURATE ORBITS

288

O

THE ATMOSPHERE OF THE EARTH
O.1. A simple isothermal atmosphere
O.2. The structure of the Earth's atmosphere
O.2.1. The variation of temperature with height
O.2.2. The upper reaches of the atmosphere
O.2.2.1. The exosphere
O.2.2.2. The thermosphere
O.2.2.3. The homopause
O.2.3. The lower reaches of the atmosphere
O.2.3.1. The mesosphere
O.2.3.2. The stratosphere and troposphere
O.3. The dynamics of the atmosphere
Problems O

293
293
296
296
297
297
301

301
301
301
302
304
306

P

THE PHYSICS OF PLANETARY INTERIORS
P.1. Introduction
P.2. Applying the Virial Theorem

307
307
307


Contents
P.3.

P.4.
P.5.
P.6.
P.7.
P.8.

The energies involved
P.3.1. The kinetic (degeneracy) energy
P.3.2. The electrostatic energy

P.3.3. The gravitational energy
P.3.4. The energies combined
Maximum radius
Conditions within a planet of maximum radius and mass
Specifying a planet: the planetary body
The minimum mass for a planetary body
P.7.1. The rigidity of a solid body
The internal structure of a planetary body
P.8.1. The crust
P.8.2. The maximum height of surface elevations
P.8.3. Hydrostatic equilibrium
P.8.4. Mantle and core
P.8.5. Variation of pressure and density with depth
P.8.6. Specifying K
Problems P

xiii
307
308
308
309
309
310
311
312
312
313
315
315
315

315
316
316
317
317

Q

THE TRANSFER OF HEAT
Q.1. Conduction of heat in a solid
Q.1.1. The equation of heat conduction in a solid
Q.2. Comments on the description of ¯uid ¯ows
Q.2.1. The ¯uid parameters
Q.2.2. The dimensionless parameters
Q.2.3. Physical interpretation: rearrangements
Problems Q

318
318
319
320
321
321
322
323

R

SEISMOLOGYÐTHE INTERIOR OF THE EARTH
R.1. The behaviour of planetary material for an impulsive release of energy

R.1.1. Waves without a boundary
R.1.2. Waves near a boundary surface
R.1.3. Full-body waves
R.2. Attenuation of seismic waves
R.3. Seismometers and seismographs
R.3.1. Travel times and seismic speeds
R.3.2. Re¯ection and refraction across a boundary
R.4. Seismic tomography
R.5. Long-term hydrostatic equilibrium of planetary material
R.6. The Adams±Williamson method using earthquake data
R.7. Moment of inertia considerations
Problem R

324
324
324
326
327
328
328
329
329
331
331
331
332
333

S

MOMENTS OF INERTIA
S.1. The moment of inertia of a uniform sphere about a diameter
S.2. The moment of inertia of a spherically symmetric distribution
S.3. The moment of inertia of a spheroid about the symmetry axis
Problem S

334
334
336
336
338


xiv

Contents

T

THE GRAVITATIONAL FIELD OF A DISTORTED PLANET
T.1. The gravitational potential of a spinning planet
Problems T

339
339
340

U

PRECESSION OF THE EARTH'S SPIN AXIS

U.1. The basic mechanism
U.2. The simple con®guration
Problem U

341
341
342
343

V

INTRINSIC PLANETARY MAGNETISM
V.1. Magnetic poles
V.2. Magnetic elements: isomagnetic charts
V.3. The form of the ®eld
V.4. Analysing the ®eld
V.5. The result for the Earth
V.5.1. The dipole approximation
V.5.2. The non-dipole component of the magnetic ®eld
V.6. Time dependencies of the magnetic ®eld
V.6.1. The dipole ®eld
V.6.2. The non-dipole secular ®eldÐthe secular variation
V.6.3. Reversals of the direction of magnetization
V.6.4. Pole wander
V.6.5. Sea ¯oor spreading
V.7. Magnetism of other Solar-System planets
V.8. Intrinsic magnetism of non-solar planets
Problem V

345

345
346
347
351
352
353
353
355
355
356
358
358
359
361
363
363

W

MAGNETIC INTERACTIONS BETWEEN PLANET AND STAR
W.1. Transient magnetic components
W.2. The origin of the atmospheric ®elds
W.3. The solar wind
W.4. Coupling between plasma streams and magnetic ®elds
W.5. E€ects of the solar wind
W.5.1. The e€ect on the Earth's ®eld
W.5.2. The trapped particles
W.5.3. Whistlers
W.5.4. The plasma tail
W.6. The magnetospheres of other planets

