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Multi-planetary systems:

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Binaries Single Star and Single Planetary Systems Multi-planetary systems

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Classification of the known multi-planet systems (S.Ferraz-Mello, 2005) Class Ia –> Planets in mean motion resonance Class Ib Low-eccentricity near-resonant planet pairs pairs Class II Non-resonant planets with significant secular dynamics secular dynamics Class III Hierarchical planet pairs

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Class Ia -- Planets in mean-motion resonance This class contains planet pairs with large masses and eccentric orbits that are relatively close to each other, where strong gravitational interactions occur. Such systems remain stable if the two planets are in mean motion resonance (MMR).

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Star Planet mass_P a_P e_P Period [M_Sun] [M_Jup] [AU] [days] GJ 876 b (0.32) c Cnc b (1.03) c HD82942 b (1.15) c HD b (1.15) c

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Class 1b -- Low-eccentricity near-resonant planet pairs A mean motion resonance of the planet pair is not needed to guarantee the long-term stability of the system. Therefore, the eccentricities of the planets have to be small to exclude a crossing of the orbits. As an example we state the 47Uma system, which is possibly near the 5:2 or 7:3 MMR but the orbital parameters show that a resonance is not needed for the stability of the system. Star Planet mass_P a_P e_P Period [M_Sun] [M_Jup] [AU] [days] 47Uma b (1.03) c

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habitable zone Unstable orbits 2:1 1.3 AU 3:1 1 AU SR 0.8 – 0.9 AU 4: AU Stable orbits Between resonances Terrestrial planet is possible!

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Class II -- Non-resonant planets with significant secular dynamics Planet pairs of this class can have strong gravitational interactions, where long-term variations are ascribed to secular perturbations, large variations of the eccentricities and dynamical effects like the alignment and anti-alignment for the apsidal lines. For the long-term stability of such a system, it is not necessary hat the planets are in MMR.

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Star Planet mass_P a_P e_P Period [M_Sun] [M_Jup] [AU] [days] 55 Cnc e (1.03) b HD b (1.4) c HD37124 b (0.91) c ? (Ups And, HD12661, HD160691)

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Class III -- Hierarchical planet pairs Roughly speaking this class is for all planet pairs with a large ratio of their orbital periods -- P1/P2 > 10. Due to the large ratio of periods the gravitational interaction are not so strong like in class II and the probability of a capture in a MMR is negligible. The weaker interactions lead to stable motion in the numerical simulations, even if the orbits of the planet are not so good determined.

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Star Planet mass_P a_P e_P Period [M_Sun] [M_Jup] [AU] [days] HD b (1.01) c HD74156 c (1.27) b HD38529 b (1.39) c

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Class 1b -- Low-eccentricity near-resonant planet pairs A mean motion resonance of the planet pair is not needed to guarantee the long-term stability of the system. Therefore, the eccentricities of the planets have to be small to exclude a crossing of the orbits.

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Motivation A study of A study of Extra-solar planetary systems Extra-solar planetary systems similar to similar to our solar system our solar system

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Initial Conditions and Computations Jupiter: on its orbit Saturn: a _sat = AU m _sat = xm_ Sat m _sat = xm_ Sat Testplanets in the HZ: a _tp = AU a _tp = AU Mercury 6 (J. Chambers) Integration time: 20 mio years HZ: maximum ecc.

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HZ im Sonnensystem: Kasting: 0.93 – 1.3 AU Mischna: 0.93 – 1.7 AU Forget: 0.93 – 2 AU a< 0.93 AU H 2 O becomes a major atmospheric compound and is rapidly lost to space after UV photolysis a>1.3 AU CO2 condensates in the atmosphere producing CO 2 - clouds, that can affect significantly the T-CO 2 coupling

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Sun – Jupiter – Saturn Sun – Jupiter – Saturn

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Sun – Jupiter – Saturn

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Influence of a third giant planet Jupiter -- Saturn Jupiter – Saturn -Uranus

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Influence of a third giant planet Jupiter -- Saturn Jupiter – Saturn -Uranus

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Sun-Jupiter-Saturn-Uranus Influence on an Earth-like planet at 1 AU

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Earth-like planets in inclined multi-planetary systems similar to the Solar system

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Motivation The discovery of The discovery of the planetary system the planetary system OGLE l OGLE l

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Initial Conditions and Computations Jupiter: on its orbit Saturn: a _sat = AU i _sat = deg i _sat = deg Testplanets in the HZ: a _tp = AU a _tp = AU Mercury 6 (J. Chambers) Integration time: 20 mio years HZ: maximum ecc.

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Sun – Jupiter – Saturn Sun – Jupiter – Saturn

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Increase of i Saturn = 10 deg

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Orbits of Venus, Earth and Mars

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i Saturn = 20 deg Escape of Saturn for a_Sat = 8.2 AU

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i Saturn = 30 deg

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i Saturn = 40 deg

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i Saturn = 50 deg

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Conclusion The inclination of Saturn influences the inner Solar system For small i -- the two planets in MMR High i -- may lead to escapes of Saturn For i > 60 all systems are unstable

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