Orbital Motion, Fourth Edition

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ISBN: 9780750310154 | 0750310154
Cover: Nonspecific Binding
Copyright: 12/31/2004

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- Long established text- Earlier editions have sold strongly and consistently (in excess of 4000)- Thoroughly updated following detailed feedback from course instructors from Europe and USA- Includes material of relevance to engineering students who are the largest growing market for this material - thanks to satellite engineering- First textbook to include the new Caledonian method- Archie Roy - well know author and renown for his style- 3rd edition, in the top list of CORE Astronomy titles- Includes problems and exercises

Preface to First Edition

Preface to Fourth Edition

xvii

The Restless Universe

(15)

Introduction

(1)

The Solar System

(8)

Kepler's laws

(1)

Bode's law

(1)

Commensurabilities in mean motion

(2)

Comets, the Edgeworth--Kuiper Belt and meteors

(2)

Conclusions

(1)

Stellar Motions

(5)

Binary systems

(1)

Triple and higher systems of stars

(2)

Globular clusters

(1)

Galactic or open clusters

(1)

Clusters of Galaxies

(1)

Conclusion

(1)

Bibliography

(1)

Coordinate and Time-Keeping Systems

(28)

Introduction

(1)

Position on the Earth's Surface

(2)

The Horizontal System

(2)

The Equatorial System

(1)

The Ecliptic System

(1)

Elements of the Orbit in Space

(2)

Rectangular Coordinate Systems

(1)

Orbital Plane Coordinate Systems

(1)

Transformation of Systems

(10)

The fundamental formulae of spherical trigonometry

(3)

Examples in the transformation of systems

(7)

Galactic Coordinate System

(1)

Time Measurement

(8)

Sidereal time

(3)

Mean solar time

(2)

The Julian date

(1)

Ephemeris Time

(1)

Problems

(1)

Bibliography

(1)

The Reduction of Observational Data

(18)

Introduction

(1)

Observational Techniques

(3)

Refraction

(1)

Precession and Nutation

(5)

Aberration

(2)

Proper Motion

(1)

Stellar Parallax

(1)

Geocentric Parallax

(4)

Review of Procedures

(2)

Problems

(1)

Bibliography

(1)

The Two-Body Problem

(39)

Introduction

(1)

Newton's Laws of Motion

(1)

Newton's Law of Gravitation

(1)

The Solution to the Two-Body Problem

(3)

The Elliptic Orbit

(13)

Measurement of a planet's mass

(1)

Velocity in an elliptic orbit

(3)

The angle between velocity and radius vectors

(1)

The mean, eccentric and true anomalies

(2)

The solution of Kepler's equation

(2)

The equation of the centre

(1)

Position of a body in an elliptic orbit

(2)

The Parabolic Orbit

(3)

The Hyperbolic Orbit

(4)

Velocity in a hyperbolic orbit

(1)

Position in the hyperbolic orbit

(2)

The Rectilinear Orbit

(2)

Barycentric Orbits

(1)

Classification of Orbits with Respect to the Energy Constant

(1)

The Orbit in Space

(4)

The f and g Series

(2)

The Use of Recurrence Relations

(1)

Universal Variables

(3)

Problems

(1)

Bibliography

100

(1)

The Many-Body Problem

101

(53)

Introduction

101

(1)

The Equations of Motion in the Many-Body Problem

102

(1)

The Ten Known Integrals and Their Meanings

103

(2)

The Force Function

105

(3)

The Virial Theorem

108

(1)

Sundman's Inequality

108

(3)

The Mirror Theorem

111

(1)

Reassessment of the Many-Body Problem

112

(1)

Lagrange's Solutions of the Three-Body Problem

112

(5)

General Remarks on the Lagrange Solutions

117

(1)

The Circular Restricted Three Body Problem

118

(22)

Jacobi's integral

118

(3)

Tisserand's criterion

121

(1)

Surfaces of zero velocity

122

(4)

The stability of the libration points

126

(4)

Periodic orbits

130

(2)

The search for symmetric periodic orbits

132

(2)

Examples of some families of periodic orbits

134

(2)

Stability of periodic orbits

136

(2)

The surface of section

138

(1)

The stability matrix

139

(1)

The General Three-Body Problem

140

(4)

The case C < 0

141

(1)

The case for C = 0

142

(1)

Jacobian coordinates

143

(1)

Jacobian Coordinates for the Many-body Problem

144

(7)

The equations of motion of the simple n-body HDS

145

(2)

The equations of motion of the general n-body HDS

147

(4)

An unambiguous nomenclature for a general HDS

151

(1)

The Hierarchical Three-body Stability Criterion

151

(3)

Problems

152

(1)

Bibliography

152

(2)

The Caledonian Symmetric N-body Problem

154

(40)

Introduction

154

(1)

The Equations of Motions

154

(3)

Sundman's Inequality

157

(5)

Boundaries of Real and Imaginary Motion

162

(2)

The Caledonian Symmetric Model for n = 1

164

(4)

The Caledonian Symmetric Model for n = 2

168

(17)

