On the stability of Earth-like planets in multi-planet systems

  • E. Pilat-Lohinger
  • P. Robutel
  • Á. Süli
  • F. Freistetter
Original Article


We present a continuation of our numerical study on planetary systems with similar characteristics to the Solar System. This time we examine the influence of three giant planets on the motion of terrestrial-like planets in the habitable zone (HZ). Using the Jupiter–Saturn–Uranus configuration we create similar fictitious systems by varying Saturn’s semi-major axis from 8 to 11 AU and increasing its mass by factors of 2–30. The analysis of the different systems shows the following interesting results: (i) Using the masses of the Solar System for the three giant planets, our study indicates a maximum eccentricity (max-e) of nearly 0.3 for a test-planet placed at the position of Venus. Such a high eccentricity was already found in our previous study of Jupiter–Saturn systems. Perturbations associated with the secular frequency g5 are again responsible for this high eccentricity. (ii) An increase of the Saturn-mass causes stronger perturbations around the position of the Earth and in the outer HZ. The latter is certainly due to gravitational interaction between Saturn and Uranus. (iii) The Saturn-mass increased by a factor 5 or higher indicates high eccentricities for a test-planet placed at the position of Mars. So that a crossing of the Earth’ orbit might occur in some cases. Furthermore, we present the maximum eccentricity of a test-planet placed in the Earth’ orbit for all positions (from 8 to 11 AU) and masses (increased up to a factor of 30) of Saturn. It can be seen that already a double-mass Saturn moving in its actual orbit causes an increase of the eccentricity up to 0.2 of a test-planet placed at Earth’s position. A more massive Saturn orbiting the Sun outside the 5:2 mean motion resonance (aS ≥9.7 AU) increases the eccentricity of a test-planet up to 0.4.


Planetary systems Planets: Jupiter, Saturn, Uranus Secular resonances Habitable zone Extra-solar planets 


