SUBJECT INDEX

Absolute rotation, 50, 51 Absorption bands, 284

coefficent, 144-145, 397 lines, 258

Accretion, 202, Secs. 16.5 and 16.6 of gas, 361-363, 365

Acoustic waves,152, 165, 187-188, 349 Action, 181, 371-372, 378, 458

general relativistic, 378 Active gravitational mass, 374 Adiabatic flow, 261

equation of state, 187 invariant, 181-182, 184-186, 202,

458 motion, 17 scale height, 137 temperature gradient, 107-108, 137 transformation, 17

Adrastea, 294 Affme parameter, 373, 381, 386 Albedo, 138, 275, 278, 284, 294,

396-397, 420 Alfven's speed, 187

waves, 167, Sec. 9.3, 194 Aliasing, 462 Alias lines, 442 Allan's variance, 429-431, 435 Amalthea, 277-278, 301 Amplifiers, 428 Andesitic magma, 112 Antennas, 397, 406-407, Sec. 19.1, 435

effective area, 419 gain, 418-419

Anticyclonic flow, 151-152 Apocentre distance, 208-209 Apollo missions, 105, 132, 446 Apsidal line, 208

period of the earth, 85 period of the moon, 85

Archimedes' force, 152 Arcsec, xiii

465

Areal velocity, 206 Argument of pericentre, 213, 305

Gauss'equation, 222 relativistic secular change, 385,

457, 459, 460 Ariel, 277-278 Artificial satellites, Ch. 18

perturbations, Sec. 18.1 Associated Legendre functions, 30, 44,

122, 410 Astenosphere, 112 Asteroids, 249, 251, 275, 276, 280, Sec. 14.3, 287-289, 292, 298, 301,

305, 322 albedos, 284 binary, 364 collisional evolution, 282, 291, 300,

303, 353 compositions, 284 families, 281-282 formation, 360-361 lightcurve amplitudes, 300, 364 mass, 282, 339 mean motions, 281 outer-belt, 287, 291, 363 poles, 283-284 resonant, 321, 323 rotation periods, 282-283, 300 secular perturbations, 311 shapes, 282, 300 taxonomic types, 284-285

Astrometry, Sec. 20.3 Astronomical Unit, xiii Aten-Apollo-Amor objects, 280, 291,

314 Atlas, 294 Atmosphere, Ch. 7

density, 229, 395 dynamics, Sec. 7.4 gray, Sec. 7.3 locally exponential, 228

466 SUBJECT INDEX

mass loss, 174-175 primary, 276 rotation rate, 231 secondary, 276 stellar, 147 structure, Secs. 7.1 and 8.4 upper, Ch. 8

Atomic time, 46 Aurorae, 162, 184, 195, 452 Averaging method, 236-237, 306-307,

321, 384-385 Axial dipole hypothesis, 126

Background radiation, 50 Bandwidth, 425, 428, 431, 435, 455

synthesis, 455 Barotropic regime, 17 Bayesian estimation, 440-442 Bernoulli's equation, 262, 361 Big bang, 258 Binary stars, 449

planets, 243 Birefringence, 166, 169, 170 Bit rate, 407, 453 Black holes, 377 Bohr-Sommerfeld rule, 181 Boltzmann's constant, xiii, 427

equation, 25 Booker's equation, 175 Boundary layer, 15-16, 153-155 Bow shock, Sec. 9.4, 271 Brehmsstrahlung, 158 Bulk modulus, 12, 101

Callisto, 277-278 Carbonaceous chondrites, 284, 291 Cassini's division, 314 Catastrophic impacts, 292, 358, 364-365 CCD, 453-454 Ceres, 282, 283, 302-303, 361 Chandler'S wobble, 52-53

frequency, 53, 68 Channel information capacity, 425 Chaotic dynamics, 287, Sec. 15.2,

319-325 Chapman's approximation, 160-161, 175 Charge-coupled device, 453-454 Charon, 277-278, 336 Chiron, 280, 287, 288 Circulation, 319-320, 323

Clairaut's relation, 57, 59 Clebsch-Gordon theorem, 56 Clemmow and Mullaly plot, 167 Close encounters, 252-253, 286, 287,

304-306, 314, 316, 318, 321, 323, 325, 340, 353-354, 360, 361 Coagulation, 345 Collision frequency, 25 Collisional accumulation, Sec. 16.4

evolution, 282 fragmentation, 280, 282, 299, 303,

353, 364-365 Collisionless dissipation, 190 Coma, 287-288 Comets, 252, 260, 280, 284, Sec. 14.4,

289, 305, 333 Encke, 288 formation, 360 Halley, 289 inclinations, 285 mass, 286 new, 286 non-gravitational forces, 285,

287-289, 335 nuclei, 285, 287-289, 290, 335 Oort cloud, 285-286, 360 semimajor axes, 285 short-period, 286-287 size, 286 Swift-Tuttle, 290 tail, 287-288 Temple 2, 290

Commensurabilities, 225, 237, 281, 288, 314, 316, 321

low-order, 237 Compressibility, 12 Compressional modes, 101 Computer algebra, 306 Concentration of a species, 6 Conductivity, electrical, 19, 127,

163-164, 267-268 thermal, 105, 109-110

Conduction, 105 Confidence level, 440 Conjunction, 315-316, 323, 324 Conservation of angular momentum,

