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Dynamics of Multiple Planet Systems

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Exoplanets

Part of the book series: Springer Praxis Books ((ASTRONOMY))

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Abstract

This chapter discusses the dynamical properties of multiple planet systems. The orbits of these planets evolve due to tidal, resonant, and/or secular (long-term) effects. Basic analytical and numerical techniques can describe these interactions. Multiple planet systems may also evolve chaotically, and some principles of chaos theory are described. Finally, this chapter discusses the current distributions of dynamical properties of exoplanetary systems, possible origins of these distributions, and compares exoplanetary systems to the Solar System.

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References

  • Adams, F.C. & Laughlin, G. 2006. Relativistic Effects in Extrasolar Planetary Systems. Int. J. Mod. Phys. D 15, 2133–2140.

    Article  MATH  ADS  Google Scholar 

  • Asghari, N. et al. 2004. Stability of terrestrial planets in the habitable zone of Gl 777 A, HD 72659, Gl 614, 47 Uma and HD 4208. A&A 426, 353–365.

    Article  ADS  Google Scholar 

  • Barnes, R. & Greenberg, R. 2006. Extrasolar Planetary Systems Near a Secular Separatrix. ApJ 638, 478–487.

    Article  ADS  Google Scholar 

  • Barnes, R. & Greenberg, R. 2006. Stability Limits in Extrasolar Planetary Systems. ApJ 647, L153–L156.

    Article  ADS  Google Scholar 

  • Barnes, R. & Greenberg, R. 2006. Behavior of Apsidal Orientations in Planetary Systems. ApJ 652, L53–L56.

    Article  ADS  Google Scholar 

  • Barnes, R. & Greenberg, R. 2007. Apsidal Behavior among Planetary Orbits: Testing the Planet-Planet Scattering Model. ApJ 659, L53–L56.

    Article  ADS  Google Scholar 

  • Barnes, R. & Greenberg, R. 2007. Stability Limits in Resonant Planetary Systems. ApJ, accepted.

    Google Scholar 

  • Barnes, R. & Quinn, T.R. 2001. A Statistical Examination of the Short-Term Stability of the υ Andromedae Planetary System. ApJ 550, 884–889.

    Article  ADS  Google Scholar 

  • Barnes, R. & Quinn, T.R. 2004. The (In)stability of Planetary Systems. ApJ 611, 494–516.

    Article  ADS  Google Scholar 

  • Barnes, R. & Raymond, S.N. 2004. Predicting Planets in Known Extrasolar Planetary Systems. I. Test Particle Simulations. ApJ 617, 569–574.

    Article  ADS  Google Scholar 

  • Bean, J.L. et al. 2007. Detection of a Third Planet in the HD 74156 System Using the Hobby-Eberly Telescope. ApJ, accepted

    Google Scholar 

  • Beaugé, C., Ferraz-Mello, S. & Michtchenko, T.A. 2003. Extrasolar Planets in Mean-Motion Resonance: Apses Alignment and Asymmetric Stationary Solutions. ApJ 593, 1124–1133.

    Article  ADS  Google Scholar 

  • Beaugé, C., Michtchenko, T.A. & Ferraz-Mello, S. 2005. Planetary migration and extrasolar planets in the 2/1 mean-motion resonance. MNRAS 365, 1160–1170.

    Article  ADS  Google Scholar 

  • Beaugé, C. et al. 2007. Co-orbital terrestrial planets in exoplanetary systems: a formation scenario. A&A 463, 359–367.

    Article  ADS  Google Scholar 

  • Bodenheimer, P., Laughlin, G. & Lin, D.N.C. 2003. On the Radii of Extrasolar Giant Planets. ApJ 592, 555–563.

    Article  ADS  Google Scholar 

  • Bois, E. et al. 2003. Conditions of Dynamical Stability for the HD 160691 Planetary System. ApJ 598, 1312–1320.

