Index

A B Absolute magnitude, 150, 172, 185Ð186, 201, (298) Baptistina, 188 304, 358, 390 Binary systems, 271, 282, 324Ð325, 329, 435, Absorption bands, 237, 243, 246 463, 477, 481, 483, 490Ð491, 503, Achilles, 199 506Ð508 Action-angle variables, 3Ð4, 20, 23Ð27, 29, 34, 36, 38Ð39, 54, 60, 96 C Adiabatic invariant, 1, 40 Canonical transformation, 3, 5, 10Ð11, 15Ð16, Albedo, 77, 146, 150, 152, 159, 172, 184Ð186, 23, 30Ð31, 39, 50, 60 238, 242, 275, 282, 295, 297Ð298, Capture, 1Ð61, 121, 324, 341, 344, 353, 359, 301, 331 369Ð370, 386, 390Ð395, 489 Andoyer’s variables, 45, 47Ð48 of comets, 341 Angular momentum, 46Ð47, 51, 181Ð182, 203, Carbonaceous chondrites, 235 289, 329, 343, 348, 355, 365, 370, 375, Cartesian coordinates, 5, 19, 31, 48, 60, 325, 378, 380Ð382, 384, 387, 408, 418, 433, 380, 406 464Ð466, 468, 476 Catastrophic Aphelion distance, 342, 344, 346Ð347, 353, collisions, 140, 153, 231Ð232, 237 368 disruption, 153, 163, 165, 183, 223, 239 Area, 3, 23Ð25, 33Ð35, 38Ð43, 45, 69, 106, Centaur, 261, 324, 332, 341, 343Ð344, 216, 262Ð264, 266, 280Ð281, 283, 289, 353Ð354, 361, 387, 394 312, 325, 327, 332, 411Ð412, 414, 422, Central bulk, 403 489, 496Ð497, 504, 507Ð508 Chaos, 63Ð68, 73, 92, 116Ð120, 229, 324, 360 Area-preserving map, 69 Chaos indicators Argument of perihelion, 141, 163, 342, fast Lyapunov indicator (FLI), 63, 67Ð68, 380Ð382, 385, 407, 409Ð411, 437, 464, 117, 484 471Ð472, 503 generalized alignment index (GALI), Arnold, 222 67Ð68, 117Ð119 Asteroid relative Lyapunov indicator (RLI), 117, 484 collisions, 232 Chaotic showers, 166Ð172 diffusion, 393 families, 138, 140Ð141, 153, 155, 157Ð158, motion, 65, 74, 167, 484Ð485, 491Ð492, 160, 162, 173Ð177, 183, 187Ð188, 191, 494, 498 223, 229Ð230, 232, 234Ð235, 239, 248 orbit, 66Ð67, 73Ð74, 76, 96Ð99, 116Ð119, Astrometry, 251, 258, 300, 305 484Ð485, 502 Asymmetric equilibria, 44Ð45 system, 65Ð66 Attractor, 98Ð99, 120 Characteristic exponent, 63Ð129, 484 Autonomous Hamiltonian system, 66, 68Ð73, Chicxulub crater, 188 87, 89 Circular restricted three-body problem, 209, Averaged Hamiltonian, 50Ð51, 382, 407Ð408 211, 221, 346, 363Ð364, 367

Souchay, J., Dvorak, R. (eds.): Index. Lect. Notes Phys. 790, 511Ð517 (2010) DOI 10.1007/978-3-642-04458-8 c Springer-Verlag Berlin Heidelberg 2010 512 Index