206, 310, 325, 338, 350, 356, 360, 363, 384, 402, 458

of mass, 8-9, 348, 361 of momentum, 9, 261, 403

SUBJECT INDEX 467

of magnetism, Sec. 1.6 of vorticity, Sec. 1.6

Continental drift, 111 Convective energy transport, 108

instability, 107-108, 152-153 Convection, 108-110, 128-129, 256 Coorbital satellites, 279, 301 Corio1is acceleration, 243

force, 244, 250 parameter, 149

Comer reflectors, 420 Corona, 256, 261, 269, 433, 435

structure, Sec. 13.3 Coronal holes, 266 Correlation coefficient, 441-442

function, 422-423, 425-426, 431, 437, 454

matrix, 438-441 time, 423

Cosmic rays, Sec. 9.6, 270 Cosmological nucleosynthesis, 258 Cosmos satellites, 229 Coupled resonances, 323 Covariance matrix, 440-441 Craters, 302 Creep deformation, 109, 302 Critical argument, 316, 322, 323

inclination, 239 Current density, 18-19 Curvature tensor, 369-370, 376-377 Cutoff, 166, 359, 361, 430 Cybele, 283 Cyclonic flow, 151-152 Cyclotron frequency, xv, 162, 178-181,

199

D' Alembert's equation, 93, 187 Davida, 283 De Broglie's waves, 165 Debye length, xiv, 25, 267-268, 335 Decibel, 418 Declination, 51-52 Deep Space Network, 420-421, 428 Deimos, 279, 363 Dessler-Parker relation, 183 Diffraction, 448, 452 Diffusion coefficient, 14

flux, 173 Digital filtering, 313 Dilatation, 10

Dione, 277-279, 323 Dipole field, Sec. 6.1, 198 Dispersion, Sec. 19.5

curves, 99, 10 1 relations, 98, 165, 187-188, 202,

349-350, 365 Displacement, 10 Distance measurements, Sec. 3.1 Distribution function, 24 Doppler effect, 48, 331, Sec. 17.5,

429-430 gravitational shift, 377-378, 382,

430, 462 in special relativity, 382-383, 430 measurements, 393, 430-431 transversal, 48, 383 tracking, 43, 430

Drag, aerodynamic, 403 atmospheric, Sec. 11.3, 391, 393,

395-396, 402, 405, 408, 445 Epstein formula, 344 -free spacecraft, 393-394, 417, 457 gravitational, 403 in planetary envelopes, 363-364 perturbations, 221, 224, Sec. 11.3,

331, 334, 344-345 Stokes' law, 344

Drift velocity, 178, 183 Dust particles, 291, Secs. 14.5 and 15.1 Dynamical equations, Sec. 1.2

families, 281-282, 324 evolution mechanisms, Ch. 15 principles, Ch. 1

Dynamics as geometry, Sec. 17.3 of dust particles, Sec. 15.1 of rigid bodies, Sec. 3.5 of solid bodies, Sec. 1.3 of the atmosphere and the oceans,

Sec. 7.4 relativistic, Secs. 17.4 and 17.6

Dynamo theory, 102, Sec. 6.4 laminar, 128

Earth, albedo, 138, 396-397 angular velocity, xv atmosphere, Ch. 7--­core, 103, 110 dynamical properties, 274 eccentricity, 304, 311 escape velocity, xiv

468 SUBJECT lNDEX

figure, Sec. 3.3 gravitational field, Ch. 2 gravitational radius, xiv, 395, 460 interior, Ch. 5 internal structure, Sec. 5.3 magnetic field, 103, Ch. 6 magnetosphere, Ch. 9 mantle, 103, 109, 122, 363-364 mass, xiv mean radius, xiv orbital mean motion, xiv perihelion, 311 physical properties, 275 quadrupole coefficient, xiii, 37-38,

224, 444, 446 rotation, Ch. 3, 325, 398, 444

Earth-moon system, 243, 246, 251, 279-280, 336, 363-365

Earthquakes, Sec. 5.1, 115 Earth-to-moon spacecraft, 249 Eccentric anomaly, 210-211, 227,

384-385 Eccentricity, 207,

forced, 323, 330 Gauss' equation, 221, 333 proper, 323

Eclipses, 86, 328, 397 Ecliptic, 51-52, 212 Eddies, 154-155 Effective area, 419

cross-section, 332 potential energy, 206 temperature, 428, 462

Elastic behaviour, 11, 92 energy, 11

Electromagnetic waves, 165 in a plasma, Sec. 8.2 in the ionosphere, Sec. 8.3

Electron charge, xiii columnar density, 170 cyclotron frequency, xv, 162 cyclotron resonance, 166 mass, xiv volt, xiii

Ellipticity, 6, 37, 57, 58 Emission intensity, 144 Enceladus, 277-278, 301

-Dione resonance, 323 Energy-momentum tensor, 380-381 Entalpy, 106

Entropy, 16-17, 106 Eos, 282 Epimetheus, 301 Equilateral triangular points, 246, 280 Equilibrium,

hydrostatic, 4, 101, 256, 341 radiative, Sec. 7.1 and 7.2, 341 shapes, Secs. 3.3, 3.4, 4.5, 297,

298, 300 Equivalence principle, 48, 74, 367, 374,

377, 381, 389, 391, 446, 456, 460-461, 463

experimental verification, 374, 446 weak, 374

Ergodic theorem, 426 Errors, 438-440 ERS-1 satellite, 392 Escape velocity, 282, 402

mean, 174 Estimation, Sec. 20.1

Bayesian, 440-442 spectral, 442

Estimator, 439, 441 Eiller equations, 372 Eillerian derivative, 8

formulation, 349 Eiller's equations, 64, 68, 372, 381

theorem, 112 Eunomia, 283 Euphrosyne, 283 Europa, 277-278, 324 Evection period, 86 Excess angle, 369, 371, 389 Exosphere, 173, 177

