Abstract
The apparent regularity of the motion of the giant planets of our solar system suggested for decades that said planets formed onto orbits similar to the current onesand that nothing dramatic ever happened during their lifetime. The discovery of extrasolar planets showed astonishingly that the orbital structure of our planetary system is not typical. Many giant extrasolar planets have orbits with semimajor axes of ∼ 1 AU,and some have even smaller orbital radii, sometimes with orbital periods of just a few days. Moreover, most extrasolar planets have large eccentricities, up to values that only comets have in our solar system. Why is there such a great diversitybetween our solar system and the extrasolar systems, as well as among the extrasolar systems themselves? This chapter aims to give a partial answer to this fundamental question. Its guideline is a discussion of the evolution of our solarsystem, certainly biased by a view that emerges, in part, from a series of works comprising the “Nice model.” According to this view, the giant planets of the solar system migrated radially while they were still embedded in a protoplanetary disk of gas and presumably achieved a multi-resonant orbital configuration, characterized by smaller interorbital spacings and smaller eccentricities and inclinations with respect to the current configuration.The current orbits of the giant planets may have been achieved during a phase of orbital instability, during which the planets acquired temporarily large-eccentricity orbits and all experienced close encounters with at least oneother planet. This instability phase occurred presumably during the putative “Late Heavy Bombardment” of the terrestrial planets, approximately ∼ 3.9 Gy ago (Tera et al. 1974). The interaction with a massive, distant planetesimal disk (the ancestor of the current Kuiper belt) eventually damped the eccentricities of the planets, ending the phase of mutual planetary encounters and parking the planets onto their current, stable orbits. This new view of the evolution of the solar system makes our system not very different from the extrasolar ones. In fact, the best explanation for the large orbital eccentricities of extrasolar planets is that the planets that are observed are the survivors of strong instability phases of original multi-planet systems on quasi-circular orbits. The main difference between the solar system and the extrasolar systems is in the magnitude of such an instability. In the extrasolar systems, encounters among giant planets had to be the norm. In our case, the two major planets (Jupiter and Saturn) never had close encounters with each other: They only encountered “minor” planets like Uranus and/or Neptune. This was probably just mere luck, as simulations show that Jupiter-Saturn encounters in principle could have occurred. Another relevant difference with the extrasolar planets is that, during the gas-disk phase, our giant planets avoided migrating permanently into the inner solar system, thanks to the specific mass ratio of the Jupiter/Saturn pair and the rapid disappearance of the disk soon after the formation of the giant planets. This chapter ends on a note on terrestrial planets. The structure of a terrestrial-planet system depends sensitively on the dynamical evolution of the giant planets and on their final orbits. It appears clear that habitable terrestrial planets, with moderate eccentricity orbits, cannot exist in systems where the giant planets became violently unstable and developed very elliptic orbits. Thus, our very existence is possible only because the instability phase experienced by the giant planets of our solar system was of “moderate” strength.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The orbital radius beyond which temperature is cold enough that water condenses into ice. The snow line is situated at about 3–5 AU from a solar-mass star, depending on time and on disk models (Min et al. 2011).
- 2.
In summary, three mechanisms have been proposed to move planets from the snow line region to large distances from the central star: (i) outward Type II migration of planets originally formed in the outer part of a disk in rapid viscous spreading (Veras and Armitage 2004), (ii) outward migration of a pair of resonant planets with a Jupiter-Saturn mass hierarchy (Crida et al. 2009), and (iii) scattering of a planet to a wide elliptic orbit (Veras et al. 2009). These mechanisms are potential alternatives to the possibility that distant planets formed in situ, by the gravitational instability mechanism (Boley 2009)
- 3.
The reader should remember that two planets are stable if their orbital separation is a few times their mutual Hill radius \({R}_{H} =\bar{ a}{[({m}_{1} + {m}_{2})/{M}_{S}]}^{1/3}\), where m1 and m2 are the masses of the two planets and \(\bar{a}\) is their mean semimajor axis, while MS is the mass of the star. Suppose now that planets tend to acquire orbits whose mutual separation is not much larger than this Hill-stability limit. If a planetary system is made of two planetary cores, when one of two objects becomes a giant planet, the system is likely to be destabilized because RH increases by a factor 3–4 as the mass of one planet grows by a factor 30–60. Instead, a stable system made of one giant planet and one core is not likely to be strongly destabilized when the core grows to the status of a giant planet, because RH increases only by a factor ∼ 2(1 ∕ 3) = 1. 25. Similarly, in a system made of one giant planet and two cores, the growth of one of the cores to the status of a giant planet is likely to destabilize the remaining core but not the first planet
- 4.
Currently, the record for the most complex resonance chain in the solar system is detained by Jupiter’s satellites Io, Europa, and Ganymede, which are locked in a 3-body resonance, also known as the Laplace resonance.
- 5.
Named for the French city of Nice, where it was developed.
- 6.
The situation was not nearly as sensitive in Gomes et al. (2005), because the planets were not assumed to be in resonance with each other.