W.6.1. The major planets
W.6.2. Examples of other planetary bodies
W.7. Motion through the interstellar medium
W.8. Companions to other stars
Problem W

364
364
366
367
369
371
371
373
373
373
375
375
377
379
379
379

X

PLANETARY ALBEDOES
X.1. The brightness of Solar-System bodies seen from Earth
X.2. The equilibrium temperature of the planets
Problems X

380
380
381
382


Contents
Y

THE
Y.1.
Y.2.
Y.3.
Y.4.

PHYSICS OF TIDES
The basics of the tide-raising mechanism
Spring tides and neap tides
The recession of the Moon from the Earth
The magnitude of the mid-ocean tide
Y.4.1. Oscillations of ¯uid spheres
Problems Y

Z

DARWIN'S THEORY OF LUNAR ORIGIN

xv
383
383

386
387
389
390
392
393

AA THE ROCHE LIMIT AND SATELLITE DISRUPTION
AA.1. The Roche limit for ¯uid bodies
AA.2. The Roche limit for a solid body
AA.3. The disruption of a solid satellite
AA.4. The sphere of in¯uence
Problems AA

395
395
396
398
400
401

AB TIDAL HEATING OF IO
AB.1. Elastic hysteresis and Q values
AB.2. Tidal stressing in Io
Problems AB

402
402
403
404

AC THE RAM PRESSURE OF A GAS STREAM
Problem AC

405
406

AD THE TROJAN ASTEROIDS
Problem AD

407
410

AE HEATING BY ACCRETION
AE.1. Models for the accretion of planets and satellites
AE.2. Accretion without melting
AE.3. Accretion with melting
AE.4. A more realistic initial thermal pro®le
Problem AE

411
411
411
412
414
415

AF PERTURBATIONS OF THE OORT CLOUD
AF.1. Stellar perturbations
AF.2. Perturbations by giant molecular clouds

AF.3. Perturbations by the galactic tidal ®eld
AF.4. Conclusion
Problem AF

416
416
419
420
422
423

AG RADIATION PRESSURE AND THE POYNTING±ROBERTSON EFFECT
AG.1. The force due to radiation pressure
AG.2. The Poynting±Robertson e€ect
Problem AG

424
424
424
425


xvi

Contents

AH ANALYSES ASSOCIATED WITH THE JEANS TIDAL THEORY
AH.1. The tidal distortion and disruption of a star
AH.2. The break-up of a ®lament and the formation of protoplanets
Problem AH

426
426
428
429

AI

THE VISCOUS-DISK MECHANISM FOR THE TRANSFER OF ANGULAR
MOMENTUM
Problem AI

430
431

AJ

MAGNETIC BRAKING OF THE SPINNING SUN
AJ.1. Coupling of particles to ®eld lines
AJ.1.1. The form of the magnetic ®eld
AJ.1.2. The present rate of loss of angular momentum
AJ.2. The early Sun
Problem AJ

432
432
432
433
434
435

AK THE SAFRONOV THEORY OF PLANET FORMATION
AK.1. Planetesimal formation
AK.2. Planets from planetesimals
Problem AK

436
436
437
439

AL THE EDDINGTON ACCRETION MECHANISM
AL.1. The accretion cross section
Problem AL

440
440
441

AM LIFE ON A HOSPITABLE PLANET
AM.1. We are here
AM.2. Early life on Earth
AM.3. Chemical composition
AM.4. General properties
AM.5. Instability due to radiation: role of an atmosphere
Ã
AM.6. Stability of the surface region
AM.7. How many planets might carry advanced life? The Drake equation
AM.8. Conclusion

442
442
443
445
445
447
448
448
449

AN THE ROLE OF SPACE VEHICLES

451

AO PLANETARY ATMOSPHERIC WARMING

456

AP

459
459
461
462
462
463

MIGRATION OF PLANETARY ORBITS
AP.1. De¯ection in a hyperbolic orbit
AP.2. Motion in an in®nite uniform planar medium

AP.3. Resistance for a highly elliptical orbit
AP.4. Resistance for a circular orbit
Problem AP