Faculae, 260 Faraday effect, 170 Fast angular variables, 236-237 Fermat's principle, 93, 170 Fermi's coordinates, 376

theorem, 376 Filters, 427-428, 454

Kalman, 438 linear, 427 low-pass, 427, 454

Fireballs, 288, 289 Fission instability, 63, 298, 363-365 Fit, least squares, Sec. 20.1 Flares, 168, 260, 266 Flat-earth approximation, 42-43, 136,

SUBJECf INDEX 469

149-150 F1uorescence, 146 Fourier expansion, 422, 424

transfonn, 423-425 Fraunhofer spectrum, 258 Free energy, 106

molecular flow, 25, 136, 344 precession, Sec. 3.5 and 3.6

Frequency standards, 45-46, 429-430, 461

Gain, 418-419, 428 Gal, 40 Galaxy, 240, 242 Galilean satellites, 277-280, 301, 324,

336, 453 Galileo mission, 453 Ganymede, 277-278, 324 Gauge, 387 Gauss' coefficients, 122-123

equations, 219, Sec. 11.1, 240, 333, 334, 336, 345, 410

theorem, 2, 204, 342, 348, 350 Gaussian curvature, 370-371

distribution, 440-441 Geminid meteor shower, 290 GEM-Tl geopotential model, 395 General covariance, 369, 381

precession, 78 relativity, Ch. 17, 395, Sec. 20.6

Geodesic deviation, equation, 376 Geodesics, Sec. 17.2, 376, 382, 459 Geoid, 9, 38, 383, 392 Geomagnetic dipole, Sec. 6.1, 179

field, Ch. 6 hannonics, Sec. 6.2 reversals, Sec. 6.4 secular changes, Sec. 6.4

Geometrical optics, 93-95, 169, 332, 435

Geopotential, Secs. 2.2, 2.3, 2.4, 398 coefficients, 38, 237-238, 395-396,

409 tidal perturbation, 400

Geostationary satellites, Sec. 18.4 Geostrophic approximation, 150-152

flow, Sec. 7.4

Giotto probe, 289 Glaciations, 38-39 Gold's theory of lo's torus, 272 GPS satellites, 116, 392 Grains, 343

coagulation, 345 growth and settling, Sec. 16.2 radial transport, 345-346

Granulation, 260 Gravimeter, 40 Gravitational acceleration, 374

cross-section, 356-357 constant, xiii, 205, 395 constant, cosmological change,

457-458 deflection of light, 386, 450, 460 energy, 3-5 equilibrium, Sec. 1.1 field, Ch. 2 frequency shift, 377-378, 382 Gauss'theorem, 2 instability, 342, Sec. 16.3, 359 mass, 374, 389, 460 N-body problem, 242 potentials, 379-380 radius, xiv, 7, 257, 305, 367, 456 sphere of influence, 412-414 waves, 209, 398, 451, 460

Gravitomagnetism, 7, 380, Sec. 17.7, 460 Gravity anomaly, 39-40

waves, 152-153, 156 Gray atmosphere, Sec. 7.3 Greenhouse effect, 139, 141-143, 147 Group velocity, 165, 167, 432 Grunesein's parameter, 108 Guiding centre approximation, Sec. 9.1 Gyroscope, 222

Half-life, 105 Halley's comet, 289 Hamiltonian function, 232, 373, 384,

385, 390, 461 systems, 232 theory, 181

Hamilton's equations, 232, 235 Heat equation, 16

Geosynchronous satellites, 394-397, Sec. 18.4, 451-452 Geothennal flux, 105

401, flow, Sec. 5.4 generation, Sec. 5.4 transfer, 105-106

Gilbert's theory, 118, 121 transport coefficient, 16, 107, 109,

470 SUBJECT INDEX

127 Hektor, 364 Helicity, 130, 133 Heliopause, 270 Heliosphere, 269 Heliosynchronous orbit, 408, 451 Heterosphere, 171-172 Hidalgo, 280, 287 Hierarchical stability, 249

systems, 242, 249 Hilda asteroids, 281, 314 Hill's curves, 245

lobe, 255 problem, 255

HIPPARCOS, 447-449 Hirayama families, 281-282, 324 Hohmann transfer orbit, 414-416 Homosphere, 171-172 Hooke's law, 11

tensor, 11 Hopf function, 148 Hot spots, 112-113, 116

volcanism, 116 Hour angle, 46, 72 Hubble's constant, xiii, 50

time, 457 Hydrogen maser, 46, 430, 435 Hydrostatic equilibrium, 4, 101, 256,

341 Hyperbolic orbits, 214-216 Hyperion, 277-278, 301

resonance with Titan, 314, 318 rotation, 324

Iapetus, 277-278 Ignorable coordinates, 198, 226 Impact parameter, 214-215, 216, 435 Inclination, 213

critical, 239 Gauss' equation, 222 proper, 323

Incompressible flow, 9 modes, 101

Indirect term, 307 Inertial frames, 49

mass, 373-374, 389 Interamnia, 283 Interferometry, 393, 450-451, 463 Internal energy, 17, 106 Interplanetary dust, 291, Sec. 15.1

material, Sec. 14.5 navigation, Sec. 18.5 probes, 249, Sec. 18.5, 435 space, 433

10, 21, 272, 324, 330-331 torus, 272 volcanism, 272, 330

Ionization, by solar radiation, Sec. 8.1, 335 cross-section, 158-159, 161 layers, 162

Ion cyclotron frequency, 162 Ionosphere, 122, Ch. 8 IRAS satellite, 290, 291 Irreducible representations, 32 Irrotational field, 96 ISEE satellites, 196