References
Abramov, O., & Mojzsis, S. J. 2009, Microbial habitability of the Hadean Earth during the late heavy bombardment. Nature, 459, 419–422
Adams, F. C., & Laughlin, G. 2003, Migration and dynamical relaxation in crowded systems of giant planets. Icarus, 163, 290–306
Agnor, C., & Asphaug, E. 2004, Accretion efficiency during planetary collisions. ApJ, 613, L157–L160
Agnor, C. B., Canup, R. M., & Levison, H. F. 1999, On the character and consequences of large impacts in the late stage of terrestrial planet formation. Icarus, 142, 219–237
Alibert, Y., Mordasini, C., & Benz, W. 2004, Migration and giant planet formation. A&A, 417, L25–L28
Asphaug, E., Agnor, C. B., & Williams, Q. 2006, Hit-and-run planetary collisions. Nature, 439, 155–160
Bailey, B. L., & Malhotra, R. 2009, Two dynamical classes of Centaurs. Icarus, 203, 155–163
Baldwin, R. B. 2006, Was there ever a Terminal Lunar Cataclysm? With lunar viscosity arguments. Icarus, 184, 308–318
Barge, P., & Sommeria, J. 1995, Did planet formation begin inside persistent gaseous vortices? A&A, 295, L1–L4
Barnes, R., & Greenberg, R. 2006, Stability limits in extrasolar planetary systems. ApJ, 647, L163–L166
Baruteau, C., & Masset, F. 2008, On the corotation torque in a radiatively inefficient disk. ApJ, 672, 1054–1067
Batygin, K., & Brown, M. E. 2010, Early dynamical evolution of the solar system: pinning down the initial condition of the nice model. ArXiv e-prints arXiv:1004.5414
Batygin, K., Brown, M. E., & Fraser, W. C. 2011, In-situ formation of the cold classical Kuiper belt. ApJ, 738, p 13.
Beauge, C., & Nesvorny, D. 2011, Multiple-planet scattering and the origin of hot Jupiters. ArXiv e-prints arXiv:1110.4392
Bernstein, G. M., Trilling, D. E., Allen, R. L., Brown, M. E., Holman, M., & Malhotra, R. 2004, The size distribution of trans-neptunian bodies. AJ, 128, 1364–1390
Binzel, R. P., Bus, S. J., Burbine, T. H., & Sunshine, J. M. 1996, Spectral properties of near-earth asteroids: evidence for sources of ordinary chondrite meteorites. Science, 273, 946–948
Bitsch, B., & Kley, W. 2010, Orbital evolution of eccentric planets in radiative discs. A&A, 523, A30
Bitsch, B., & Kley, W. 2011, Range of outward migration and influence of the disc’s mass on the migration of giant planet cores. A&A, 536, A77
Bodenheimer, P., Hubickyj, O., & Lissauer, J. J. 2000, Models of the in situ formation of detected extrasolar giant planets. Icarus, 143, 2–14
Boley, A. C. 2009, The two modes of gas giant planet formation. ApJ, 695, L53–L57
Booth, M., Wyatt, M. C., Morbidelli, A., Moro-Martín, A., & Levison, H. F. 2009, The history of the Solar system’s debris disc: observable properties of the Kuiper belt. MNRAS, 399, 385–398
Boss, A. P. 2000, Possible rapid gas giant planet formation in the Solar Nebula and other protoplanetary disks. ApJ, 536, L101–L104
Boss, A. P. 2001, Formation of planetary-mass objects by protostellar collapse and fragmentation. ApJ, 551, L167–L170
Boss, A. P. 2002, Stellar metallicity and the formation of extrasolar gas giant planets. ApJ, 567, L149–L153
Bottke, W. F., Levison, H. F., Nesvorný, D., & Dones, L. 2007, Can planetesimals left over from terrestrial planet formation produce the lunar Late Heavy Bombardment? Icarus, 190, 203–223
Bottke, W. F., Vokrouhlicky, D., Nesvorny, D., Minton, D., Morbidelli, A., & Brasser, R. 2010, The E-belt: a possible missing link in the late heavy bombardment. Lunar Planet. Inst. Sci. Conf. Abstr., 41, 1269
Bottke, W. F., Vokrouhlicky, D., Minton, D., Nesvorny, D., Brasser, R., & Simonson, B. 2011, The great archean bombardment, or the late heavy bombardment. Lunar Planet. Inst. Sci. Conf. Abstr., 42, 2591
Brasser, R., Morbidelli, A., Gomes, R., Tsiganis, K., & Levison, H. F. 2009, Constructing the secular architecture of the solar system II: the terrestrial planets. A&A, 507, 1053–1065
Burbine, T. H., Binzel, R. P., Bus, S. J., Buchanan, P. C., Hinrichs, J. L., Hiroi, T., Meibom, A., & Sunshine, J. M. 2000, Forging asteroid-meteorite relationships through reflectance spectroscopy. Lunar Planet. Inst. Sci. Conf. Abstr., 31, 1844
Butler, R. P., et al. 2006, Catalog of nearby exoplanets. ApJ, 646, 505–522
Cameron, A. G. W. 1978, Physics of the primitive solar accretion disk. Moon Planets, 18, 5–40
Canup, R. M., & Asphaug, E. 2001, Origin of the Moon in a giant impact near the end of the Earth’s formation. Nature, 412, 708–712
Canup, R. M., & Esposito, L. W. 1996, Accretion of the moon from an impact-generated disk. Icarus, 119, 427–446
Canup, R. M., & Ward, W. R. 2006, A common mass scaling for satellite systems of gaseous planets. Nature, 441, 834–839
Capobianco, C. C., Duncan, M., & Levison, H. F. 2011, Planetesimal-driven planet migration in the presence of a gas disk. Icarus, 211, 819–831