    Article  ADS  Google Scholar 

  • Butler, R.P. et al. 1999. Evidence for Multiple Companions to υ Andromedae. ApJ 526, 916–927.

    Article  ADS  Google Scholar 

  • Butler, R.P. et al. 2002. On the Double-Planet System around HD 83443. ApJ 578, 565–572.

    Article  ADS  Google Scholar 

  • Butler, R.P. et al. 2006. Catalog of Nearby Exoplanets. ApJ 646, 505–522.

    Article  ADS  Google Scholar 

  • Chambers, J.E. 1999. A hybrid symplectic integrator that permits close encounters between massive bodies. MNRAS 304, 793–799.

    Article  ADS  Google Scholar 

  • Chambers, J.E., Wetherill, G.W. & Boss, A. 1996. The Stability of Multi-Planet Systems. Icarus 119, 261–268.

    Article  ADS  Google Scholar 

  • Chiang, E.I. & Murray, N. 2002. Eccentricity Excitation and Apsidal Resonance Capture in the Planetary System υ Andromedae. ApJ 576, 473–477.

    Article  ADS  Google Scholar 

  • Chiang, E.I., Tabachnik, S. & Tremaine, S. Apsidal Alignment in υ Andromedae. AJ 122, 1607–1615.

    Google Scholar 

  • Chirikov, B.V. 1979. A universal instability of many-dimensional oscillator systems. Phys. Rep. 52, 263–379.

    Article  ADS  MathSciNet  Google Scholar 

  • Cincotta, P. & Simó, C. 2000. Simple tools to study global dynamics in nonaxisymmetric galactic potentials-I. A&AS 147, 205–228.

    Article  ADS  Google Scholar 

  • Cochran, W.D. et al. 2007. A Planetary System Around HD 155358: The Lowest Metallicity Planet Host Star. ApJ, in press.

    Google Scholar 

  • Correia, A.C.M. et al. 2005. The CORALIE survey for southern extra-solar planets. XIII. A pair of planets around HD 202206 or a circumbinary planet? A&A 440, 751–758.

    Article  ADS  Google Scholar 

  • Cuntz, M. et al. 2003. On the possibility of earth-type habitable planets around 47 UMa. Icarus 162, 214–221.

    Article  ADS  Google Scholar 

  • D’Angelo, G., Lubow, S.H. & Bate, M.R. 2006. Evolution of Giant Planets in Eccentric Disks. ApJ 652, 1698–1714.

    Article  ADS  Google Scholar 

  • Dvorak, R. et al. 2003. A study of the stable regions in the planetary system HD 74156-Can it host earthlike planets in habitable zones? A&A 410, L13–L16.

    Article  ADS  Google Scholar 

  • Dvorak, R. et al. 2004. Extrasolar Trojan planets close to habitable zones. A&A, 426, L37–L40.

    Article  ADS  Google Scholar 

  • Érdi, B. et al. 2004. The dynamical structure of the habitable zone in the HD 38529, HD 168443 and HD 169830 systems. MNRAS 351, 1043–1048.

    Article  ADS  Google Scholar 

  • Érdi, B, & Sándor, Zs. 2005. Stability of Co-Orbital Motion in Exoplanetary Systems. CeMDA 92, 113–121.

    MATH  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Ferraz-Mello, S., Michtchenko, T.A. & Beaugé, C. 2005. The Orbits of the Extrasolar Planets HD 82943c and b. ApJ 621, 473–481.

    Article  ADS  Google Scholar 

  • Fischer, D.A. et al. 2002. A Second Planet Orbiting 47 Ursae Majoris. ApJ 564, 1028–1034.

    Article  ADS  Google Scholar 

  • Fischer, D.A. et al. 2003. A Planetary Companion to HD 40979 and Additional Planets Orbiting HD 12661 and HD 38529. ApJ 586, 1394–1408.