Circulation, 18, 22Ð24, 27, 40, 43, 382, 385, transit, 261, 263Ð264, 266, 277, 348, 468, 470 367, 482 Classical Impulse Approximation, 376, 416 Deviation vector, 67Ð73, 75, 90Ð96, 100Ð101, Classical Kuiper Belt, 389, 393 105Ð111, 117Ð123 Close encounters, 167, 170, 179, 201, 298Ð299, Diameter, 149Ð150, 156, 164, 179, 185, 188, 301, 342, 344, 346, 351, 360Ð361, 232, 236, 239, 256, 273Ð276, 301, 303 363Ð369, 371, 373Ð374, 376Ð377, Differentiated parent body, 235 379Ð380, 386, 418, 427, 435Ð436, Direct method, 121Ð123, 231 459Ð460 Direct perturbations, 344Ð345, 373Ð374 Coalescence, 231 Discrete dynamical system, 64, 89, 110 CODAM, 242, 245, 248 Discrete method, 110 Collisional disruption, 140Ð141, 231 Disk tide, 380Ð383, 386, 402 Collisionally relaxed population, 153, 159 Dissipative system, 66, 68, 75Ð76, 98, 120Ð123 Comet Dohnanyi, 153, 159, 161 activity of, 271, 341Ð342, 351Ð354, 358 Dora family, 149Ð150 Halley-type, 344Ð346, 348Ð350, 392 D/Shoemaker-Levy, 9, 344, 368 long-period, 344Ð345, 350, 354Ð355, Dynamical astronomy, 431Ð477 357Ð358, 360, 370, 375, 379, 384, 391 Dynamical families, 137Ð191, 223, 297 new comets, 344, 355Ð356, 358, 371, Dynamical lifetime, 168, 172, 181 382Ð383, 387, 390Ð392, 402, 424, 427 Dynamical system, 32, 39, 64Ð70, 73, 76Ð78, Oort cloud, 343, 345, 360, 372, 376, 85Ð87, 89, 91Ð92, 110Ð111, 116Ð117, 380Ð382, 386, 389Ð392, 401Ð428 139, 320, 433, 455 orbits, 341Ð342, 345, 356, 360, 370, 373, with divided phase space, 120 376, 384, 403 returning, 355Ð358 E short-period, 342, 345Ð350, 352Ð353, 358, Earth, 48, 55Ð57, 59, 61, 148, 152, 166, 168, 360, 384Ð385, 390, 395 170Ð171, 179, 197Ð198, 201Ð202, Shower, 345, 379, 391, 402, 418, 422, 424, 232Ð233, 247, 255Ð256, 261Ð263, 427 278Ð279, 281, 292, 297, 307, 313Ð314, Cometary fading, 354Ð355, 358 316Ð317, 324, 332, 365Ð366, 379, 387, Completeness limit, 154, 159Ð162 389Ð390, 433, 435, 481Ð483, 501, Condition R, 84Ð86, 89 503Ð506 Cone technique, 111 Eccentricity, 189, 495, 498 Conservative system, 66, 76, 100, 120 Edgeworth-Kuiper Belt, 344 Continuous dynamical system, 64, 86, 110Ð111 Ejection velocities, 141, 182Ð184 Continuous method, 66, 110, 115Ð116 Elis Stromgren,¬ 354 Cosmic rays exposure, 172, 180Ð181 Elliptic function of the first kind, 408 Cretaceous, 188, 232 Embedded cluster, 389 Encounter velocity, 348Ð349, 363Ð366, D 375, 419 D/1770 L1 (Lexell), 345, 370 Energy integral, 346, 381, 433 D’Alembert characteristic, 7Ð8 Eos family, 151Ð152, 183, 235 Datura cluster, 232, 238Ð239 Equilateral, 196Ð198, 201, 204Ð222, 224 Delaunay’s elements, 406Ð407 Equilibria, 18, 22Ð23, 31Ð35, 44Ð45, 51, Delay coordinates, 121 59Ð61, 198Ð199, 220 Democratic heliocentric variables, 461 Equilibrium, 18, 27Ð29, 31Ð34, 40, 45, 51Ð54, Dendrogram, 144 196Ð198, 203Ð204, 216Ð221, 256, 289 Detection methods Ernst Opik,¬ 364 astrometric measurements, 271, 302, 482 Escape velocity, 364, 365 direct imaging, 482 Euler, 46, 198, 306, 479 gravitational lensing, 482 Eunomia family, 159Ð160, 162, 235 radial velocity measurements, Exocatalogue, 484, 486, 503 481Ð482, 499 Explicit one-step methods, 436 Index 513