Carpenter, J. M., et al. 2009, Formation and evolution of planetary systems: properties of debris dust around solar-type stars. ApJSS, 181, 197–226
Cassen, P. M., Smith, B. F., Miller, R. H., & Reynolds, R. T. 1981, Numerical experiments on the stability of preplanetary disks. Icarus, 48, 377–392
Chambers, J. E. 2001, Making more terrestrial planets. Icarus, 152, 205–224
Chambers, J. 2006, A semi-analytic model for oligarchic growth. Icarus, 180, 496–513
Chambers, J. E., & Cassen, P. 2002, The effects of Nebula surface density profile and giant-planet. Meteoritics and Planetary Science 37, 1523–1540
Chambers, J. E., & Wetherill, G. W. 1998, Making the terrestrial planets: N-body integrations of planetary embryos in three dimensions. Icarus, 136, 304–327
Chapman, C. R., Cohen, B. A., & Grinspoon, D. H. 2007, What are the real constraints on the existence and magnitude of the late heavy bombardment? Icarus, 189, 233–245
Chatterjee, S., Ford, E. B., Matsumura, S., & Rasio, F. A. 2008, Dynamical outcomes of planet-planet scattering. ApJ, 686, 580–602
Chiang, E. I. 2003, Excitation of orbital eccentricities by repeated resonance crossings: requirements. ApJ, 584, 465–471
Cohen, B. A., Swindle, T. D., & Kring, D. A. 2000, Support for the lunar cataclysm hypothesis from lunar meteorite impact melt ages. Science, 290, 1754–1756
Cresswell, P., Dirksen, G., Kley, W., & Nelson, R. P. 2007, On the evolution of eccentric and inclined protoplanets embedded in protoplanetary disks. A&A, 473, 329–342
Crida, A., & Morbidelli, A. 2007, Cavity opening by a giant planet in a protoplanetary disc and effects on planetary migration. MNRAS, 377, 1324–1336
Crida, A., Morbidelli, A., & Masset, F. 2006, On the width and shape of gaps in protoplanetary disks. Icarus, 181, 587–604
Crida, A., Sándor, Z., & Kley, W. 2008, Influence of an inner disc on the orbital evolution of massive planets migrating in resonance. A&A, 483, 325–337
Crida, A., Masset, F., & Morbidelli, A. 2009, Long range outward migration of giant planets, with application to fomalhaut b. ApJ, 705, L148–L152
D’Angelo, G., Lubow, S. H., & Bate, M. R. 2006, Evolution of giant planets in eccentric disks. ApJ, 652, 1698–1714
Dauphas, N., & Pourmand, A. 2011, Hf-W-Th evidence for rapid growth of Mars and its status as a planetary embryo. Nature, 473, 489–492
di Sisto, R. P., & Brunini, A. 2007, The origin and distribution of the Centaur population. Icarus, 190, 224–235
Durisen, R. H., Boss, A. P., Mayer, L., Nelson, A. F., Quinn, T., & Rice, W. K. M. 2007, Gravitational instabilities in gaseous protoplanetary disks and implications for giant planet formation, in Protostars and Planets V, ed. B. Reipurth, D. Jewitt, & K. Keil (Tucson: University of Arizona Press), 607–622
Fernandez, J. A., & Ip, W.-H. 1984, Some dynamical aspects of the accretion of Uranus and Neptune – the exchange of orbital angular momentum with planetesimals. Icarus, 58, 109–120
Ferraz-Mello, S., Beaugé, C., & Michtchenko, T. A. 2003, Evolution of migrating planet pairs in resonance. Celest. Mech. Dyn. Astron., 87, 99–112
Fischer, D. A., & Valenti, J. 2005, The planet-metallicity correlation. ApJ, 622, 1102–1117
Fogg, M. J., & Nelson, R. P. 2005, Oligarchic and giant impact growth of terrestrial planets in the presence of gas giant planet migration. A&A, 441, 791–806
Fogg, M. J., & Nelson, R. P. 2007, On the formation of terrestrial planets in hot-Jupiter systems. A&A, 461, 1195–1208
Ford, E. B., Havlickova, M., & Rasio, F. A. 2001, Dynamical instabilities in extrasolar planetary systems containing two giant planets. Icarus, 150, 303–313
Ford, E. B., & Rasio, F. A. 2008, Origins of eccentric extrasolar planets: testing the planet-planet scattering model. ApJ, 686, 621–636
Fouchet, T., Moses, J. I., & Conrath, B. J. 2009, Saturn: composition and chemistry, ed. M. Dougherty, L. Esposito, S. Krimigis et al. (Springer). Saturn from Cassini-Huygens, 83
Fuentes, C. I., & Holman, M. J. 2008, a SUBARU archival search for faint trans-neptunian objects. AJ, 136, 83–97
Gáspár, A., Rieke, G. H., Su, K. Y. L., Balog, Z., Trilling, D., Muzzerole, J., Apai, D., & Kelly, B. C. 2009, The low level of debris disk activity at the time of the late heavy bombardment: a spitzer study of Praesepe. ApJ, 697, 1578–1596
Goldreich, P., & Sari, R. 2003, Eccentricity evolution for planets in gaseous disks. ApJ, 585, 1024–1037
Goldreich, P., & Tremaine, S. 1979, The excitation of density waves at the Lindblad and corotation resonances by an external potential. ApJ, 233, 857–871
Goldreich, P., & Tremaine, S. 1980, Disk-satellite interactions. ApJ, 241, 425–441
Goldreich, P., Lithwick, Y., & Sari, R. 2004, Final stages of planet formation. ApJ, 614, 497–507