    Article  ADS  Google Scholar 

  • Ford, E.B., Lystad, V. & Rasio, F.A. 2005. Planet-planet scattering in the upsilon Andromedae system. Nature 434, 873–876.

    Article  ADS  Google Scholar 

  • Funk, B. et al. 2004. Resonances in Multiple Planetary Systems. CeMDA 90, 43–50.

    MATH  ADS  MathSciNet  Google Scholar 

  • Gladman, B. 1993. Dynamics of systems of two close planets. Icarus 106, 247–263.

    Article  ADS  Google Scholar 

  • Gladman, B., Duncan, M. & Candy, J. 1991. Symplectic integrators for long-term integrations in celestial mechanics. CeMDA 52, 221–240.

    MATH  ADS  MathSciNet  Google Scholar 

  • Goździewski, K. 2002. Stability of the 47 UMa planetary system. A&A 393, 997–1013.

    Article  ADS  Google Scholar 

  • Goździewski, K. 2003. Stability of the HD 12661 Planetary System. A&A 398, 1151–1161.

    Article  ADS  Google Scholar 

  • Goździewski, K. & Konacki, M. 2004. Dynamical Properties of the Multiplanet System around HD 169830. ApJ 610, 1093–1106.

    Article  ADS  Google Scholar 

  • Goździewski, K. & Konacki, M. 2006. Trojan Pairs in the HD 128311 and HD 82943 Planetary Systems? ApJ 647, 573–586.

    Article  ADS  Google Scholar 

  • Goździewski, K., Konacki, M. & Maciejewski, A. 2006. Orbital Configurations and Dynamical Stability of Multiplanet Systems around Sun-like Stars HD 202206, 14 Herculis, HD 37124, and HD 108874. ApJ 645, 688–703.

    Article  ADS  Google Scholar 

  • Goździewski, K. & Maciejewski, A. 2001. Dynamical Analysis of the Orbital Parameters of the HD 82943 Planetary System. ApJ 563, L81–L85.

    Article  ADS  Google Scholar 

  • Goździewski, K. & Maciejewski, A. 2003. The Janus Head of the HD 12661 Planetary System. ApJ 586, L153–L156.

    Article  ADS  Google Scholar 

  • Goździewski, K., Maciejewski, A. & Migaszewski, C. 2007. On the Extrasolar Multiplanet System around HD 160691. ApJ 657, 546–558.

    Article  ADS  Google Scholar 

  • Goźdzeiwski, K. et al. 2001. Global dynamics of planetary systems with the MEGNO criterion. A&A 378, 569–586.

    Article  ADS  Google Scholar 

  • Greenberg, R. 1977. Orbit-orbit resonances in the solar system-Varieties and similarities. Vistas in Astron. 21 209–239.

    Article  ADS  Google Scholar 

  • Hadjidemetriou, J.D. 2002. Resonant Periodic Motion and the Stability of Extrasolar Planetary Systems. CeMDA 83, 141–154.

    MATH  ADS  MathSciNet  Google Scholar 

  • Hadjidemetriou, J.D. 2006. Symmetric and asymmetric librations in extrasolar planetary systems: a global view. CeMDA 95, 225–244.

    MATH  ADS  MathSciNet  Google Scholar 

  • Ito, T. & Miyama, S.M. 2001. An Estimation of Upper Limit Masses of 03c5 Andromedae Planets. ApJ 552, 372–379.

    Article  ADS  Google Scholar 

  • Jiang, I.-G. & Ip, W.-H. 2001. The planetary system of upsilon Andromedae. A&A 367, 943–948.

    Article  ADS  Google Scholar 

  • Ji, J-H. & Liu, L. 2006. Stability and 2:1 resonance in the planetary system HD 829431. ChA&A 30, 75–86.

    ADS  Google Scholar 

  • Ji, J., Liu, L. & Li, G.-Y. 2002. The Dynamical Simulations of the Planets Orbiting GJ 876. ApJ 572, 1041–1047.