AQ INTERACTIONS IN AN EMBEDDED CLUSTER
AQ.1. The initial conditions

464
464


Contents

xvii

AQ.2. Conditions for an interaction
AQ.3. Numerical calculations
Problem AQ

465
465
466

APPENDIX I

467

PHYSICAL CONSTANTS

474

SOLUTIONS TO PROBLEMS

476

REFERENCES

499

INDEX

501



INTRODUCTION

In choosing a title we had in mind that there are many planetary systems other than the Solar System.
The book is concerned with the science associated with the planets, the stars that they orbit and the
interactions between them. The relationships of several extra-solar planets to their parent stars
di€er from that of any Solar-System planet to the Sun and this can give clues either about the way
that planets are formed or the way that they evolve after formation. For this reason we conclude
with a chapter giving current ideas about the way that planetary systems come into being. There is
general agreement that the formation of planets is intimately connected with the formation of
starsÐalthough there are important di€erences of view about the nature of the connection. To give
a rounded and complete picture we include material on the formation, evolution and death of stars
and those properties of the Sun that in¯uence the planets of the Solar System.
The origin of the study of the Solar System, at a truly scienti®c level, occurred in the seventeenth
century when Newton explained the motion of Solar-System bodies by the application of the laws of
mechanics combined with the inverse-square law of gravitational attraction. With subsequent

improvements in telescope technology and, more latterly, through the achievements of space science
we now have detailed descriptions of many Solar-System bodies and have been able to analyse
samples from some of them. The range of what constitutes stellar and planetary science has
expanded in almost explosive fashion in the past few decades and includes aspects of many di€erent
conventional sciencesÐalthough physics and astronomy certainly predominate.
There are many excellent textbooks that describe stars and the Solar System in some detail and
give qualitative explanations for some features and quantitative explanations where the underlying
science is not too complicated. At the other extreme there are monographs and papers in learned
journals that deal with aspects of stellar and planetary science in a rigorous and formal way that is
suitable for the specialist and where, sometimes, jargon is used that is incomprehensible to the
outsider. The readership we have in mind for the present work is the senior undergraduate student
in physics or astronomy or the new graduate student working in planetary science who requires an
overview of the whole subject before embarking on detailed study of one narrow aspect of it. Our
analyses of aspects of stellar and planetary science are aimed to be accessible to such studentsÐor,
indeed, to any others meeting the ®eld for the ®rst time.
There are two main components of this text. The ®rst of these is a general overview of the nature of
stars and of the Solar System that can be read independently and quotes the important results that have
been obtained by scienti®c analysis. For those unfamiliar with stellar properties or the overall structure of
the Solar System we recommend that this part should be read before looking at the other material, to
acquire a general picture of the system as a whole and the interrelationships of the bodies within it.
xix


xx

Introduction

The second component is that which justi®es the title of this work. It is a set of 41 topics in which
the detailed science is described. The topics are very variable in length. Some, for example Topic A that
deals with mineralogy, are as long as a normal chapter of a book. Others, for example Topic AG

concerned with the mechanical interactions of radiation and matter, are one or two pages long.
Together these topics provide a description of the great bulk of the underlying science required to
explain the main features of the Solar System.
Problems are given at the end of chapters and most topics, designed to give the reader a
quantitative feeling for stellar and Solar-System phenomena. Solving such problems clearly has
some educational value but, even when the reader fails to solve a problem, reference to the provided
solution may o€er useful insights.
Our Earth and the other planets have undergone substantial changes in their states over many
aeons by the action of natural forces. An understanding of the nature of the Solar System and of
the in¯uences that govern its behaviour may allow an appreciation to be developed of what can
in¯uence our planet in the future.


CHAPTER 1

THE UNITY OF THE UNIVERSE

Studies of the Universe, especially in recent times, have brought us to the realization that it is an entity
and not a number of disconnected and unrelated units. Viewing stars, galaxies and gas clouds, either
nearby or in deepest space (which is also equivalent to observing the Universe either in very recent
times or long ago), shows the same formations involving broadly the same chemical compositions.
The galaxies are made of essentially the same components with common mean chemical compositions.
Gas clouds form a family of like objects. For this reason it is possible to consider a representative
galaxy, a representative star or a representative cloud of material. There are, of course, variations
of composition but the variations will be small deviations about some mean.
1.1.