The Szebehely Ladder and Szebehely's Constant

173

(1)

Regions of real motion in the ρ1, ρ2, ρ12 space

174

(3)

Climbing the rungs of Szebehely's Ladder

177

(5)

The case when E0 < 0

182

(1)

Unequal masses μ1 ≠ μ2 in the n = 2 case

182

(1)

Szebehely's Constant

183

(1)

Loks and Sergysels study of the general four-body problem

184

(1)

The Caledonian Symmetric Model for n = 3

185

(6)

The Caledonian Symmetric N-Body Model for odd N

191

(3)

Bibliography

193

(1)

General Perturbations

194

(40)

The Nature of the Problem

194

(1)

The Equations of Relative Motion

195

(2)

The Disturbing Function

197

(1)

The Sphere of Influence

198

(3)

The Potential of a Body of Arbitrary Shape

201

(5)

Potential at a Point Within a Sphere

206

(2)

The Method of the Variation of Parameters

208

(15)

Modification of the mean longitude at the epoch

212

(2)

The solution of Lagrange's planetary equations

214

(3)

Short- and long-period inequalities

217

(3)

The resolution of the disturbing force

220

(3)

Lagrange's Equations of Motion

223

(3)

Hamilton's Canonic Equations

226

(5)

Derivation of Lagrange's Planetary Equations from Hamilton's Canonic Equations

231

(3)

Problems

232

(1)

Bibliography

233

(1)

Special Perturbations

234

(29)

Introduction

234

(1)

Factors in Special Perturbation Problems

235

(1)

The type of orbit

235

(1)

The operational requirements

235

(1)

The formulation of the equations of motion

235

(1)

The numerical integration procedure

235

(1)

The available computing facilities

235

(1)

Cowell's Method

236

(1)

Encke's Method

237

(2)

The Use of Perturbational Equations

239

(12)

Derivation of the perturbation equations (case h ≠ 0)

241

(3)

The relations between the perturbation variables, the rectangular co-ordinates and velocity components, and the usual conic-section elements

244

(2)

Numerical integration procedure

246

(3)

Rectilinear or almost rectilinear orbits

249

(2)

Regularization Methods

251

(2)

Numerical Integration Methods

253

(10)

Recurrence relations

255

(1)

Runge--Kutta four

255

(1)

Multistep methods

256

(1)

Numerical methods

256

(5)

Problems

261

(1)

Bibliography

261

(2)

The Stability and Evolution of the Solar System

263

(36)

Introduction

263

(1)

Chaos and Resonance

264

(2)

Planetary Ephemerides

266

(1)

The Asteroids

266

(3)

Rings, Shepherds, Tadpoles, Horseshoes and Co-Orbitals

269

(15)

Ring systems

269

(1)

Small satellites of Jupiter and Saturn

270

(3)

Spirig and Waldvogel's analysis

273

(8)

Satellite--ring interactions

281

(3)

Near-Commensurable Satellite Orbits

284

(2)

Large-Scale Numerical Integrations

286

(6)

The outer planets for 120 000 years

286

(1)

Element plots for 1 000 000 years

286

(1)

Does Pluto's perihelion librate or circulate?

287

(1)

The outer planets for 108 years---and longer!

288

(2)

The analytical approach against the numerical approach

290

(1)

The whole planetary system

291

(1)

Empirical Stability Criteria

292

(3)

Conclusions

295

(4)

Bibliography

296

(3)

Lunar Theory

299

(16)

Introduction

299

(1)

The Earth--Moon System

299

(2)

The Saros

301

(2)

Measurement of the Moon's Distance, Mass and Size

303

(1)

The Moon's Rotation

304

(2)

Selenographic Coordinates

306

(1)

The Moon's Figure

306

(1)

The Main Lunar Problem

307

(2)

The Sun's Orbit in the Main Lunar Problem

309

(1)

The Orbit of the Moon

310

(1)

Lunar Theories

311

(2)

The Secular Acceleration of the Moon

313

(2)

Bibliography

314

(1)

Artificial Satellites

315

(30)

Introduction

315

(1)

The Earth as a Planet

315

(11)

The Earth's shape

317

(1)

Clairaut's formula

318

(3)

The Earth's interior

321

(1)

The Earth's magnetic field

321

(1)

The Earth's atmosphere

322

(2)

Solar--terrestrial relationships

324

(2)

Forces Acting on an Artificial Earth Satellite

326

(1)

The Orbit of a Satellite About an Oblate Planet

327

(8)

The short-period perturbations of the first order

330

(3)

The secular perturbations of the first order

333

(1)

Long-period perturbations from the third harmonic

333

(1)

Secular perturbations of the second-order and long-period perturbations

334

(1)

The Use of Hamilton--Jacobi Theory in the Artificial Satellite Problem

335

(2)

The Effect of Atmospheric Drag on an Artificial Satellite

337

(5)

Tesseral and Sectorial Harmonics in the Earth's Gravitational Field

342

(3)

Problems

343

(1)

Bibliography

343

(2)

Rocket Dynamics and Transfer Orbits

345

(35)

Introduction

345

(1)