Jacobian determinant, 248, 251 Jacobi constant, Sec. 12.1, 248-249,252,

255 ellipsoids, 61-63, 90

Janus, 295, 301 Jeans' frequency, 101, 347, 352

instability, Sec. 16.3 Joule heating, 164 Juno, 283 Jupiter, 276, 339-340, 453

atmosphere, 136 dynamical properties, 274 formation, 362-363 heat balance, 139 magnetic field, 121, 132, 295 magnetosphere, 271-272 mass, xiv perihelion, 311-313 physical properties, 275 radio emission, 271 ring, 292-295 satellites, 277-279, 301, 303,

363-364 -scattered planetesimals, 361

Kalman fIltering, 438, 463 Kaula's rule, 41, 44, 124 Kelvin-Helmoltz process, 195 Keplerian elements, Sec. 10.2-3, 219,

305-306 orbits, Sec. 10.2

Kepler's equation, 211, 214, 215-216,

SUBJECT lNDEX 471

217. 223. 308 laws. 204 second law. 206 third law. 206. 209. 220-221. 235.

243. 252. 296. 317. 326. 333. 385. 394. 395. 409. 410. 445

Kinematical viscosity. 15. 153 Kinetic theory. Sec. 1.7 Kirchhoff'S law. 143-144 Kirkwood gaps. 281. 314. 323. 360 Kleopatra. 364 Kolmogorov's spectrum. 154-155. 156.

434 Koronis. 282 Knudsen flow. 25 K40. 105

Lag. 422-423. 433 LAGEOS satellite. 38, 49. 50, 54. 116,

336, 392, 394-398, 401-402, 409, 420, Sec. 20.2, 460, 462

area-to-mass ratio. 443 non-gravitational forces. 445-446 orbital elements, 444 semimajor axis decay, 445

Lagrangean derivative. 8 formulation, 348-349

Lagrange's brackets. 233-234. 240 function. 198. 372. 378, 380. 382.

383, 384, 386. 387. 390 perturbation equations. 219.

Sec. 1 1.4. 234. 235. 239. 306-310, 316-318, 322-323. 336

reduced function, 198 solution, 310-311 theorem, 307

Lagrangian points, Sec. 12.2. 354 stability, Sec. 12.3

Lame's constants. 11. 93 Laminar dynamo. 128

viscosity coefficient. 156 Landau damping. 27 Laplace resonance. 324. 330 Larmor gyration. 22. 182

radius. 178 Laser ranging. 49, 328. 392, 409. 420.

Sec. 20.2 lunar. 328, 402. 420. 435, 443.

446. 460 Latent heat of fusion. 299

Laval nozzle, 265. 272 Least squares fit. Sec. 20.1 Legendre equation, 44

polynomials. 30. 395 Length of the day, 51. 157, 408.

455-456 increase. 328 variations, 400-401

Lense-Thirring precession, 388-389. 460 Lenz's law. 19

vector. 207-208. 216. 309 Libration. 311-312. 316, 320. 322-323 Lightcurve amplitude. 300

photometry. 282 Light year. xiii Limb darkening. 148. 258 Linear filters. 427

solution. 310-311 Litosphere. 106, 109. 112 Little ice age. 260 Longitude of the ascending node. 213

Gauss' equation. 221 Longitudinal plasma waves, 164, 166 LONGSTOP integration. 312-314 Lorentz force. 18, 178. 295. 336

gas. 267 gauge. 387 transformations. 368. 379

Loss cone. 184. 202 Love numbers. 58. 81-82. 328, 399-400

waves. 99 Lunakhod missions, 446 Lunisolar precession. 52. Sec. 4.1. 222.

381 period. 77

L, •... L, lagrangian points. 246-249. 255, 354

Mach's cone, 189 number. 189. 191-193, 271 principle. 49-50

Maclaurin spheroids. 61-62. 90 Magnetic anomalies, Sec. 6.2

bipolar regions. 260 colatitude. 119, 126 confinement. 20 coupling, 340 declination, 118. 126 diffusion coefficient, 127 diffusion equation, 21, 127

472 SUBJECT INDEX

dip angle, 118, 126 dipole field, Sec. 6.1 field generation, Sec. 6.4 frozen-in field, 22-23, 127, 268,

340 hannonics, Sec. 6.2 lines of force, 121 moment, 180 potential, 119, 121 pressure, 270 Reynolds number, 128-129, 267 rigidity, 202 sheath, 194-195 storm, 196 stress tensor, 20 tail, 194 transitions, 267 trapping, Sec. 9.2, 197

Magnetohydrodynamics, Sec. 1.5, 187 equations, 19-20

Magnetopause, 190, 194-195 Magnetosonic waves, 188 Magnetosphere, Ch. 9, 260

energetic particles, Sec. 9.6 planetary, Sec. 13.4

Magnitude, xiii, 300, 447 MAGSAT, 119, 124 Main asteroid belt, 280, 287, 325 Mappings, 321 Mariner 4, 453 Mariner 7, 458 Mariner 10, 132 Mars, 276, 305, 361, 457-458

atmosphere, 136 climate changes, 140 dynamical properties, 274 physical properties, 275 satellites, 301, 363 tracking, 48-49

Mas, xiv Mass, active gravitational, 374

gravitational 374 inertial, 373-374 loss, 342, 402-403

Maunder minimum, 139, 260 Maxwellian distribution, 24, 173, 174 Maxwell's equations, xi, 19, 163-165,