COSMIC ABUNDANCE OF THE CHEMICAL ELEMENTS

In most cases the composition of an object can only be studied from a distance. The radiation it emits is

analysed in a spectrometer to determine the frequencies present and also the relative intensities of the
spectral emission or absorption lines. Modern studies cover the whole range of the electromagnetic
spectrum from the most energetic regions (gamma rays and X-rays) to the least energetic (radio
waves). Radioactive elements emit particles during decay and these can also be detected. Each chemical
element emits a characteristic range of frequencies when stimulated in di€erent ways so that the
component chemical elements can be determined. Molecules usually have vibration and electronic
transitions, closely spaced in energy, that give characteristic spectral bands so enabling their presence
to be determined if they are stable under the prevailing conditions.
This procedure has its limitations. Bodies cannot be examined in interior regions if the radiation
or particles cannot escape so that, for example, the composition of the Sun can be found directly only
in its surface regions. To infer the composition of the inner regions requires the exercise of theory,
which may need to be modi®ed as more information accumulates. Bearing this in mind, the cosmic
abundance of the chemical elements is generally accepted as that given in table 1.1. The abundances
are given relative to silicon as the unit.
Hydrogen and helium are overwhelmingly the most abundant elements. Helium is an inert gas; the
second most abundant chemically active element is oxygen. The oxide of hydrogen is water, H2 O, so we
will not be surprised to meet a high abundance of water in its various phases. The third and fourth most
abundant elements, carbon and nitrogen, are also chemically active giving simple compounds such as
CO, CO2 , NH3 , CH4 and many others. The vast number of carbon-based organic compounds, many
very complex and almost completely consisting of C, N, O and H, is the basis of life on Earth.
1


2

The unity of the Universe
Table 1.1. The cosmic abundance of the chemical elements relative to silicon.
Element

Relative abundance

(number of atoms with Si ˆ 1)

Hydrogen, H
Helium, He
Oxygen, O
Carbon, C
Nitrogen, N
Neon, Ne
Magnesium, Mg
Silicon, Si
Aluminium, Al
Iron, Fe
Sulphur, S
Calcium, Ca
Sodium, Na
Nickel, Ni

3X18 Â 104
2X21 Â 103
22.1
11.8
3.64
3.44
1.06
1
0.85
0.83
0.50
0.072
0.060

0.048

Relative abundance
by mass

0.9800
)
0.0133
9
>
>
>
>
>
>
>
>
>
>
>
=
>
>
>
>
>
>
>
>
>

>
>
;

0.0017

0.00365

Silicon is a relatively abundant element, as are magnesium, aluminium, calcium, sodium,
potassium and iron. These elements, together with oxygen, form the great bulk of the silicate
materials that constitute most of the Earth. Other non-silicate minerals, such as oxides and sulphides,
also occur but they are much less common. Minerals form according to the local conditions of
pressure and temperature and whether, in particular, cooling processes take place quickly or
slowly. A systematic description of di€erent kinds of minerals and the rocks that they form is
given in Topic A.
For condensed matter, there are a few rules that control the general form. The controlling
features are the anities of di€erent atoms to di€erent types of crystalline bonds. In many cases the
elements segregate into silicate, sulphide and metal according to the following general rules.
.

.

.

Elements in Groups 1 and 2 of the Periodic Table have a tendency to combine with oxygen in
oxides and silicates. Elements such as K, Ba, Na, Sr, Ca, Mg and Rb are called lithophilic elements
(from the Greek for stone, lithos) because they tend to be found in stones.
Elements in Groups 10 and 11 of the Periodic Table tend to appear as sulphides. Thus Cu, Zn, Pb,
Sn and Ag are called chalcophilic elements (after the Greek khalkos for their leading member,
copper).

Some elements may combine in compounds as, for instance, silicates but may also appear in
metallic form. Such elements are Fe, Ni, Co, As, Ir, Pt, Au and Ag. These are called siderophilic
(after the Greek sideros for iron, their representative element).

A detailed analysis of the chemical anities in di€erent conditions is quite complicated but these
simple rules are often useful in understanding particular situations.
1.2.