    Article  ADS  Google Scholar 

  • Ji, J. et al. 2002. The stabilising mechanism of the HD 82943 planetary system. ChA&A 26, 379–385.

    ADS  Google Scholar 

  • Ji, J. et al. 2003. The apsidal motion in multiple planetary systems. ChA&A 27, 127–132.

    ADS  Google Scholar 

  • Ji, J. et al. 2003. Could the 55 Cancri Planetary System Really Be in the 3:1 Mean Motion Resonance? ApJ 585, L139–L142.

    Article  ADS  Google Scholar 

  • Ji, J. et al. 2003. The Librating Companions in HD 37124, HD 12661, HD 82943, 47 Ursa Majoris, and GJ 876: Alignment or Antialignment? ApJ 591, L57–L60.

    Article  ADS  Google Scholar 

  • Ji, J. et al. 2005. Could the 47 Ursae Majoris Planetary System be a Second Solar System? Predicting the Earth-like Planets. ApJ 631, 1191–1197.

    Article  ADS  Google Scholar 

  • Ji, J. et al. 2007. The Secular Evolution and Dynamical Architecture of the Neptunian Triplet Planetary System HD 69830. ApJ 657, 1092–1097.

    Article  ADS  Google Scholar 

  • Jones, B.W. & Sleep, P.N. The stability of the orbits of Earth-mass planets in the habitable zone of 47 Ursae Majoris. A&A 393, 1015–1026.

    Google Scholar 

  • Jones, B.W., Sleep, P.N. & Chambers, J.E. 2001. The stability of the orbits of terrestrial planets in the habitable zones of known exoplanetary systems. A&A 366, 254–262.

    Article  ADS  Google Scholar 

  • Kasting, J.F., Whitmire, D.P. & Reynolds, R.T. 1993. Habitable Zones around Main Sequence Stars. Icarus 101, 108–128.

    Article  ADS  Google Scholar 

  • Kinoshita, H. & Nakai, H. 2001. Stability of the GJ 876 Planetary System. PASJ 53, L25–L26.

    ADS  Google Scholar 

  • Kley, W. et al. 2005. Modeling the resonant planetary system GJ 876. A&A 437, 727–742.

    Article  ADS  Google Scholar 

  • Kley, W., Peitz, J. & Bryden, G. 2004. Evolution of planetary systems in resonance. A&A 414, 735–747.

    Article  ADS  Google Scholar 

  • Kirkwood, D. 1888. The Asteroids, or Minor Planets Between Mars and Jupiter, J. B. Lippencott, Philadelphia.

    Google Scholar 

  • Kiseleva-Eggleton, L. et al. 2002. Global Dynamics and Stability Limits for Planetary Systems around HD 12661, HD 38529, HD 37124, and HD 160691. ApJ 578, L145–L148.

    Article  ADS  Google Scholar 

  • Laakso, T., Rantala, J. & Kaasalainen, M. 2006. Gravitational scattering by giant planets. A&A 456, 373–378.

    Article  MATH  ADS  Google Scholar 

  • Laskar, J. 1989. A numerical experiment on the chaotic behaviour of the solar system. Nature 338, 237–238.

    Article  ADS  Google Scholar 

  • Laskar, J. On the Spacing of Planetary Systems. Phys. Rev. Lett. 84, 3240–3243.

    Google Scholar 

  • Laughlin, G. & Adams, F.C. 1999. Stability and Chaos in the υ Andromedae Planetary System. ApJ 526, 881–889.

    Article  ADS  Google Scholar 

  • Laughlin, G. & Chambers, J.E. 2001. Short-Term Dynamical Interactions among Extrasolar Planets. ApJ 551, L109–L113.

    Article  ADS  Google Scholar 

  • Laughlin, G. & Chambers, J.E. 2002. Extrasolar Trojans: The Viability and Detectability of Planets in the 1:1 Resonance. AJ 124, 592–600.