Exponential divergence of nearby orbits, 67, Generating function, 38Ð39 73Ð74, 92 Genetic algorithm, 290Ð296, 315 Exterior algebra, 68, 123Ð129 Giant Molecular Cloud, 375, 386, 402, 426 Extrapolation method Gliese 86, 481, 491, 497Ð500, 503, 506 Aitken-Neville scheme, 444, 447 GMC encounters, 387 Bulirsh-Stoer, 240, 320, 436, 443Ð448, (6489) Golevka, 179, 294Ð295 460, 463Ð464, 466Ð469, 471Ð472, Gram-Schmidt orthonormalization, 75, 103, 474Ð477, 480 105Ð108, 110 Extra-solar planets, 252, 315, 325, 481Ð508 Gravitational perturbations, 139, 202, 222, 307 F resonance, 1, 55Ð61 Families, identification, 137, 145, 248 scattering, 342, 386, 388 Filtration, 80, 91 Guiding trajectory, 39Ð40 Finite-dimensional dynamical system, 66 Finite time mLCE, 93, 119 H Finite time p-mLCE, 100 Habitable zone, 483, 499Ð508 Fixed point, 120, 211Ð212, 215Ð216, Hale-Bopp, 352 218Ð221, 271 Hamiltonian Flora family, 188, 234 equations of motion, 68, 71Ð72, 92, 95, Flux 105, 109 background flux, 356, 421, 427 formalism, 1Ð2, 5, 58Ð59, 72, 406 Fragments, 140Ð141, 148, 153Ð156, 158, N-body, gravitational, 431, 435Ð436, 439, 163Ð164, 167, 171Ð173, 176Ð177, 183, 455, 476 187Ð188, 231, 237, 240, 289 HamiltonÐJacobi, 3, 38 Fundamental matrix, 70 Harmonic oscillator, 27Ð28, 210 Fundamental model of resonance, 14, 20, HD41004 AB, 481, 491Ð492, 499Ð501, 503 29Ð37, 40, 42Ð44 Hector, 199 HED achondrites, 148 G HenonÐHeiles« system, 70, 75 Gaia, 191, 202, 251Ð333 Hierarchical Clustering Method (HCM), 142, Galactic 240 bulge, 381 Hill sphere, 197, 363, 367, 384 centre, 376, 380 HST, 272, 394 disk, 342, 355, 380Ð383, 386 Hybrid integrator, 459Ð464, 470 density, 406 Hydrocode, 177, 183Ð184, 232, 240 latitude, 382Ð383, 391, 402, 424Ð425 Hyperbolic deflection, 363Ð367, 377 mid-plane, 403Ð404, 406 normal component, 406 I potential, 404 Impact radial component, 406, 408, 410, 413Ð415 distance, 418 tide, 343Ð345, 360, 380Ð384, 386, energy, 172 390Ð391, 401Ð403, 407, 410, 416, 419, plane, 416 421Ð424, 426Ð427 Impulse approximation, 376Ð378, 415Ð416 Galaxy, 255, 357, 360, 381, 384, 401Ð404, 406 Inclination, 4Ð6, 18Ð19, 21, 48, 52, 54, 57, Gamma Cephei, 481, 491, 494Ð497 138Ð139, 145, 152, 167, 175, 179, 184, Gascheau, 198, 222 189Ð190, 211, 223Ð224, 230, 239, 262, Gas drag, 388Ð389 328Ð329, 331, 342, 344, 346Ð347, Gaston Fayet, 354 349Ð351, 353, 364, 368, 371Ð372, Gauss formulae, 140 379Ð381, 384Ð385, 387, 391Ð393, 411, Gaussian Gravitational Constant, 432, 449 434, 437, 464, 468, 482, 498, 503, 508 Gauss Radau Indirect perturbations, 344Ð345, 373Ð374 Quadratures, 440Ð443 Information dimension, 99 Spacings, 443 Inner core (Oort Cloud), 345, 379, 383, Gefion family, 171, 159, 166 387Ð388, 390, 424, 427 514 Index