187 Mean anomaly, 211, 305, 306-307

anomaly at epoch, 212 escape velocity, 174

field electrodynamics, 128 free path, 13-14, 25, 135, 269,

344 longitude, 235 longitude at epoch, 235 motion, 211, 306

Measurement errors, 438-440 Megaimpact hypothesis, 364-365 Mercury, 132, 275, 276, 280, 302, 305,

308, 457 dynamical properties, 274 lack of satellites, 364 magnetic field, 121, 132 magnetosphere, 194, 196, 271 perihelion advance, 240, 367, 457,

459-460 physical properties, 275 spin-orbit coupling, 314, 324

Mesosphere, 171 Meteorites, 105, 284, Sec. 14.5, 314,

398 achondrites, 291 ages, 291 . chondrites, 284, 291 falls, 290 iron, 284, 291 stony-iron, 284, 291

Meteoroids, 288, 289-290, 333 Meteors, 288, 289

showers, 290 sporadic, 290

Metis, 294 Metric, 369, 376, 383

corrections, 370, 376, 378-380 minkowskian, 368-370, 374, 377 Schwarzschild, 380-381 tensor, 369, 376

Michelson interferometers, 450-451 Milankovitch's theory, 13 8-139 Mimas, 277-279, 295, 301

-Tethys resonance, 324 Minkowski coordinates, 370

metric, 368-370, 374, 377, 456 space-time, 369-371

Minor planets, 243 Miranda, 277-279 Moho, 99 Molnyia-type satellites, 239 Moments of inertia, 36, 44 Monopole field, 29, 35, 36

acceleration, 219, 394, 396

SUBJECf INDEX 473

Month, anomalistic, 86 draconitic, 86 synodic, 86 tropic, 84

Moon, 105, 280, 305, 324, 333 apsidal period, 84 laser ranging, 328, 402, 420, 435,

443, 446, 460 magnetic field, 121, 132 nodal period, 85 orbital data, 277 origin, 358, 363-364 physical properties, 278 rotation, 325, 329 semimajor axis increase, 325,

327-329 synchronization distance, 327 synodic period, 398-399

Multiple stars, 242 Murnaghan's equation, 102

Natural satellites, 249 Navier-Stokes equation, 15 N-body problem, 242, 305 Nebular theory, 338 Neptune, 276, 302, 340

dynamical properties, 274, 312-313 formation, 359 magnetic field, 121, 133 magnetosphere, 271 orbital energy, 312-313 physical properties, 275 -Pluto resonance, 314, 324, 360 rings, 292-294 satellites, 277-279, 363

Nereid, 277-278 Neutral sheet, 193 Newton's canals, 58, 60, 89 Noise, Sec. 19.3

photon, 451 thermal, 427-428 white frequency, 429, 431 white phase, 430, 431

Non-gravitational forces, 285, 287-289, 304, 305, Sec. 15.4, 352, Sec. 18.1, 445-446, 457

Non-singular orbital elements, 235, 305, 308-310

Normal modes, 163, 348, 349 Nortvedt effect, 446, 463

Numerical error, 312-314 integrations, 242, 311-314, 321

Nutations, 52, 78, 400 Nyquist frequency, 442

-Johnson effect, 427 spectrum, 427-428

Oberon, 277-278 Oblate shapes, 64 Oblique rotators, 133, 271 Obliquity, 51-52

of the ecliptic, xiv, 76 Oceanic loading, 399 Oceans, dynamics, Sec. 7.4 Ohm's law, 19, 163-164, 187, 193 Oort cloud, 285-286, 303

formation, 360 Opacity, 105, 140, 144-145, 147, 256,

257-258 Optical depth, 140, 146, 228

path, 432, 435 thickness, 140

Orbital commensurabilities, 225 elements, Sec. 10.2-3, 219,

305-306 elements, three-dimensional,

Sec. 10.3 period, 209 resonances, 225, 280-281

Ordinary chondrites, 284, 291 Origin of the solar system, 305, Ch. 16 Osculating elements, 219, 232, 323

Paleomagnetic excursions, 126 Paleoclimatology, 304-305, 311 Paleomagnetism, 111, 126 Pallas, 283 Pandora, 294 Parabolic orbits, 214-215-Parallax, 49, 71-72, 447-450 Parallel transport, 376 Parker's theory, Sec. 13.2 Parking orbit, 414 Parsec, xiv Payload, 404 Pericentre distance, 207, 208-209 Perigee distance, 402 Perseid meteor shower, 290 Perturbations, 205, Sec. 18.1

by a drag force, 224, Sec. 11.3

474 SUBJECT INDEX

by an oblate primary, 223-224, Sec. 11.6, 323, 395-396

by a third body, 224-225 by orbital resonances, 225 by tidal forces, 224-225 long-periodic, 227 qualitative discussion, Sec. 11.2 singular, 15, 181, 202 synthetic theory, 313 theory, Ch. 11

Perturbative solution methods, 236 Perturbing acceleration, 219, 232

function, 231-232, 307-309, 316-317, 321, 323

Phase-locked loops, 430 Phase measurements, Secs. 19.4-5

velocity, 163, 164, 167, 169, 189 Phobos, 225, 279, 328, 363 Phoebe, 277-278, 284, 301 Photo-ionization, Sec. 8.1 Photon gas, 18

noise, 451 Photosphere, 257, 265-266, 269 Pioneer, 132 Pitch angle, 178-179, 184-186 Pixel, 452-454 Planck constant, xiii, 181, 427

distribution, 143 Planetary accretion, Sec. 16.5

accumulation, 276, 292, Secs. 16.4-5, 364

atmospheres, Ch. 7, compositions, 339-340, 343 embryos, 276, Secs. 16.4-5, 364,

365 ephemerides, 395 imaging, 436, Sec. 20.4 interiors, Ch. 5 magnetic fields, 110, Ch. 6 magneto spheres, Sec. 13.4 radar, 284, 419-420, 436 rings, 279, 280, Sec. 14.6, 334,