    Article  ADS  Google Scholar 

  • Laughlin, G., Chambers, J.E. & Fischer, D.A. 2002. A Dynamical Analysis of the 47 Ursae Majoris Planetary System. ApJ 579 455–467.

    Article  ADS  Google Scholar 

  • Laughlin, G. et al. 2005. The GJ 876 Planetary System: A Progress Report. ApJ 622 1182–1190.

    Article  ADS  Google Scholar 

  • Lecar, M. et al. 2001. Chaos in the Solar System. ARA&A 39, 581–631.

    Article  ADS  Google Scholar 

  • Lee, M.H. 2004. Diversity and Origin of 2:1 Orbital Resonances in Extrasolar Planetary Systems. ApJ 611, 517–527.

    Article  ADS  Google Scholar 

  • Lee, M.H. et al. 2006. On the 2:1 Orbital Resonance in the HD 82943 Planetary System. ApJ 641, 1178–1187.

    Article  ADS  Google Scholar 

  • Lee, M.H. & Peale, S. 2002. Dynamics and Origin of the 2:1 Orbital Resonances of the GJ 876 Planets. ApJ 567, 596–609.

    Article  ADS  Google Scholar 

  • Lee, M.H. & Peale S. 2003. Secular Evolution of Hierarchical Planetary Systems. ApJ 592, 1201–1216.

    Article  ADS  Google Scholar 

  • Levison, H. & Duncan, M. 1994. The long-term dynamical behavior of short-period comets. Icarus 108, 18–36.

    Article  ADS  Google Scholar 

  • Libert, A.-S. & Henrard, J. 2005. Analytical Approach to the Secular Behaviour of Exoplanetary Systems. CeMDA 93, 187–200.

    MATH  ADS  MathSciNet  Google Scholar 

  • Libert, A.-S. & Henrard, J. 2006. Secular apsidal configuration of non-resonant exoplanetary systems. Icarus 183, 186–192.

    Article  ADS  Google Scholar 

  • Libert, A.-S. & Henrard, J. 2007. Analytical study of the proximity of exoplanetary systems to mean-motion resonances. A&A 461, 759–763.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Lissauer, J.J. 2007. Planets Formed in Habitable Zones of M Dwarf Stars Probably Are Deficient in Volatiles. ApJ 660, L149–L152.

    Article  ADS  Google Scholar 

  • Lissauer, J.J. & Rivera, E.J. 2001. Stability Analysis of the Planetary System Orbiting υ Andromedae. II. Simulations Using New Lick Observatory Fits. ApJ 554, 1141–1150.

    Article  ADS  Google Scholar 

  • Lovis, C. et al. 2006. An extrasolar planetary system with three Neptune-mass planets. Nature 441, 305–309.

    Article  ADS  Google Scholar 

  • Malhotra, R. 1993. The Origin of Pluto’s Peculiar Orbit. Nature 365, 819–821.

    Article  ADS  Google Scholar 

  • Malhotra, R. 2002. A Dynamical Mechanism for Establishing Apsidal Resonance. ApJ 575, L33–L36.

    Article  ADS  Google Scholar 

  • Marchal, C. & Bozis, G. 1982. Hill Stability and Distance Curves for the General Three-Body Problem. CeMDA 26, 311–333.

    MATH  MathSciNet  Google Scholar 

  • Marcy, G.W. et al. 2001. A Pair of Resonant Planets Orbiting GJ 876. ApJ 556, 296–301.

    Article  ADS  Google Scholar 

  • Marcy, G.W. et al. 2002. A Planet at 5 AU around 55 Cancri. ApJ 581 1375–1388.

    Article  ADS  Google Scholar 

  • Marcy, G.W. et al. 2005. Five New Extrasolar Planets. ApJ 619, 570–584.

    Article  ADS  Google Scholar 

  • Marzari, F. & Weidenschilling, S. 2002. Eccentric Extrasolar Planets: The Jumping Jupiter Model. Icarus 156, 570–579.