Integrability, 402, 408, 413Ð415 Liouville, 198 Integrable system, 91 Loss cone, 389 Integral of motion, 90, 98Ð99 Loss cylinder, 379, 382, 390Ð392 Interlopers, 149Ð150, 152, 191, 233Ð234, 240 L-type motion, 490 Interplanetary dust, 232, 240, 248 Lyapunov characteristic exponent of order p IRAS, 159, 232, 275 (p-LCE), 67, 79, 83, 86, 88Ð89, 100 Lyapunov characteristic exponents (LCEs), J 63Ð129 Jacobi integral, 346, 363 Lyapunov dimension, 64, 99 Jan Oort, 355 Lyapunov time, 92, 117 Jump, 43, 371 Jupiter M family, 342Ð343, 346, 348Ð351, 353, Main Belt, 7, 13, 44, 137Ð139, 141Ð144, 148, 358Ð359, 367Ð368, 379, 384, 390, 150Ð152, 159, 161Ð162, 166Ð167, 170, 392Ð394 178Ð182, 184Ð186, 189, 200, 230Ð233, -Saturn system, 504Ð505 235, 237Ð240, 261, 274Ð276, 281Ð282, 286, 292, 296Ð297, 324Ð327, 332, 334, K 379, 506 KAM, 221Ð222 Mapping, 69, 240, 344, 435Ð436, 449Ð450, KaplanÐYorke conjecture, 99Ð100 456Ð458, 462Ð463, 470, 476 (832) Karin, 187, 239Ð241, 243Ð244, 248 Maria family, 165Ð166, 169 Karin cluster, 238Ð240 Markov chain, 371 Karin family, 187, 238Ð245, 248 Mars, 152, 179, 201, 224, 231Ð232, 298, 300, Kaula, 57 307, 310, 384Ð385, 503Ð505 Kepler Mars-crossers, 179 Orbital Elements, 434, 465, 474 Mature and fresh surfaces, 246 Problem, 431, 464Ð470 Max-e, 484, 504, 506Ð507 Kinetic energy, 47, 49, 172Ð173 Maximal Lyapunov characteristic exponent Kirkwood, 12, 44, 139, 148, 166Ð167, 180, (mLCE), 64Ð65, 67, 74Ð75, 82, 84, 507 91Ð98, 102, 116Ð119, 121Ð123, 484 gaps, 44, 139, 148, 166Ð167, 507 Maximal Lyapunov characteristic exponent of Kolmogorov-Sinai (KS) entropy, 64, 99, 438 order p (p-mLCE), 67, 83, 86, 100, Koronis family, 179Ð180, 182, 187, 191, 102Ð103, 122 235Ð236, 238, 243Ð244 Mean estimated convergence behavior, 448 Kozai Mean motion resonance, 1, 7Ð15, 17, 20, 147, cycle, 344Ð345, 368, 370, 379Ð385 151, 166Ð167, 169, 179, 189, 224, 230, resonance, 17Ð18, 380, 384 232, 342, 385, 485Ð487, 490, 500, 504 Kreutz group, 384Ð385 9:4 mean motion resonance, 151 Kuiper belt object, 393Ð394, 403 Mercury6, 464, 474Ð477 Meteorites, 151Ð152, 172, 180Ð181, 233, L 236Ð237, 240, 243, 297 Laboratory experiments, 164, 172, 289 Mineralogy, 236 Laboratory hypervelocity collisions, 164 composition, 146 Lagrange, 127, 195Ð202, 216, 223Ð224, solution, 235, 248 306, 309 Modified midpoint method, 444 Lagrangian point, 222, 255, 367Ð368 Monte Carlo simulation, 273, 328Ð329, Largest remnant, 154Ð157 371, 416 Libration, 18, 29, 36, 40, 42, 54, 202, 271, 300, MPC (Minor Planet Center), 355Ð356, 394 342, 382Ð383, 490 Multi-planet system, 481, 483, 486Ð490 Lie-Operator, 450Ð451, 454 hierarchical planet pairs, 489Ð490 Lie-Series, 466Ð467 mean motion resonance, 486Ð487 Lightcurve, 236, 241Ð242, 244, 263, 279Ð281, near-resonant planets, 487 285, 287Ð289 non-resonant planets, 17, 393, 489 LINEAR, 352, 390 Multiplicative cocycle, 77Ð78, 86Ð87 Index 515