Gomes, R. S., Morbidelli, A., & Levison, H. F. 2004, Planetary migration in a planetesimal disk: why did Neptune stop at 30 AU? Icarus, 170, 492–507
Gomes, R., Levison, H. F., Tsiganis, K., & Morbidelli, A. 2005, Origin of the cataclysmic Late Heavy Bombardment period of the terrestrial planets. Nature, 435, 466–469
Gradie, J., & Tedesco, E. 1982, Compositional structure of the asteroid belt. Science, 216, 1405–1407
Greenberg, R., Hartmann, W. K., Chapman, C. R., & Wacker, J. F. 1978, Planetesimals to planets – numerical simulation of collisional evolution. Icarus, 35, 1–26
Greenzweig, Y., & Lissauer, J. J. 1992, Accretion rates of protoplanets. II – Gaussian distributions of planetesimal velocities. Icarus, 100, 440–463
Guillot, T. 2005, The interiors of giant planets: models and outstanding questions. Annu. Rev. Earth Planet. Sci., 33, 493–530
Guillot, T., & Hueso, R. 2006, The composition of Jupiter: sign of a (relatively) late formation in a chemically evolved protosolar disc. MNRAS, 367, L47–L51
Guillot, T., Santos, N. C., Pont, F., Iro, N., Melo, C., & Ribas, I. 2006, A correlation between the heavy element content of transiting extrasolar planets and the metallicity of their parent stars. A&A, 453, L21–L24
Haisch, K. E., Jr., Lada, E. A., & Lada, C. J. 2001, Disk frequencies and lifetimes in young clusters. ApJ, 553, L153–L156
Hansen, B. M. S. 2009, Formation of the terrestrial planets from a narrow annulus. ApJ, 703, 1131–1140
Hartmann, W. K., Ryder, G., Dones, L., & Grinspoon, D. 2000, The time-dependent intense bombardment of the primordial earth/moon system, in Origin of the Earth and Moon, ed. R. M. Canup, K. Righter, et al. (Tucson: University of Arizona Press), 493–512
Hartmann, W. K., Quantin, C., & Mangold, N. 2007, Possible long-term decline in impact rates. 2. Lunar impact-melt data regarding impact history. Icarus, 186, 11–23
Hayashi, C. 1981, Structure of the Solar Nebula, growth and decay of magnetic fields and effects of magnetic and turbulent viscosities on the Nebula. Prog. Theor. Phys. Suppl., 70, 35–53
Henrard, J. 1993, The adiabatic invariants in classical mechanics. Dyn. Rep., 2, 117–235
Hillenbrand, L. A., Carpenter, J. M., Kim, J. S., Meyer, M. R., Backman, D. E., Moro-Martín, A., Hollenbach, D. J., Hines, D. C., Pascucci, I., & Bouwman, J. 2008, The complete census of 70 μm-bright Debris Disks within “the Formation and Evolution of Planetary Systems” Spitzer Legacy Survey of Sun-like Stars. ApJ, 677, 630–656
Horn, B., Lyra, W., Mac Low, M.-M., & Sándor, Z. 2012, Orbital migration of interacting low-mass planets in evolutionary radiative turbulent models. ArXiv e-prints arXiv:1202.1868
Ida, S., & Lin, D. N. C. 2004, Toward a deterministic model of planetary formation. II. The formation and retention of gas giant planets around stars with a range of metallicities. ApJ, 616, 567–572
Ida, S., & Lin, D. N. C. 2008, Toward a deterministic model of planetary formation. V. Accumulation near the ice line and super-earths. ApJ, 685, 584–595
Ida, S., & Makino, J. 1993, Scattering of planetesimals by a protoplanet – slowing down of runaway growth. Icarus, 106, 210
Ida, S., Bryden, G., Lin, D. N. C., & Tanaka, H. 2000, Orbital migration of neptune and orbital distribution of trans-neptunian objects. ApJ, 534, 428–445
Johansen, A., Youdin, A., & Mac Low, M.-M. 2009, Particle clumping and planetesimal formation depend strongly on metallicity. ApJ, 704, L75–L79
Jurić, M., & Tremaine, S. 2008, Dynamical origin of extrasolar planet eccentricity distribution. ApJ, 686, 603–620
Kalas, P., Graham, J. R., Chiang, E., Fitzgerald, M. P., Clampin, M., Kite, E. S., Stapelfeldt, K., Marois, C., & Krist, J. 2008, Optical images of an exosolar planet, 25 light-years from Earth. Science, 322, 1345
Kelsall, T., et al. 1998, The COBE diffuse infrared background experiment search for the cosmic infrared background. II. Model of the interplanetary dust cloud. ApJ, 508, 44–73
Kenyon, S. J., & Bromley, B. C. 2006, Terrestrial planet formation. I. The transition from oligarchic growth to chaotic growth. AJ, 131, 1837–1850
Kenyon, S. J., Bromley, B. C., O’Brien, D. P., & Davis, D. R. 2008, Formation and collisional evolution of Kuiper belt objects, in The Solar System Beyond Neptune, ed. M. A. Barucci et al. (Tucson: University of Arizona Press), 293–313
Kirsh, D. R., Duncan, M., Brasser, R., & Levison, H. F. 2009, Simulations of planet migration driven by planetesimal scattering. Icarus, 199, 197–209
Kleine, T., Touboul, M., Bourdon, B., Nimmo, F., Mezger, K., Palme, H., Jacobsen, S. B., Yin, Q.-Z., & Halliday, A. N. 2009, Hf-W chronology of the accretion and early evolution of asteroids and terrestrial planets. Geochim. Cosmochim. Acta, 73, 5150–5188