    Article  ADS  Google Scholar 

  • Marzari, F., Scholl, H. & Tricarico, P. 2005. Frequency map analysis of the 3/1 resonance between planets b and c in the 55 Cancri system. A&A 442, 359–364.

    Article  ADS  Google Scholar 

  • Marzari, F., Scholl, H. & Tricarico, P. 2006. A numerical study of the 2:1 planetary resonance. A&A 453, 341–348.

    Article  ADS  Google Scholar 

  • Mayor, M. et al. 2004. The CORALIE survey for southern extra-solar planets. XII. Orbital solutions for 16 extra-solar planets discovered with CORALIE. A&A 415, 391–402.

    Article  ADS  Google Scholar 

  • McArthur, B.E. et al. 2004. Detection of a Neptune-Mass Planet in the ρ Cancri System Using the Hobby-Eberly Telescope. ApJ 614, L81–L84.

    Article  ADS  Google Scholar 

  • Menou, K. & Tabachnik, S. 2003. Dynamical Habitability of Known Extrasolar Planetary Systems. ApJ 583, 473–488.

    Article  ADS  Google Scholar 

  • Milani, A. & Nobili, A.M. 1983. On topological stability in the general three-body problem. CeMDA 31, 213–240.

    MATH  MathSciNet  Google Scholar 

  • Michtchenko, T.A. & Ferraz-Mello, S. 2001. Modeling the 5: 2 Mean-Motion Resonance in the Jupiter-Saturn Planetary System. Icarus 149, 357–374.

    Article  ADS  Google Scholar 

  • Michtchenko, T.A., Beaugé, C. & Ferraz-Mello, S. 2006. Stationary Orbits in Resonant Extrasolar Planetary Systems. CeMDA 94, 411–432.

    MATH  ADS  Google Scholar 

  • Michtchenko, T.A., Ferraz-Mello, S. & Beaugé, S. 2006. Modeling the 3-D secular planetary three-body problem. Icarus 181, 555–571.

    Article  ADS  Google Scholar 

  • Michtchenko, T.A. & Malhotra, R. 2004. Secular dynamics of the three-body problem: application to the υ Andromedae planetary system. Icarus 168, 237–248.

    Article  ADS  Google Scholar 

  • Moons, M. 1997. Review of the dynamics in the Kirkwood gaps. CeMDA 65, 175–204.

    MATH  ADS  MathSciNet  Google Scholar 

  • Murray, C.D. & Dermott, S.F. 1999. Solar System Dynamics. Cambridge UP, Cambridge.

    MATH  Google Scholar 

  • Murray, N. & Holman, M. 1999. The Origin of Chaos in the Outer Solar System. Science 283, 1877–1881.

    Article  ADS  Google Scholar 

  • Naef, D. et al. 2004. The ELODIE survey for northern extra-solar planets. III. Three planetary candidates detected with ELODIE. A&A 414, 351–359.

    Article  ADS  Google Scholar 

  • Namouni, F. 2005. On the Origin of the Eccentricities of Extrasolar Planets. AJ 130, 280–294.

    Article  ADS  Google Scholar 

  • Noble, M., Musielak, Z.E. & Cuntz, M. 2002. Orbital Stability of Terrestrial Planets inside the Habitable Zones of Extrasolar Planetary Systems. ApJ 572, 1024–1030.

    Article  ADS  Google Scholar 

  • Papaloizou, J.C.B. & Terquem, C. 2006. Planet formation and migration. Rept. Prog. Phys. 69 119-.

    Article  ADS  Google Scholar 

  • Peale, S. 1976. Orbital resonances in the solar system. ARA&A 14, 215–246.

    Article  ADS  Google Scholar 

  • Pepe, F. et al. 2007. The HARPS search for southern extra-solar planets. VIII. μ Arae, a system with four planets. A&A 462, 769–776.