364 rotation, Ch. 3, 276, 436 system, Ch. 14

Planetesimals, 292, 353 collisional accumulation, Sec. 16.' fonnation, Sec. 16.3

Planets, Sec. 14.1 dynamical properties, 274 inner, 276

Jovian, 276, Sec. 16.6 outer, 276 terrestrial, 276, 339, 358

Plasma, 25, 432 delay, 458 dispersion relation, 165 frequency, xv, 162, 165, 267-268,

347, 432 mantle, 195 waves, Sec. 8.2, 348

Plates, 111-113 angular velocities, 114-116 motions, 112-116 tectonics, Sec. 5.5, 444

Pluto, 275, 279, 280, 302, 308, 314, 324, 360

argument of perihelion, 324 dynamical properties, 274 physical properties, 275 satellite, 277-278

Pluto-Charon system, 279-280, 328, 336, 363

Poinsot's construction, 65-67 POINTS project, 451 Poisson's equation, 9, 348, 380

integral, 9, 35, 389 Polarimetry, 284 Polarization, 166-167, 169-170, 420-421

circular, 421 linear, 420-421

Polar cusps, 195 motion, Secs. 3.5-6, 111, 400-402,

444, 446, 455-456 Poloidal fields, 102, 128-131, 198 Polytropic flow, 262, 361

index, 17, 109, 362 regime, 17, 109

Poynting-Robertson force, 288, 291, 332-336, 398

Poyinting's flux, 420 Precession, 51-52

constant, xv, 52, 54 general, 78 geodetic, 387-389 Lense-Thirring, 388-389 lunisolar, 52, Sec. 4.1, 381 nodal, 444 of spacecraft, 406-407

Pressure, 11, 269-270 magnetic, 270 of radiation, 331, 333, 334, 391,

SUBJECT INDEX 475

393, 396-397, 446, 457 Prolate shapes, 64 Prometheus, 294 Prominences, 260 Proper distance, 376

eccentricity, 323 elements, 281, 323 inclination, 323 interval, 48, 371 motions, 54, 446-447, 449 time, 370-373, 376, 382

Propulsion velocity increment, 403 Protection mechanisms, 316, 322,

324-325 Proton mass, xiv Pseudo-riemannian manifold, 369, 373 Pseudoscalars, 130 Pulsar, 209, 217, 367 P-waves, Sec. 5.1

Q-switched lasers, 443 Quadrupole coefficient, 35, 37-38, 224,

237-238, 444, 446 field, 29, 35, 328, 400 tensor, 35

Quality factor, 71, 329-330 QUASAT, 393 Quasi-periodic solutions, 320-321

systems, 181

Radar, 284, 418-420 planetary, 284, 419-420, 436, 457

Radiation forces, 288, 304, Sec. 15.4 pressure, 331, 333, 334, 391, 39?

396-397, 446, 457 Radiative transfer, Sec. 7.2

recombination, 158 Radioactive heating, 104-105, 331

nuclei, 104-105 Radiometry, 284

water vapour, 456 Radio sources, 449, 454

tracking, Ch. 19, 457 waves, 168, Ch. 19

Radius of influence, 414 Random functions, 425-427

medium, Sec. 19.6 phase method, 425-427 variables, 437, 439 walk, 157, 353, 395, 434

Rayleigh waves, Sec. 5.2

Recombination coefficient, 158-159, 161 Reconnection process, 193, 195 Redshift, 377-378 Reference systems, Sec. 3.2, 449 Refraction, Sec. 19.5

tropospheric, 444, 463 Refractive index, 156, 164-165, 167,

170, 431-434, 463 turbulent, 434

Regularized time, 217 Relative coordinates, 205, 231

velocity at encounters, 253-254 Relativistic angular momentum, 384

astrophysics, 456 deflection of light, 386, 450, 460 delay, 458-459 Doppler shift, 377-378, 382, 430,

462 effects, 240, 305, Ch.17, 395-396,

398, Sec. 20.6 mass, 197 momentum, 197 theories of gravitation, 456, 459

Resonances, 166, 225, 237, 280-281, 292, 294-295, 304, Sec. 15.2, 330, 397, 408, 430

coupled, 323 high-order, 323 laplacian, 324, 330 locking, 314 Mimas-Tethys, 324 modes, 317-320 Neptune-Pluto, 314 order, 281, 323 origin, 325, 360 protection mechanisms, 316 secular, 314, 322-23 spin-orbit, 314, 324 sweeping, 360-361 three-body, 324 Titan-Hyperion, 314-318, 324

Restricted three-body problem , Ch. 12, 315

equations of motion, Sec. 12.1 Jacobi constant, Sec. 12.1

Retroreflectors, 420, 435, 443, 446 Reynolds' number, 15-16, 153, 155

magnetic, 128-129, 267 Rhea, 277-278 Ridges, 106, 111-113 Riemannian geometry, 369-371, 375-376