Kley, W., & Crida, A. 2008, Migration of protoplanets in radiative discs. A&A, 487, L9–L12
Kley, W., & Dirksen, G. 2006, Disk eccentricity and embedded planets. A&A, 447, 369–377
Kley, W., Peitz, J., & Bryden, G. 2004, Evolution of planetary systems in resonance. A&A, 414, 735–747
Kley, W., Lee, M. H., Murray, N., & Peale, S. J. 2005, Modeling the resonant planetary system GJ 876. A&A, 437, 727–742
Kokubo, E., & Genda, H. 2010, Formation of terrestrial planets from protoplanets under a realistic accretion condition. ApJ, 714, L21–L25
Kokubo, E., & Ida, S. 1998, Oligarchic growth of protoplanets. Icarus, 131, 171–178
Kokubo, E., Kominami, J., & Ida, S. 2006, Formation of terrestrial planets from protoplanets. I statistics of basic dynamical properties. ApJ, 642, 1131–1139
Lambrechts, M., & Johansen, A. 2012, Rapid growth of gas-giant cores by pebble accretion. A&A (in press)
Levison, H. F., & Agnor, C. 2003, The role of giant planets in terrestrial planet formation. AJ, 125, 2692–2713
Levison, H. F., & Morbidelli, A. 2007, Models of the collisional damping scenario for ice-giant planets and Kuiper belt formation. Icarus, 189, 196–212
Levison, H. F., Lissauer, J. J., & Duncan, M. J. 1998, Modeling the diversity of outer planetary systems. AJ, 116, 1998–2014
Levison, H. F., Dones, L., Chapman, C. R., Stern, S. A., Duncan, M. J., & Zahnle, K. 2001, Could the Lunar “Late Heavy Bombardment” Have Been Triggered by the Formation of Uranus and Neptune? Icarus, 151, 286–306
Levison, H. F., Morbidelli, A., Gomes, R., & Backman, D. 2007, Planet migration in planetesimal disks, in Protostars and Planets V, ed. B. Reipurth, D. Jewitt, & K. Keil (Tucson: University of Arizona Press), 669–684
Levison, H. F., Morbidelli, A., Vanlaerhoven, C., Gomes, R., & Tsiganis, K. 2008, Origin of the structure of the Kuiper belt during a dynamical instability in the orbits of Uranus and Neptune. Icarus, 196, 258–273
Levison, H. F., Bottke, W. F., Gounelle, M., Morbidelli, A., Nesvorný, D., & Tsiganis, K. 2009, Contamination of the asteroid belt by primordial trans-Neptunian objects. Nature, 460, 364–366
Levison, H. F., Thommes, E., & Duncan, M. J. 2010, Modeling the formation of giant planet cores. I. evaluating key processes. AJ, 139, 1297–1314
Levison, H. F., Morbidelli, A., Tsiganis, K., Nesvorny, D., & Gomes, R. 2011, Late orbital instabilities in the outer planets induced by interaction with a self-gravitating planetesimal disk. AJ, 142, 152
Lin, D. N. C., & Ida, S. 1997, On the origin of massive eccentric planets. ApJ, 477, 781
Lin, D. N. C., & Papaloizou, J. 1986a. On the tidal interaction between protoplanets and the primordial solar nebula. II – self-consistent nonlinear interaction. ApJ, 307, 395–409
Lin, D. N. C., & Papaloizou, J. 1986b, On the tidal interaction between protoplanets and the protoplanetary disk. III – orbital migration of protoplanets. ApJ, 309, 846–857
Lin, D. N. C., Bodenheimer, P., & Richardson, D. C. 1996, Orbital migration of the planetary companion of 51 Pegasi to its present location. Nature, 380, 606–607
Lodders, K. 2003, Solar system abundances and condensation temperatures of the elements. ApJ, 591, 1220–1247
Lynden-Bell, D., & Pringle, J. E. 1974, The evolution of viscous discs and the origin of the Nebular variables. MNRAS, 168, 603–637
Lyra, W., Johansen, A., Klahr, H., & Piskunov, N. 2009a. Standing on the shoulders of giants. Trojan Earths and vortex trapping in low mass self-gravitating protoplanetary disks of gas and solids. A&A, 493, 1125–1139
Lyra, W., Johansen, A., Zsom, A., Klahr, H., & Piskunov, N. 2009b. Planet formation bursts at the borders of the dead zone in 2D numerical simulations of circumstellar disks. A&A, 497, 869–888
Lyra, W., Paardekooper, S.-J., & Mac Low, M.-M. 2010, Orbital migration of low-mass planets in evolutionary radiative models: avoiding catastrophic infall. ApJ, 715, L68–L73
Malhotra, R. 1993, The origin of Pluto’s peculiar orbit. Nature, 365, 819–821
Malhotra, R. 1995, The origin of pluto’s orbit: implications for the solar system beyond Neptune. AJ, 110, 420
Marchi, S., Bottke, W. F., Kring, D. A., & Morbidelli, A. 2012, The onset of the lunar cataclysm as recorded in its ancient crater populations. Earth Planet. Sci. Lett., 325, 27–38
Marois, C., Macintosh, B., Barman, T., Zuckerman, B., Song, I., Patience, J., Lafrenière, D., & Doyon, R. 2008, Direct imaging of multiple planets orbiting the star HR 8799. Science, 322, 1348
Marzari, F., & Weidenschilling, S. J. 2002, Eccentric extrasolar planets: the jumping Jupiter model. Icarus, 156, 570–579
Marzari, F., Baruteau, C., & Scholl, H. 2010, Planet-planet scattering in circumstellar gas disks. A&A, 514, L4