    Article  ADS  Google Scholar 

  • Psychoyos, D. & Hadjidemetriou, J.D. 2005. Dynamics of Populations of Planetary Systems, Proceedings of IAU Colloquium #197. Eds Z. Knezevic and A. Milani. Cambridge: Cambridge UP, p.55–62(2005)

    Google Scholar 

  • Psychoyos, D. & Hadjidemtriou, J.D. 2005. Dynamics Of 2/1 Resonant Extrasolar Systems Application to HD82943 and GLIESE876. CeMDA 92, 135–156.

    MATH  ADS  Google Scholar 

  • Rasio, F.A. & Ford, E.B. 1996. Dynamical instabilities and the formation of extrasolar planetary systems. Science 274, 954–956.

    Article  ADS  Google Scholar 

  • Rasio, F.A. et al. 1996. Tidal Decay of Close Planetary Orbits. ApJ 470, 1187–1191.

    Article  ADS  Google Scholar 

  • Raymond, S.N. & Barnes, R. 2005. Predicting Planets in Known Extrasolar Planetary Systems. II. Testing for Saturn Mass Planets. ApJ 619, 549–557.

    Article  ADS  Google Scholar 

  • Raymond, S.N., Barnes, R. & Kaib, N.A. 2006. Predicting Planets in Known Extrasolar Planetary Systems. III. Forming Terrestrial Planets. ApJ 644, 1223–1231.

    Article  ADS  Google Scholar 

  • Raymond, S.N., Quinn, T.R. & Lunine, J.I. 2004. Making other earths: dynamical simulations of terrestrial planet formation and water delivery. Icarus 168, 1–17.(2004)

    Article  ADS  Google Scholar 

  • Rivera, E.J. & Haghighipour, N. 2007. On the stability of test particles in extrasolar multiple planet systems. MNRAS 374, 599–613.

    Article  ADS  Google Scholar 

  • Rivera, E.J. & Lissauer, J.J. 2000. Stability Analysis of the Planetary System Orbiting ε Andromedae. ApJ 530, 454–463.

    Article  ADS  Google Scholar 

  • Rivera, E.J. & Lissauer, J.J. 2001. Dynamical Models of the Resonant Pair of Planets Orbiting the Star GJ 876. ApJ 558, 392–402.

    Article  ADS  Google Scholar 

  • Rivera, E.J. et al. 2005. A ∼ 7.5M ⊕ Planet Orbiting the Nearby Star, GJ 876. ApJ 634, 625–640.

    Article  ADS  Google Scholar 

  • Rodríguez, A. & Gallardo, T. 2005. The Dynamics of the HD 12661 Extrasolar Planetary System. ApJ 628, 1006–1013.

    Article  ADS  Google Scholar 

  • Sándor, Zs. & Kley, W. 2006. On the evolution of the resonant planetary system HD 128311. A&A 451, L31–L34.

    Article  ADS  Google Scholar 

  • Sándor, Zs., Kley, W. & Klagyivik, P. 2007. Stability and Formation of the Resonant System HD 73526. A&A, accepted.

    Google Scholar 

  • Schwarz, R. et al. 2005. Trojans in Habitable Zones. AsBio 5, 579–586.

    ADS  Google Scholar 

  • Schwarz, R. et al. 2007. Trojan planets in HD 108874? A&A 462, 1165–1170.

    Article  ADS  Google Scholar 

  • Stepinski, T.F., Malhotra, R. & Black, D.C. 2000. The ε Andromedae System: Models and Stability. ApJ 545, 1044–1057.

    Article  ADS  Google Scholar 

  • Sussman, G.J. & Wisdom, J. 1988. Numerical evidence that the motion of Pluto is chaotic. Science 241, 433–437.

    Article  ADS  Google Scholar 

  • Sussman, G.J. & Wisdom, J. 1992. Chaotic evolution of the solar system. Science 257, 56–62.