Motion of a Rocket

345

(5)

Motion of a rocket in a gravitational field

346

(1)

Motion of a rocket in an atmosphere

347

(1)

Step rockets

348

(2)

Alternative forms of rocket

350

(1)

Transfer Between Orbits in a Single Central Force Field

350

(18)

Transfer between circular, coplanar orbits

351

(3)

Parabolic and hyperbolic transfer orbits

354

(1)

Changes in the orbital elements due to a small impulse

355

(2)

Changes in the orbital elements due to a large impulse

357

(1)

Variation of fuel consumption with transfer time

358

(2)

Sensitivity of transfer orbits to small errors in position and velocity at cut-off

360

(4)

Transfer between particles orbiting in a central force field

364

(4)

Transfer Orbits in Two or More Force Fields

368

(12)

The hyperbolic escape from the first body

368

(2)

Entry into orbit about the second body

370

(2)

The hyperbolic capture

372

(1)

Accuracy of previous analysis and the effect of error

373

(3)

The fly-past as a velocity amplifier

376

(2)

Problems

378

(1)

Bibliography

379

(1)

Interplanetary and Lunar Trajectories

380

(28)

Introduction

380

(1)

Trajectories in Earth--Moon Space

380

(1)

Feasibility and Precision Study Methods

381

(1)

The Use of Jacobi's Integral

382

(1)

The Use of the Lagrangian Solutions

382

(1)

The Use of Two-Body Solutions

383

(3)

Artificial Lunar Satellites

386

(5)

Relative sizes of lunar satellite perturbations due to different causes

387

(3)

Jacobi's integral for a close lunar satellite

390

(1)

Interplanetary Trajectories

391

(2)

The Solar System as a Central Force Field

393

(1)

Minimum-Energy Interplanetary Transfer Orbits

394

(5)

The Use of Parking Orbits in Interplanetary Missions

399

(6)

The Effect of Errors in Interplanetary Orbits

405

(3)

Problems

406

(1)

Bibliography

407

(1)

Orbit Determination and Interplanetary Navigation

408

(22)

Introduction

408

(1)

The Theory of Orbit Determination

409

(2)

Laplace's Method

411

(2)

Gauss's Method

413

(2)

Olbers' Method for Parabolic Orbits

415

(2)

Orbit Determination with Additional Observational Data

417

(4)

The Improvement of Orbits

421

(3)

Interplanetary Navigation

424

(6)

Stabilized platforms and accelerometers

424

(2)

Navigation by on-board optical equipment

426

(2)

Observational methods and probable accuracies

428

(1)

Bibliography

429

(1)

Binary and Other Few-Body Systems

430

(28)

Introduction

430

(2)

Visual Binaries

432

(3)

The Mass--Luminosity Relation

435

(1)

Dynamical Parallaxes

436

(1)

Eclipsing Binaries

437

(5)

Spectroscopic Binaries

442

(3)

Combination of Deduced Data

445

(1)

Binary Orbital Elements

445

(2)

The Period of a Binary

447

(1)

Apsidal Motion

447

(1)

Forces Acting on a Binary System

448

(1)

Triple Systems

448

(3)

The Inadequacy of Newton's Law of Gravitation

451

(1)

The Figures of Stars in Binary Systems

452

(1)

The Roche Limits

453

(1)

Circumstellar Matter

454

(2)

The Origin of Binary Systems

456

(2)

Problems

457

(1)

Bibliography

457

(1)

Many-Body Stellar Systems

458

(36)

Introduction

458

(1)

The Sphere of Influence

458

(1)

The Binary Encounter

459

(3)

The Cumulative Effect of Small Encounters

462

(2)

Some Fundamental Concepts

464

(1)

The Fundamental Theorems of Stellar Dynamics

465

(3)

Jeans's theorem

467

(1)

Some Special Cases for a Stellar System in a Steady State

468

(1)

Galactic Rotation

469

(16)

Oort's constants

470

(2)

The period of rotation and angular velocity of the galaxy

472

(1)

The mass of the Galaxy

473

(2)

The mode of rotation of the Galaxy

475

(4)

The gravitational potential of the Galaxy

479

(1)

Galactic stellar orbits

480

(4)

The high-velocity stars

484

(1)

Spherical Stellar Systems

485

(4)

Application of the virial theorem to a spherical system

486

(1)

Stellar orbits in a spherical system

487

(2)

The distribution of orbits within a spherical system

489

(1)

Modern Galactic Studies

489

(5)

Problems

492

(1)

Bibliography

493

(1)

Answers to Problems

494

(8)

Appendix I: Astronomical and Related Constants

502

(4)

Appendix II: The Earth's Gravitational Field

506

(2)

Appendix III

508

(2)

Mean Elements of the Planetary Orbits

508

(1)

Approximate Elements of the Ten Largest Asteroids

509

(1)

Appendix IV

510

(4)

Physical Elements of the Planets

510

(1)

Planetary Ring Systems

511

(1)

Satellite Elements and Dimensions

512

(2)

Index

514

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Orbital Motion, Fourth Edition

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Table of Contents

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