Masset, F. S., & Casoli, J. 2010, Saturated torque formula for planetary migration in viscous disks with thermal diffusion: recipe for protoplanet population synthesis. ApJ, 723, 1393–1417
Masset, F., & Snellgrove, M. 2001, Reversing type II migration: resonance trapping of a lighter giant protoplanet. MNRAS, 320, L55–L59
Masset, F. S., Morbidelli, A., Crida, A., & Ferreira, J. 2006, Disk surface density transitions as protoplanet traps. ApJ, 642, 478–487
Maurer, P., Eberhardt, P., Geiss, J., Grogler, N., Stettler, A., Brown, G. M., Peckett, A., & Krahenbuhl, U. 1978, Pre-Imbrian craters and basins – ages, compositions and excavation depths of Apollo 16 breccias. Geochim. Cosmochim. Acta, 42, 1687–1720
Milani, A., Nobili, A. M., & Carpino, M. 1987, Secular variations of the semimajor axes – theory and experiments. A&A, 172, 265–279
Militzer, B., & Hubbard, W. B. 2009, Comparison of Jupiter interior models derived from first-principles simulations. Astrophys. Space Sci., 322, 129–133
Min, M., Dullemond, C. P., Kama, M., & Dominik, C. 2011, The thermal structure and the location of the snow line in the protosolar Nebula: axisymmetric models with full 3-D radiative transfer. Icarus, 212, 416–426
Minton, D. A., & Malhotra, R. 2009, A record of planet migration in the main asteroid belt. Nature, 457, 1109–1111
Moeckel, N., & Armitage, P. J. 2012, Hydrodynamic outcomes of planet scattering in transitional discs. MNRAS, 419, 366–376
Moekel, N., Raymond, S. N., & Armitage, Ph. J. 2008, Extrasolar planets eccentricities from scattering in the presence of residual gas-disks. ApJ, 688, 1361–1367
Moorhead, A. V., & Adams, F. C. 2005, Giant planet migration through the action of disk torques and planet scattering. Icarus, 178, 517–539
Morbidelli, A., & Crida, A. 2007, The dynamics of Jupiter and Saturn in the gaseous protoplanetary disk. Icarus, 191, 158–171
Morbidelli, A., Chambers, J., Lunine, J. I., Petit, J. M., Robert, F., Valsecchi, G. B., & Cyr, K. E. 2000, Source regions and time scales for the delivery of water to Earth. Meteorit. Planet. Sci., 35, 1309–1320
Morbidelli, A., Tsiganis, K., Crida, A., Levison, H. F., & Gomes, R. 2007, Dynamics of the giant planets of the solar system in the gaseous protoplanetary disk and their relationship to the current orbital architecture. AJ, 134, 1790–1798
Morbidelli, A., Crida, A., Masset, F., & Nelson, R. P. 2008a, Building giant-planet cores at a planet trap. A&A, 478, 929–937
Morbidelli, A., Levison, H. F., & Gomes, R. 2008b. The dynamical structure of the Kuiper belt and its primordial origin, in The Solar System Beyond Neptune, ed. M. A. Barucci et al. (Tucson: University of Arizona Press), 275–292
Morbidelli, A., Brasser, R., Gomes, R., Levison H. F., & Tsiganis, K., 2010, Evidence from the asteroid belt for a violent past evolution of Jupiter’s orbit. AJ, 140, 1391–1401
Morbidelli, A., Marchi, S., & Bottke, W. F. 2012, The saw timeline of the first billion year of Lunar bombardment. LPI Contrib., 1649, 53–54
Morishima, R., Stadel, J., & Moore, B. 2010, From planetesimals to terrestrial planets: N-body simulations including the effects of Nebular gas and giant planets. Icarus, 207, 517–535
Morfill, G. E., & Voelk, H. J. 1984, Transport of dust and vapor and chemical fractionation in the early protosolar cloud. ApJ, 287, 371–395
Nelson, R. P. 2005, On the orbital evolution of low mass protoplanets in turbulent, magnetised disks. A&A, 443, 1067–1085
Nelson, R. P., & Papaloizou, J. C. B. 2003, The interaction of a giant planet with a disc with MHD turbulence – II. The interaction of the planet with the disc. MNRAS, 339, 993–1005
Nesvorný, D. 2011, Young solar system’s fifth giant planet? ApJ, 742, L22
Nesvorný, D., & Morbidelli, A., 2012, Statistical study of the early solar systems instability with 4, 5 and 6 giant planets. AJ (in press)
Nesvorný, D., Jenniskens, P., Levison, H. F., Bottke, W. F., Vokrouhlický, D., & Gounelle, M. 2010, Cometary origin of the zodiacal cloud and carbonaceous micrometeorites. Implications for hot debris disks. ApJ, 713, 816–836
Nettelmann, N., Holst, B., Kietzmann, A., French, M., Redmer, R., & Blaschke, D. 2008, Ab initio equation of state data for hydrogen, helium, and water and the internal structure of Jupiter. ApJ, 683, 1217–1228
Neukum, G. 1983, Habilitation Dissertation for Faculty Membership (Munich: University of Munich)
Neukum, G., & Ivanov, B. A. 1994, Crater size distributions and impact probabilities on Earth from Lunar, terrestrial-planet, and asteroid cratering data, in Hazards Due to Comets and Asteroids, ed. T. Gehrels (Tucson: University of Arizona Press), 359
Neukum, G., & Wilhelms, D. E. 1982, Ancient lunar impact record. Lunar Planet. Inst. Sci. Conf. Abstr., 13, 590–591