    Article  ADS  MathSciNet  Google Scholar 

  • Thébault, P., Marzari, F. & Scholl, H. 2002. Terrestrial planet formation in exoplanetary systems with a giant planet on an external orbit. A&A 384, 594–602.

    Article  ADS  Google Scholar 

  • Tinney, C.G. et al. 2006. The 2:1 Resonant Exoplanetary System Orbiting HD 73526. ApJ 647, 594–599.

    Article  ADS  Google Scholar 

  • Tsiganis, K, Varvoglis, H. & Hadjidemetriou, J.D. 2002. Stable Chaos versus Kirkwoodc Gaps in the Asteroid Belt: A Comparative Study of Mean Motion Resonances. Icarus 159, 284–299.

    Article  ADS  Google Scholar 

  • Udry, S. et al. 2007. The HARPS search for southern extra-solar planets. XI. Super-Earths (5 and 8 ⊕M) in a 3-planet system. A&A, accepted.

    Google Scholar 

  • Veras, D. & Armitage, P. 2007. Extrasolar Planetary Dynamics with a Generalized Planar Laplace-Lagrange Secular Theory. ApJ 661 1311–1322.

    Article  ADS  Google Scholar 

  • von Bloh, W. et al. 2003. On the Possibility of Earth-Type Habitable Planets in the 55 Cancri System. AsBio 3, 681–688.

    ADS  Google Scholar 

  • Varadi, F., Ghil, M. & Kaula, W.M. 1999. Jupiter, Saturn, and the Edge of Chaos. Icarus 139, 286–294.

    Article  ADS  Google Scholar 

  • Vogt, S.S. et al. 2005. Five New Multicomponent Planetary Systems. ApJ 632, 638–658.

    Article  ADS  Google Scholar 

  • Voyatzis, G. & Hadjidemetriou, J.D. 2006. Symmetric and asymmetric 3:1 resonant periodic orbits with an application to the 55Cnc extra-solar system. CeMDA 95, 259–271.

    MATH  ADS  MathSciNet  Google Scholar 

  • Weidenschilling, S. & Marzari, F. 1996. Gravitational scattering as a possible origin for giant planets at small stellar distances. Nature 384, 619–621.

    Article  ADS  Google Scholar 

  • Wright, J.T. et al. 2007. Four New Exoplanets and Hints of Additional Substellar Companions to Exoplanet Host Stars. ApJ 657, 533–545.

    Article  ADS  Google Scholar 

  • Wu, Y. & Goldreich, P. 2002. Tidal Evolution of the Planetary System around HD 83443. ApJ 564, 1024–1027.

    Article  ADS  Google Scholar 

  • Wu, Y. & Murray, N. 2003. Planet Migration and Binary Companions: The Case of HD 80606b. ApJ 589, 605–614.

    Article  ADS  Google Scholar 

  • Yoshida, H. 1993. Recent Progress in the Theory and Application of Symplectic Integrators. CeMDA 56, 27–43.

    MATH  ADS  Google Scholar 

  • Zhou, J.-L. & Sun, Y.-S. 2003. Occurrence and Stability of Apsidal Resonance in Multiple Planetary Systems. ApJ 598, 1290–1300.

    Article  ADS  Google Scholar 

  • Zhou, J.-L. et al. 2004. Apsidal corotation in mean motion resonance: the 55 Cancri system as an example. MNRAS 350, 1495–1502.

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Lunar and Planetary Laboratory, University of Arizona, 1629 E. University Blvd., Tucson, Arizona AZ, 85721, USA

    Rory Barnes

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  1. Rory Barnes
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  1. Olympus Mons, 51 Orchard Way, Barnham West Sussex, PO22 0HX, UK

    John W. Mason

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Barnes, R. (2008). Dynamics of Multiple Planet Systems. In: Mason, J.W. (eds) Exoplanets. Springer Praxis Books. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74008-7_7

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