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On the stability of Earth-like planets in multi-planet systems. (English) Zbl 1154.70320
Summary: 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 \(g_5\) 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 (\(a_S \geq 9.7\) AU) increases the eccentricity of a test-planet up to 0.4.

MSC:
70F15 Celestial mechanics
85A99 Astronomy and astrophysics
Software:
GAUDI
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[1] Agnor, C.B., Lin, D.N.: Planet Migration and System Coupling. American Astronomical Society, DPS meeting #39, #60.03 (2007)
[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) · doi:10.1051/0004-6361:20040390
[3] Barnes R., Raymond S.N.: Predicting planets in known extrasolar planetary systems I. Test particle simulations. Astrophys. J. 617, 569–574 (2004) · doi:10.1086/423419
[4] Chambers J.E.: A hybrid symplectic integrator that permits close encounters between massive bodies. Mon. Not. R. Astron. Soc. 304, 793–799 (1999) · doi:10.1046/j.1365-8711.1999.02379.x
[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) · doi:10.1051/0004-6361:20031404
[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) · doi:10.1111/j.1365-2966.2004.07845.x
[7] Ferraz-Mello S., Michtchenko T.A., Beaugé C., Callegari Jr. N.: Extrasolar planetary systems. Lect. Notes Phys. 683, 219–271 (2005) · doi:10.1007/10978337_4
[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)
[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) · doi:10.1086/300552
[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) · doi:10.1086/432787
[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) · doi:10.1051/0004-6361:20021138
[12] Jones B.W., Underwood D.R., Sleep P.N.: Prospects for habitable ”Earths” in known exoplanetary systems. Astrophys. J. 622, 1091–1101 (2005) · doi:10.1086/428108
[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) · doi:10.1086/506557
[14] Kasting J.F., Whitmire D.P., Reynolds R.T.: Habitable zones around main sequence stars. Icarus 101, 108–128 (1993) · doi:10.1006/icar.1993.1010
[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) · doi:10.1016/0019-1035(90)90084-M
[16] Laskar J.: Chaotic diffusion in the solar system. Icarus 196, 1–15 (2008) · doi:10.1016/j.icarus.2008.02.017
[17] Laughlin G., Chambers J., Fischer D.: A dynamical analysis of the 47 Ursae majoris planetary system. Astrophys. J. 579, 455–467 (2002) · doi:10.1086/342746
[18] Menou K., Tabachnik S.: Dynamical habitability of known extrasolar planetary systems. Astrophys. J. 583, 473–488 (2003) · doi:10.1086/345359
[19] Morbidelli A., Crida A.: The dynamics of Jupiter and Saturn in the gaseoous protoplanetary disk. Icarus 191, 158–171 (2007) · doi:10.1016/j.icarus.2007.04.001
[20] Murray C.D., Dermott S.F.: Solar System Dynamics. Cambridge University Press, Cambridge (1999) · Zbl 0957.70002
[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) · doi:10.1086/587501
[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) · doi:10.1086/503594
[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) · doi:10.1111/j.1365-2966.2006.11172.x
[24] Rivera E., Lissauer J.: Stability analysis of the planetary system orbiting \(\nu\) Andromedae. Astrophys. J. 530, 454–463 (2000) · doi:10.1086/308345
[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: 1141L
[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) · doi:10.1111/j.1365-2966.2006.11008.x
[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) · doi:10.1111/j.1365-2966.2006.11414.x
[28] Schwarz R., Dvorak R., Pilat-Lohinger E., Süli Á., Érdi B.: Trojan planets in HD 108874?. Astron. Astrophys. 462, 1165–1170 (2007) · doi:10.1051/0004-6361:20066284
[29] Süli Á., Dvorak R., Érdi B.: On the global stability of single-planet systems. Astronomische Nachrichten 328, 781 (2007) · doi:10.1002/asna.200710788
[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) · doi:10.1038/nature03539
[31] Williams D.M., Pollard D.: Earth-like worlds on eccentric orbits: excursions beyond the habitable zone. Int. J. Astrobiol. 1, 61–69 (2002) · doi:10.1017/S1473550402001064
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