Multiplicative Ergodic Theorem (MET) Ð Ordinary chondrites, 243 Oseledec’s theorem, 65, 67, 86Ð87, 91, Ordinary differential equations, 64, 110, 215, 96, 116 431, 436, 443, 480 Osculating elements, 139, 230, 238Ð239, 305, N 354, 407, 410 N-body, 1, 177, 184, 202, 221, 229, 307, 320, 431, 433, 435, 439, 449, 453, 455, 458, P 460, 464, 476 Pan-STARRS, 191, 256Ð257, 287, 297, 333 Near-Earth Asteroid (NEA), 148, 152, 171, Parabolic limit, 379, 386 179, 232, 324, 433, 435 Parent body, 140Ð141, 148, 150, 153Ð157, 159, Near-Earth Object (NEO), 168, 261, 278, 292, 161, 163, 170, 173Ð174, 187Ð188, 223, 297, 334 231Ð232, 235, 237, 239Ð240, 243 Near-infrared, 234, 242, 244, 246 Partially differentiated genitor, 233 Nekhoroshev, 222 Passing star, 342, 355, 390Ð391, 402, 415, New comet, 344, 352, 355Ð356, 358, 371, 422Ð424 382Ð383, 387, 390Ð392, 402, 424, 427 Patroclus, 199 Newton 95P/Chiron, 353, 361 Law of Universal Gravity, 432 Pendulum, 1, 14, 16, 20, 21Ð29, 39Ð41, 53 Nice Model, 389 Perihelia/perihelion, 207, 344Ð345, 351, 353, Nongravitational 355, 358, 374Ð375, 382, 391, 402, effect, 355 426, 428 force, 302, 341 Perturbation theory, 432Ð433 Normal basis, 80Ð81, 88, 101, 124Ð125, Perturbing function, 299, 360 127Ð128 Phase Numerical integration, 18, 71Ð73, 114, angle, 186, 200, 271, 273Ð274, 279Ð280, 179Ð180, 184, 187, 220, 223Ð224, 282Ð283, 288 231Ð232, 238Ð239, 318Ð320, 377, error, symplectic, 470 384Ð385, 402, 407, 431Ð477 space, 3, 18, 20Ð23, 33Ð36, 40, 44, 47, 61, 64, 66, 68, 73Ð74, 87, 89, 99, 116, O 120Ð121, 123, 190, 221Ð222, 345, 382, Obliquity angle, 178, 182, 189, 279 389, 424, 428, 433, 444, 455Ð456, 458, Observable lifetimes, 345, 355 460, 462, 483 Observations, 114, 138, 259Ð260, 320Ð325 Phase space reconstruction, 121 OC paradigm, 237 111P/Helin-Roman-Crockett, 369 Olivine, 146, 150, 235, 242, 248 Photometry, 251Ð254, 256, 262, 279, 281Ð288, Oort 291, 293Ð296, 302, 332Ð333 central cloud, 415, 427 153P/Ikeya-Zhang, 345 constants, 380, 406 Planetary perturbations, 152, 232, 304, 306, Inner cloud, 411Ð412, 418, 427 341, 354, 356Ð357, 370, 375, 379, 384, outer cloud, 390, 411, 415, 421, 426Ð427 390Ð392, 401, 411, 426 peak, 355, 357, 395, 401 Planetary region, 402, 415 Orbital elements, 56, 138Ð142, 163, 167, 169, Planetary