476 SUBJECT INDEX

manifold, 369 Riemann tensor, 369-371 Right ascension, 51-52 Rigid-body dynamics, Sec. 3.5 Rigidity, 12, 298, 330

of the earth, 69-70 Ring current, 183, 196, 203 Rings, 279, 280, 314, 331, 334

albedos, 294 formation, 364 particle sizes, 292-294 radial structure, 294

Roche ellipsoids, Sec. 4.5, 298 limit, Secs. 4.5 and 14.6, 294-298,

303, 326, 329, 342, 346-347, 352, 363-364

Rockets, 402-405 multi-stage, 404-405

Rossby number, 150 Rotation

group, 32, 56 of the earth, Ch. 3, 325, 398, 444 planetary, Ch. 3, 276, 436

Rotational fission, 63, 298, 363-365 Rotating frames, Sec. 3.2 Rounding-off error, 313, 320 Rubble pile asteroids, 282, 300 Runaway growth process, 355-356

Safronov's theory, Ch. 16, 355, 365 Saros period, 86 Satellites, Sec. 14.2, 305

artificial, Ch.18 capture, 280, 363 circum planetary accumulation, 364 collisional history, 301 formation, 363-365 geodesy, Secs. 18.1 and 20.2 geostationary, Sec. 18.4 icy, 302 laser ranging, 392, Sec. 20.2 launch, Sec. 18.2 megaimpact formation, 364-365 reconnaissance, 451-452 resonances, 314 rotation, 325 small, 279-280, 300-301 shepherding, 294-295

Saturn, 276, 339-340 dynamical properties, 274 magnetic field, 121, 132-133

magnetosphere, 271 physical properties, 275 rings, 292-295, 314, 325, 345, 347 satellites, 251, 277-279, 301, 302,

303, 363-364 S-band, 425, 435, 455 Scale height, 137, 159-161, 173-174,

228-229 Schwarzschi1d metric, 380-381 Scintillation, 156, 434-435, 446, 452 SEASAT satellite, 392 Sea surface topography, 393 Secular effects, 236

of an oblate primary, 237 Secular Love number, 58

perturbations, Sec. 15.1 resonances, 314, 322-323

Seeing, 156, 434-435, 446 Seismic boundary effects, Sec. 5.2

rays, Sec. 5.1 waves. Sec. 5.1

Seismogram, 99 Semimajor axis, 208-210

Gauss' equation, 220, 445 Semiminor axis, 208-209 Shear

deformation, 11 turbulent, 155 stress, 11

Shepherding satellites, 294-295 Shock waves, 189 Sidereal time, 85 Signals, 424-425

bandwidth, 425 digitally modulated, 424-425, 428 information capacity, 425, 428 noise, 424, Sec. 19.3 -to-noise ratio, 428

Singular perturbation theory, 181-182, 202

Skylab, 229 Slow motion approximation, Sec. 17.4,

383, 389 Small satellites, 279-280

solar system bodies, 280, Sec. 14.7 and 16.6

SMM satellite, 139 Snell's law, 169, 170 Solar activity, 260

bipolar magnetic regions, 260 cells, 407

SUBJECT INDEX 477

constant, xv, 138, 156, 311, 332 corona, 256, 261, 269, 433, 435,

459 cycle, 260 faculae, 260 flares, 168, 260, 266 granulation, 260 nebula, Sec.16.1 photosphere, 257, 265, 269 prominences, 260 wind, 26, 155, 179, 188-189, Secs. 9.4-5, Ch. 13, 257, Secs. 13.2-3, 270-271, 331, 335, 361

Solenoidal field, 96 Sound speed, 17, 187, 261-264, 348 Space astrometry, Sec. 20.3

debris, 407-408 interferometry, 450-451 loss, 419 measurements, Ch. 20 telecommunications, Ch. 19, 457 Telescope, 449-450, 454

Spacecraft, Sec. 18.3, Ch. 19 spinning, 406 three-axis stabilized, 406

Space-time curvature, Sec. 17.1 curved, 369 locally flat, 369 Minkowskian, 369 variables, 367

Special relativity, Ch. 17 Specific heat, 17

impulse, 403 intensity, 144

Spectral energy density, 154 estimation, 442 theory, Sec. 19.2

Spectrophotometry, 284 Sphere of influence, 412-414, 416 Spherical harmonics, Sec. 2.1, 102,

122-125, 238, 395 addition theorem, 37 coefficients, 32, 34 degree, 29, 31 normalization, 31 order, 30-31, 395 zeros, 33

Spheroidal modes, 101 Sputnik 2, 231 Stability of lagrangian points, Sec. 12.3,

324

of the solar system, Sec. 15.1 Stationary random functions, 426-427 Station-keeping manoeuvres, 409-412 Stefan-Boltzmann constant, xv, 138, 334

law, 140 Stellar atmospheres, 147

clusters, 242, 353, 450 masses, 209, 450

Stochastic forces, 438 Stokes' formula, 180 Stormer's theory, 177, Sec. 9.6 Strain, 10, 92 Stratopause, 171 Stratosphere, 171 Strength, 295, 298-301, 303 Stress, 10, 92, 299 Subduction zones, 106, 112-113 Summation convention, 232, 367 Sun, Ch. 13

atmosphere, 135 central density, 256 central pressure, 256 central temperature, 256 composition, 256, 258-259, 275,

339 -earth system. 414 escape velocity, 257 gravitational energy, 256 gravitational radius, xiv, 257. 305,

384. 457 luminosity, xiii, 138-139, 257 mass, xiv. 256. 275, 305 mean density, 256, 275 nuclear reactions, 256-257 oscillations, 459 photosphere, 257, 265-266 quadrupole coefficient, 459-460 radiation flux, 138, Sec. 13.1 radio emission, 258 radius, xiv, 138, 256, 275, 276 redshift. 377 rest energy, 256 rotation, 257, 274, 276, 340 spectrum, 258-259 surface temperature, 257 X-ray emission, 258