SOME EXAMPLES

Before moving on it is useful to give some examples of the universality of chemical materials. The ®rst
involves the comparison between the mean compositions of the Solar System, the Orion nebula and a


Some examples

3

Table 1.2. Log10 (relative abundance), normalized to hydrogen as 12, for three di€erent entities.
Element

Solar system

Orion nebula

Planetary nebula

H
He
C

N
O
F
Ne
Na
S
Cl
Ar
K
Ca

12.00
10.9
8.6
8.0
8.8
4.6
7.6
6.3
7.2
5.5
6.0
5.5
6.4

12.0
11.04
8.37
7.63
8.79

12.00
11.23
8.7
8.1
8.9
4.9
7.9
6.6
7.9
6.9
7.0
5.7
6.4

7.86
7.47
4.94
5.95

planetary nebula. Data for 13 chemical elements are listed in table 1.2. The similarities between the
three lists are very striking.
As expected, similar bodies frequently display similar mineral compositions. This is displayed
in table 1.3 for a selection of minerals on the Earth and Venus, often regarded as sister planets because
of their similar size and mass. As will be seen there are di€erent compositions for di€erent kinds of site
on Earth and for the sites of the Russian Venera landers. The Venus data tend to be similar to the
oceanic material on Earth. This suggests that Venus never underwent the processes forming crustal
and continental material.
Meteorites form a rich source of information about minerals present in the Solar System. The
ages of meteorites, as measured by radioactive dating (Topic B), are about 4X5 Â 109 yearsÐthe

accepted age for the Solar System as a whole. A list of the most common minerals found in meteorites
is given in table 1.4. They are similar to those on Earth although they must originate from some
condition or event in the very early Solar System.
These examples involving minerals exclude the most abundant elements, H and He, but these
latter can be included by consideration of larger bodies. It is known that all normal stars are made
Table 1.3. The relative abundance by percentage mass for regions of the Earth and Venus. The hostile
conditions on Venus made rapid measurements essential; pressure, temperature and chemical attack destroyed
each probe after about twenty minutes.
Oxide

Earth (continental
crust) (%)

Earth (oceanic
crust) (%)

Venera 13
site (%)

Venera 14
site (%)

SiO2
Al2 O3
MgO
FeO
CaO
TiO2
K2 O

60.1
15.6
3.6
3.9
5.2
1.1
3.2

49.9
17.3
7.3
6.9
11.9
1.5
0.2

45
16
10
9
7
1.5
4

49
18
8
9
10
1.2

0.2


4

The unity of the Universe
Table 1.4. The minerals most commonly found in meteorites.
Mineral

Composition

Kamacite
Taenite
Troilite
Olivine
Orthopyroxine
Pigeonite
Diopside
Plagioclase

(Fe, Ni) (`7% Ni)
(Fe, Ni) (b13% Ni)
FeS
(Mg, Fe)2 SiO4
(Mg, Fe) SiO3
(Ca, Mg, Fe) SiO3
Ca(Mg, Fe) Si2 O6
(Na, Ca)(Al, Si)4 O8

Table 1.5. The main components of the visible regions of the Sun and the major planets by mass percentage.

Molecule

Sun
(%)

Jupiter
(%)

Saturn
(%)

Uranus
(%)

Neptune
(%)

H2
He
H2 O
CH4
NH3
H2 S

85
15
0.11
0.06
0.016
0.003

89.9
10.2
4 Â 10ÿ4
0.3
0.026
Ð

96.3
3.3
Ð
0.3
0.012
Ð

82.5
15.2
Ð
2.3
Ð
Ð

80.0
19.0
Ð
1.5
Ð
Ð

mostly of hydrogen with a substantial component of helium and a small admixture of other elements.

This also applies to the major planets of the Solar System. A comparison between the main surface
components of the Sun and the major planets is shown in table 1.5.
There is a general similarity between the di€erent bodies but it must be stressed that these are
surface components and do not refer directly to the interiors. There is, nevertheless, for Saturn and
Jupiter the implicit assumption that these percentages would be very broadly the same if the full planetary inventory could be taken. The basis of this assumption is that these large and massive planets
would have been formed from similar material that formed the Sun and that the escape velocity
from them is so large that they would have retained all their original material. On this basis, the interior
behaviour of Saturn, for example, is described in terms of a greater helium concentration than in
surface regions. On the other hand the lesser proportion of hydrogen detected in Uranus and Neptune
may be due to losses from these lower mass planets for which escape velocities are also lower.
Wherever we look in the cosmos we are seeing a very similar grouping of the chemical elements. It
would seem safe to assume that the material composition of the Solar System and its neighbourhood is
not untypical of such systems everywhere.
Problem 1
1.1

The density distribution of Saturn is modelled as
(
 1a4 )
r
& ˆ &0 1 ÿ
R