systems, 1, 252, 481, 483, 488, 501 184, 200, 230Ð231, 271, 297, 304, 306, Planetesimals, 151, 229Ð230, 287, 289 309, 311, 316, 323, 327, 345Ð346, 355, Plutino, 393Ð394 374, 383, 385, 416, 434, 465, 469, 471, (134340) Pluto, 354 474, 503, 505 Poincare« surface of section (PSS), 67, Orbital energy, 201, 343Ð344, 360, 365, 116Ð117, 483Ð484 369Ð371, 375, 380, 386, 390, 401, 418 Poisson bracket, 456, 460, 465 Orbits Poisson’s equation, 405 future, 354 Polana family, 152 original, 141, 354Ð355, 383, 402 Polarimetry, 147, 297 Order Polynomial interpolation, 444, 446 of algorithm, 443 39P/Oterma, 369 control, 454Ð455, 476 Probability of capture, 37Ð45 516 Index

Proper elements, 139, 141Ð145, 150, 152, 158, Secular resonance, 1, 17, 19Ð21, 44, 167, 224, 163, 168, 172, 174, 188Ð189, 191, 223, 233, 237, 393 230Ð231, 240, 297, 323 (90377) Sedna, 343, 388, 394 Proper elements space, 139, 141, 150, 152, Semimajor axis, 6, 144, 179, 181, 349, 409, 168, 223 414, 418, 469, 498, 504 29P/Schwassmann-Wachmann, 1, 352 Sensitive dependence on initial conditions, P-type motion, 490 65, 73 Pyroxene, 242, 248 Separatrix, 18, 22, 35, 40Ð42, 382, 384 Sequential Impulse Approximation, Q 377Ð378 QR decomposition, 66Ð67, 106Ð110, Single-planet system, 483Ð486, 503 112Ð113, 123 Singular value decomposition (SVD), 66Ð67, Quadrantid meteor stream, 385 110, 115Ð116, 118, 321Ð322 Quasi-Hildas, 368 Singular values, 115Ð116, 321Ð322 Quasi-integral of motion, 139, 230 Size distribution, 152Ð158, 184Ð186, 394 Quasi-random population, 143, 145 Sloan Digital Sky Survey (SDSS), 177, 243 Small Main-Belt Asteroid Spectroscopic R Survey, 235 Radial tide, 380Ð381, 383 Solar nebula, 342, 388Ð389 Reaccumulation, 156 Space weathering, 233, 236Ð238, 241Ð244, Reflectance 246Ð247, 296 properties, 147Ð149, 241, 271 Spectral behaviors, 233Ð234 spectra, 151Ð152, 247, 278 Spectral slope, 233, 241 Regolith, 236 Spectroscopy, 147Ð148, 150, 152, 233, 238, Regular matrix function, 81, 86 241Ð244, 296, 332 Regular motion, 74, 117, 119Ð120, 498 properties, 146, 152 Regular orbitÐordered orbit, 66 Spectrum of LCEs, 64, 67, 80, 88Ð91, 98Ð116, Remote sensing, 229 121Ð122 Resonance Sphere of influence, 361Ð364 secondary, 16, 44 Spin axis, 140, 178, 181Ð182, 188Ð189, secular, 17, 19Ð21, 167, 233 235Ð236, 254, 256, 259, 265, 271, 277, spin orbit, 45, 48, 51, 53Ð54, 182, 189 279Ð282, 288, 292, 303 3:1 resonance, 148, 169 Spin-down, 182 5:2 resonance, 171, 179, 489 Spin-orbit resonance, 1, 45, 48, 51, 53Ð54, Restricted three-body problem, 4Ð7, 196, 202, 182, 189 205Ð207, 210Ð211, 220Ð222, 346, 348, Spin-up, 324 363Ð364, 367 Splitting, 358, 384Ð385, 443Ð444, 447, 