Sundial, 175 Sun-Jupiter system, 246, 251 Sun-Jupiter-comet problem, 252-254 Sunspots, 260 Surface water waves, 157

478 SUBJECT INDEX

S-waves, Sec. 5.1 Swing-by orbits, 415-416 Sylvia, 283 Synchronization of clocks, 383, 461 Synchronous orbit, 294 Synodic longitude, 461

period, 399 Synthetic perturbation theory, 313

Taxonomic types, 284-285 Tectonic motions, Sec. 5.5 Tethys, 277-279, 324 Themis, 282 Thermal conductivity, 105, 136

emission, 146 noise, 427-428, 435 speed, 24

Thermodynamical equilibrium, 24, 353 local, 23-35, 135, 143-145,

172-173 Thermosphere, 171 Three-body problem, 199, Ch. 12, 412

equilibrium points, Sec. 12.2 general, 243, 254 restricted, Ch. 12 three-dimensional, 245, 249, 251

Thule, 281 Th232, 105 Tidal acceleration, 74, 376, 460

deformation, Sec. 4.3 despinning, 270 dissipation rate, 329-331 effects, Ch. 4, 301, 363, 364,

398-400, 460 equipotential, 81-82 evolution of orbits, 316, 324-325,

Sec. 15.3, 363 friction, 326-327, 330 generalized equation, 377 gravity anomaly, 81-82 harmonics, Sec. 4.4 inequality, 80, 84 phase lag, 83, 328 potential, Sec. 4.2, 328 quality factor, 329-330 synchronization, 326-328, 336 tilt of the vertical, 81-82 torque, 75-76. 328-~29 waves, 83

Tides, Ch. 4, 298, 304 effects on sic orbits, 398-400

in a non-rigid earth, Sec. 4.3 inverted, 83 marine, 83, 400

Time measurements, Sec. 3.1 mean lunar, 84 mean solar, 85 proper, 370-373, 376, 382, 461 sidereal, 85 universal, 46

Tisserand's invariant, Sec. 12.4 Titan, 277-278, 280, 301

-Hyperion resonance, 314-318, 324 Titania, 277-278 Titius-Bode law, 275, 280, 302, 358 Toroidal fields, 102, 128-13 1 Transfer orbit, 406, 414-415

Hohmann, 414-416 Transform faults, 111, 113-114 Transport, Sec. 1.4 Transversal Doppler effect, 48

plasma waves, 165 Trenches, 111 Triangular equilibrium points, 246, 251,

280, 324 Triton, 225, 277-278, 280, 328, 363 Trojan asteroids, 251, 280-281, 314,

324, 363 satellites, 251, 279

Tropic month, 84 year, 84

Tropopause, 171 Troposphere, Sec. 7.5, 171 True anomaly, 208, 210 Truncation error, 313, 320 T -Tauri phases, 340 Turbulence,

in the solar nebula, 340, 346, 352 of the solar wind, 269, 434 tropospheric, Sec. 7.5, 434

Turbulent cells, 433-434 coefficient, 154-155 coupling, 340 medium, Sec. 19.6 viscosity, 155, 340

Twin paradox, 461-463 Two-body problem, Ch. 10

one-dimensional, 217

Ultrarelativistic particles, 18 UmbrieI, 277-278 Unbiased estimate, 440

SUBJECT INDEX 479

Unbound orbits, Sec. 10.4, 359 Uncertainty principle, 423, 435, 442 Universal time, 46 Urania, 277-278 Uranus, 276, 340

dynamical properties, 274, 312-3l3 eccentricity, 311 formation, 359 magnetic field, 121, l33 magnetosphere, 271 orbital energy, 312-3l3 perihelion, 311-313 physical properties, 275 rings, 292-294 rotation, 276, 358 satellites, 277-279, 303, 364

U235, 105 U238, 105

Vliisruii's frequency, 108, 153 VanAllen belt, 184 Variation period, 86 Variational equations, 372-373

principles, 371-372, 378-379, 381-382, 389

Vectorial supercomputers, 314 Vector potential, 379-380, 387 Velocity losses, 403 Venus, 271, 395, 457

atmosphere, 136 dynamical properties, 274 greenhouse effect, 142-143 lack of satellites, 364 physical properties, 275

Vernal equinox, 52, 75-76, 212 Vesta, 283 Viking spacecraft, 48, 457-458 Viscosity, 13, 109, 155, 190, 299, 302,

362 coefficient, 14, 155 of air, 154-155 of the earth's interior, 71 of the solar nebula, 340 temperature dependence, 302

Viscous stress tensor, 14-15 Vlasov's equations, 26-27, 190, 270 VLBI, x, 50, 54, 393, 400, 402, 420,

449-450, Sec. 20.5, 462 differential, 460

Volume expansion coefficient, 107 Vorticity, 23

Vostok ice core, 140 Voyager probes, l32, 292, 302, 330,

452-453 cameras, 452-453

Water vapour radiometer, 456 Weak field approximation, 370, 378 Wegener's theory, 111-112 Whipple's model, 287 Whistler effect, 167-168 White noise, 429-431 World lines, 368, 371-373, 376, 461

null, 372-373, 459

X-band, 425

Yarkovsky force, 335

Zeeman effect, 102, 260 Zenith rube, 54 Zero-velocity curves, 245, Sec. 12.2,

354 topology, 248-249

Zodiacal light, 291, 333

a-effect, l30 a'-effect, l31 aco-effect, 131 y point, 46, 52, 75, 78, 212 co-effect, 128

1985U1, 1986U7, 1986U8, 1986U9, 294 1989N1, 1989N2, 277-278