  1. Agnor, C.B., Lin, D.N.: Planet Migration and System Coupling. American Astronomical Society, DPS meeting #39, #60.03 (2007)Google Scholar
  2. Asghari N., Broeg C., Carone L., Casas-Miranda R. et al.: Stability of terrestrial planets in the habitable zone of Gl777A, HD72659, Gl614, 47Uma and HD4208. Astron. Astrophys. 426, 353–365 (2004)CrossRefADSGoogle Scholar
  3. Barnes R., Raymond S.N.: Predicting planets in known extrasolar planetary systems I. Test particle simulations. Astrophys. J. 617, 569–574 (2004)CrossRefADSGoogle Scholar
  4. Chambers J.E.: A hybrid symplectic integrator that permits close encounters between massive bodies. Mon. Not. R. Astron. Soc. 304, 793–799 (1999)CrossRefADSGoogle Scholar
  5. Dvorak R., Pilat-Lohinger E., Funk B., Freistetter F.: A study of the stable regions in the planetary system HD74156 – can it host earthlike planets in the habitable zones?. Astron. Astrophys. 410, L13 (2003)CrossRefADSGoogle Scholar
  6. Érdi B., Dvorak R., Sándor Zs., Pilat-Lohinger E., Funk B.: The dynamical structure of the habitable zone in the HD38529, HD168443 and HD169830 systems. Mon. Not. R. Astron. Soc. 351, 1043–1048 (2004)CrossRefADSGoogle Scholar
  7. Ferraz-Mello S., Michtchenko T.A., Beaugé C., Callegari Jr. N.: Extrasolar planetary systems. Lect. Notes Phys. 683, 219–271 (2005)CrossRefADSGoogle Scholar
  8. Gaudi, S., Bennett, D., Udalski, A., Gould, A., Chritsie, G., & 62 co-authors: Discovery of a Jupiter/Saturn analog with gravitational microlensing. Science 319, 927 (2008)Google Scholar
  9. Innanen K., Mikkola S., Wiegert P.: The Earth-Moon system and the dynamical stability of the inner solar system. Astron. J. 116, 2055 (1998)CrossRefADSGoogle Scholar
  10. Ji J., Lui L., Kinoshita H., Li G.: Could the 47 Ursae majoris planetary system be a second solar system? Predicting the earth-like planets. Astrophys. J. 631, 1191–1197 (2005)CrossRefADSGoogle Scholar
  11. Jones B.W., Sleep P.N.: The stability of the orbits of Earth-mass planets in the habitable zone of 47 Ursae Majoris. Astron. Astrophys. 393, 1015–1026 (2002)CrossRefADSGoogle Scholar
  12. Jones B.W., Underwood D.R., Sleep P.N.: Prospects for habitable “Earths” in known exoplanetary systems. Astrophys. J. 622, 1091–1101 (2005)CrossRefADSGoogle Scholar
  13. Jones B.W., Sleep P.N.: Underwood, D.R.: Habitability of known exoplanetary systems based on measured stellar properties. Astrophys. J. 649, 1010–1019 (2006)CrossRefADSGoogle Scholar
  14. Kasting J.F., Whitmire D.P., Reynolds R.T.: Habitable zones around main sequence stars. Icarus 101, 108–128 (1993)CrossRefADSGoogle Scholar
  15. Laskar J.: The chaotic motion of the solar system-a numerical estimate of the size of the chaotic zones. Icarus 88, 266–291 (1990)CrossRefADSGoogle Scholar
  16. Laskar J.: Chaotic diffusion in the solar system. Icarus 196, 1–15 (2008)CrossRefADSGoogle Scholar
  17. Laughlin G., Chambers J., Fischer D.: A dynamical analysis of the 47 Ursae majoris planetary system. Astrophys. J. 579, 455–467 (2002)CrossRefADSGoogle Scholar
  18. Menou K., Tabachnik S.: Dynamical habitability of known extrasolar planetary systems. Astrophys. J. 583, 473–488 (2003)CrossRefADSGoogle Scholar
  19. Morbidelli A., Crida A.: The dynamics of Jupiter and Saturn in the gaseoous protoplanetary disk. Icarus 191, 158–171 (2007)CrossRefADSGoogle Scholar
  20. Murray C.D., Dermott S.F.: Solar System Dynamics. Cambridge University Press, Cambridge (1999)MATHGoogle Scholar
  21. Pilat-Lohinger E., Süli Á., Robutel P., Freistetter F.: The influence of giant planets near a mean motion resonance on Earth-like planets in the habitable zone of Sun-like stars. Astrophys. J. 681, 1639–1645 (2008)CrossRefADSGoogle Scholar
  22. Raymond S.N., Barnes R., Kaib N.A.: Predicting planets in known extrasolar planetary systems III. Forming terrestrial planets. Astrophys. J. 644, 1223–1231 (2006)CrossRefADSGoogle Scholar
  23. Rivera E., Haghighipour N.: On the stability of test-particles in extrasolar multiple planet systems. Mon. Not. R. Astron. Soc. 374, 599–613 (2007)CrossRefADSGoogle Scholar
  24. Rivera E., Lissauer J.: Stability analysis of the planetary system orbiting ν Andromedae. Astrophys. J. 530, 454–463 (2000)CrossRefADSGoogle Scholar
  25. Rivera E., Lissauer J. (2001) Stability analysis of the planetary system orbiting nu Andromedae II simulations using new lick observatory fits. Astrophys. J. 554: 1141LGoogle Scholar
  26. Robutel P., Gabern F.: The resonant structure of Jupiter’s Trojan asteroids—I. Long-term stability and diffusion. Mon. Not. R. Astron. Soc. 372, 1463–1482 (2006)CrossRefADSGoogle Scholar
  27. Sándor Zs., Süli Á., Érdi B., Pilat-Lohinger E., Dvorak R.: A stability catalogue of the habitable zones in extrasolar planetary systems. Mon. Not. R. Astron. Soc. 375, 1495–1502 (2007)CrossRefADSGoogle Scholar
  28. Schwarz R., Dvorak R., Pilat-Lohinger E., Süli Á., Érdi B.: Trojan planets in HD 108874?. Astron. Astrophys. 462, 1165–1170 (2007)CrossRefADSGoogle Scholar
  29. Süli Á., Dvorak R., Érdi B.: On the global stability of single-planet systems. Astronomische Nachrichten 328, 781 (2007)CrossRefADSGoogle Scholar
  30. Tsiganis K., Gomes R., Morbidelli A., Levison H.F.: Origin of the orbital architecture of the giant planets of the solar system. Nature 435, 459–461 (2005)CrossRefADSGoogle Scholar
  31. Williams D.M., Pollard D.: Earth-like worlds on eccentric orbits: excursions beyond the habitable zone. Int. J. Astrobiol. 1, 61–69 (2002)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • E. Pilat-Lohinger
    • 1
  • P. Robutel
    • 2
  • Á. Süli
    • 3
  • F. Freistetter
    • 4
  1. 1.Institute for AstronomyUniversity of ViennaViennaAustria
  2. 2.Astronomie et Systèmes Dynamiques, IMCCE-CNRS UMR 2028, Observatoire de ParisParisFrance
  3. 3.Department of AstronomyEötvös UniversityBudapestHungary
  4. 4.Astrophysikalisches InstitutFriedrich-Schiller-Universität JenaJenaGermany

Personalised recommendations