449, Rotation, 28, 45Ð50, 54Ð55, 57Ð58, 60, 127, 456, 458 178, 181Ð182, 189, 191, 205, 211, 214, Stability 218Ð219, 235Ð236, 251, 258Ð259, 271, dynamical stability, 481Ð508 279Ð283, 286Ð290, 292, 302, 305, Stable periodic orbit, 66, 91, 96, 202 318Ð319, 328, 380, 404 Stalactite diagrams, 144Ð145 Rotational phase, 241Ð242, 247, 279, 288, Standard method, 66Ð67, 100Ð110, 123 290Ð291 Statistical Asteroid Model (SAM), 184 Runge-Kutta Stellar Cash-Karp embedded, 431, 436, 438Ð440, encounter, 345, 375Ð377, 379, 386, 388, 464, 476Ð477 403, 415, 418 Nystrom,¬ 439 mass, 331, 376, 418, 459, 462 Symplectic, 110, 439 passage, 345, 357, 360, 376Ð377, 386, 402, 415Ð417, 420 S perturbations, 355, 375Ð376, 379, 382, Scattered disk, 341Ð344, 387Ð395 402Ð403, 415Ð427 Secular perturbations, 379Ð380, 489 velocity, 418 Index 517

Step-size control population, 343, 353, 389 adaptive, 435Ð436, 449, 463, 476 Transparency, 426 Stochastic, 74, 265, 322, 330, 357, 370, Trojan, 10, 195Ð224, 231, 310, 324, 342, 361, 418Ð419, 427 503 Strange attractor, 98Ð99, 120 True anomaly, 4, 6, 141, 163, 174, 187, 219 S-type motion, 490Ð494 Truncation error, 432, 453, 470, 479Ð480 Sungrazers, 344, 384Ð385 Tumbling rotation, 182 Symplectic integrator, 476 U map, 66Ð73, 87, 89, 92, 96, 111, 116, 120, Unstable periodic orbit, 66, 91 435Ð436, 450, 457Ð458 Untangling transformation, 54 phase error, 470Ð474 Synergy, 390, 403, 423Ð424, 426Ð428 Synodic period, 241 V Variational equations, 67, 69Ð73, 92, 94Ð96, T 100, 105Ð106, 110Ð111, 299, 317, 319 Tangent map, 67, 69Ð70, 73, 92, 94Ð95, 100, Vector field, 64 105Ð106, 109 Vertical tide, 411 Tangent space, 69, 73, 77, 85Ð87, 119, 123 Vesta asteroid, 168, 237 method, 123 Vesta family, 145, 147Ð149, 156, 165, 168, 237 Taxonomic class Visible, 185, 233Ð235, 242Ð246, 248, 258, A-type, 150, 234 277, 283, 289, 325, 482, 495, 508 F-type, 152, 297 2004 VN112, 394 K-type, 152 L-type, 490 W M-type, 150 Wavelet Analysis Method (WAM), 142 V-type, 147Ð148, 150 Wedge product - exterior product, 124 Taxonomy, 251, 278, 296Ð298, 300 Temporary satellite capture, 344, 349, 368Ð369 Themis family, 166, 232 Y Thermal inertia, 178Ð179, 232, 302Ð303, 333 Yarkovsky effect, 177Ð184, 188Ð189, 191, Thermal IR, 159, 177, 185 232, 236, 238Ð240, 302Ð303 Thermilazed Oort cloud, 410 Yarkovsky–O’KeefeÐRadzievskiiÐPaddack Time series, 66Ð68, 76, 117, 120Ð123 effect (YORP), 181 Tisserand Yoshihide Kozai, 380 criterion, 346Ð347 Young families of asteroids, 230, 238 parameter, 345Ð349, 370, 372, 375, 393 Topologically transitive, 65 Z Transneptunian Zero-velocity object (TNO), 261, 308, 329, 331, 332, curve, 367Ð368 334, 341 surface, 363, 367