Norman, M. D., Duncan, R. A., & Huard, J. J. 2010, Imbrium provenance for the Apollo 16 Descartes terrain: argon ages and geochemistry of lunar breccias 67016 and 67455. Geochim. Cosmochim. Acta, 74, 763–783
O’Brien, D. P., Morbidelli, A., & Levison, H. F. 2006, Terrestrial planet formation with strong dynamical friction. Icarus, 184, 39–58
O’Brien, D. P., Morbidelli, A., & Bottke, W. F. 2007, The primordial excitation and clearing of the asteroid belt – Revisited. Icarus, 191, 434–452
Öpik, E. J., 1976, Interplanetary Encounters: Close Range Gravitational Interactions (Elsevier, New York)
Paardekooper, S.-J., & Mellema, G. 2006, Halting type I planet migration in non-isothermal disks. A&A, 459, L17–L20
Paardekooper, S.-J., & Papaloizou, J. C. B. 2009, On corotation torques, horseshoe drag and the possibility of sustained stalled or outward protoplanetary migration. MNRAS, 394, 2283–2296
Paardekooper, S.-J., Baruteau, C., Crida, A., & Kley, W. 2010, A torque formula for non-isothermal type I planetary migration – I. Unsaturated horseshoe drag. MNRAS, 401, 1950–1964
Papaloizou, J. C. B., Nelson, R. P., & Masset, F. 2001, Orbital eccentricity growth through disc-companion tidal interaction. A&A, 366, 263–275
Papanastassiou, D. A., & Wasserburg, G. J. 1971a. Rb-Sr ages of igneous rocks from the Apollo 14 mission and the age of the Fra Mauro formation. Earth Planet. Sci. Lett., 12, 36
Papanastassiou, D. A., & Wasserburg, G. J. 1971b. Lunar chronology and evolution from Rb-Sr studies of Apollo 11 and 12 samples. Earth Planet. Sci. Lett., 11, 37
Petit, J.-M., Morbidelli, A., & Chambers, J. 2001, The primordial excitation and clearing of the asteroid belt. Icarus, 153, 338–347
Pierens, A., & Nelson, R. P. 2008, Constraints on resonant-trapping for two planets embedded in a protoplanetary disc. A&A, 482, 333–340
Podolak, M., & Zucker, S. 2004, A note on the snow line in protostellar accretion disks. Meteorit. Planet. Sci., 39, 1859–1868
Pollack, J. B., Hubickyj, O., Bodenheimer, P., Lissauer, J. J., Podolak, M., & Greenzweig, Y. 1996, Formation of the giant planets by concurrent accretion of solids and gas. Icarus, 124, 62–85
Rafikov, R. R. 2004, Fast accretion of small planetesimals by protoplanetary cores. AJ, 128, 1348–1363
Rasio, F. A., & Ford, E. B. 1996, Dynamical instabilities and the formation of extrasolar planetary systems. Science, 274, 954–956
Raymond, S. N., Quinn, T., & Lunine, J. I. 2004, Making other earths: dynamical simulations of terrestrial planet formation and water delivery. Icarus, 168, 1–17
Raymond, S. N., Quinn, T., & Lunine, J. I. 2005, Terrestrial planet formation in disks with varying surface density profiles. ApJ, 632, 670–676
Raymond, S. N., Quinn, T., & Lunine, J. I. 2006a, High-resolution simulations of the final assembly of Earth-like planets I. Terrestrial accretion and dynamics. Icarus, 183, 265–282
Raymond, S. N., Mandell, A. M., & Sigurdsson, S. 2006b. Exotic Earths: forming habitable worlds with giant Planet migration. Science, 313, 1413–1416
Raymond, S. N., Quinn, T., & Lunine, J. I. 2007, High-resolution simulations of the final assembly of Earth-like Planets. 2. Water delivery and planetary habitability. Astrobiology, 7, 66–84
Raymond, S. N., Barnes, R., Veras, D., Armitage, P. J., Gorelick, N., & Greenberg, R. 2009a, Planet-Planet scattering leads to tightly packed planetary systems. ApJ, 696, L98–L101
Raymond, S. N., O’Brien, D. P., Morbidelli, A., & Kaib, N. A. 2009b. Building the terrestrial planets: constrained accretion in the inner Solar System. Icarus, 203, 644–662
Raymond, S. N., Armitage, P. J., Moro-Martín, A., Booth, M., Wyatt, M. C., Armstrong, J. C., Mandell, A. M., Selsis, F., & West, A. A. 2011, Debris disks as signposts of terrestrial planet formation. A&A, 530, A62
Ryder, G., 2002, Mass flux in the ancient Earth-Moon system and the benign implications for the origin of life on Earth. J. Geophys. Res.-Planets, 107, 6–14
Sándor, Z., Lyra, W., & Dullemond, C. P. 2011, Formation of planetary cores at type I migration traps. ApJ, 728, L9
Saslaw, W. C. 1985, Thermodynamics and galaxy clustering – relaxation of N-body experiments. ApJ, 297, 49–60
Stamatellos, D., & Whitworth, A. P. 2008, Can giant planets form by gravitational fragmentation of discs? A&A, 480, 879–887
Stewart, G., & Wetherill, G. 1988, Evolution of planetesimal velocities. Icarus, 79, 542–553
Shakura, N. I., & Sunyaev, R. A. 1973, Black holes in binary systems. Observational appearance. A&A, 24, 337–355
Stöffler, D., & Ryder, G. 2001, Stratigraphy and isotope ages of lunar geologic units: chronological standard for the inner solar system. Space Sci. Rev., 96, 9–54
Tanaka, H., Takeuchi, T., & Ward, W. R. 2002, Three-Dimensional Interaction between a Planet and an isothermal gaseous disk. I. Corotation and Lindblad torques and planet migration. ApJ, 565, 1257–1274
Tera, F., Papanastassiou, D. A., & Wasserburg, G. J. 1974, Isotopic evidence for a terminal lunar cataclysm. Earth Planet. Sci. Lett., 22, 1
Thommes, E. W., Duncan, M. J., & Levison, H. F. 1999, The formation of Uranus and Neptune in the Jupiter-Saturn region of the Solar System. Nature, 402, 635–638
Thommes, E. W., Duncan, M. J., & Levison, H. F. 2003, Oligarchic growth of giant planets. Icarus, 161, 431–455
Thommes, E., Nagasawa, M., & Lin, D. N. C. 2008, Dynamical shake-up of planetary systems. II N-body simulations of solar system terrestrial planet formation induced by secular resonance sweeping. ApJ, 676, 728–739
Tiscareno, M. S., & Malhotra, R. 2003, The dynamics of known centaurs. AJ, 126, 3122–3131 Trail, D., Mojzsis, S. J., & Harrison, T. M. 2007, Thermal events documented in Hadean zircons by ion microprobe depth profiles. Geochim. Cosmochim. Acta, 71, 4044–4065
Trilling, D. E., Bryden, G., Beichman, C. A., Rieke, G. H., Su, K. Y. L., Stansberry, J. A., Blaylock, M., Stapelfeldt, K. R., Beeman, J. W., & Haller, E. E. 2008, Debris disks around sun-like stars. ApJ, 674, 1086–1105
Tsiganis, K., Gomes, R., Morbidelli, A., & Levison, H. F. 2005, Origin of the orbital architecture of the giant planets of the Solar System. Nature, 435, 459–461
Turner, G., Cadogan, P. H., & Yonge, C. J. 1973, Apollo 17 age determinations. Nature, 242, 513–515
Valley J. W., Peck W. H., King E. M., & Wilde S. A. 2002, A cool early Earth. Geology, 30, 351–354
Valsecchi, A., & Manara, G. B. 1997, Dynamics of comets in the outer planetary region. II. Enhanced planetary masses and orbital evolutionary paths. A&A, 323, 986–998
Veras, D., & Armitage, P. J. 2004, Outward migration of extrasolar planets to large orbital radii. MNRAS, 347, 613–624
Veras, D., Crepp, J. R., & Ford, E. B. 2009, Formation, survival, and detectability of planets beyond 100 AU. ApJ, 696, 1600–1611
Walsh, K. J., Morbidelli, A., Raymond, S. N. O’Brien, D. P., & Mandell, A. M. 2011, A low mass for Mars from Jupiter’s early gas-driven migration. Nature, 475, 206–209
Ward, W. R. 1986, Density waves in the solar Nebula – differential Lindblad torque. Icarus, 67, 164–180
Ward, W. R. 1997, Protoplanet migration by Nebula tides. Icarus, 126, 261–281
Weidenschilling, S. J. 1977, The distribution of mass in the planetary system and solar Nebula. Astrophys. Space Sci., 51, 153–158
Weidenschilling, S. J., & Davis, D. R. 1985, Orbital resonances in the solar Nebula – implications for planetary accretion. Icarus, 62, 16–29
Weidenschilling, S. J., & Marzari, F. 1996, Gravitational scattering as a possible origin for giant planets at small stellar distances. Nature, 384, 619–621
Weidenschilling, S. J., Spaute, D., Davis, D. R., Marzari, F., & Ohtsuki, K. 1997, Accretional evolution of a planetesimal swarm. Icarus, 128, 429–455
Wetherill, G. W. 1992, An alternative model for the formation of the asteroids. Icarus, 100, 307–325
Wetherill, G. W., & Stewart, G. R. 1989, Accumulation of a swarm of small planetesimals. Icarus, 77, 330–357
Wetherill, G. W., & Stewart, G. R. 1993, Formation of planetary embryos – effects of fragmentation, low relative velocity, and independent variation of eccentricity and inclination. Icarus, 106, 190
Villeneuve, J., Chaussidon, M., & Libourel, G. 2009, Homogeneous distribution of 26Al in the solar system from the Mg isotopic composition of chondrules. Science, 325, 985–988
Wasserburg, G. J., & Papanastassiou, D. A. 1971, Age of an Apollo 15 mare basalt: lunar crust and mantle evolution. Earth Planet. Sci. Lett., 13, 97
Wong, M. H., Mahaffy, P. R., Atreya, S. K., Niemann, H. B., & Owen, T. C. 2004, Updated Galileo probe mass spectrometer measurements of carbon, oxygen, nitrogen, and sulfur on Jupiter. Icarus, 171, 153–170
Wyatt, M. C., Smith, R., Greaves, J. S., Beichman, C. A., Bryden, G., & Lisse, C. M. 2007, Transience of hot dust around sun-like stars. ApJ, 658, 569–583
Zhang, H., & Zhou, J.-L. 2010, On the orbital evolution of a giant planet pair embedded in a gaseous disk. I. Jupiter-Saturn configuration. ApJ, 714, 532–548
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media Dordrecht
About this entry
Cite this entry
Morbidelli, A. (2013). Dynamical Evolution of Planetary Systems. In: Oswalt, T.D., French, L.M., Kalas, P. (eds) Planets, Stars and Stellar Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5606-9_2
Download citation
DOI: https://doi.org/10.1007/978-94-007-5606-9_2
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-5605-2
Online ISBN: 978-94-007-5606-9
eBook Packages: Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics