Transcript Document

Multi-planetary systems:
Multi-planetary systems
Binaries
 Single Star and Single Planetary Systems
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
Class II Non-resonant planets with significant
secular dynamics
Class III Hierarchical planet pairs
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).
Star
Planet
[M_Sun]
mass_P
[M_Jup]
GJ 876
(0.32)
b
c
0.597
1.90
0.13
0.21
0.218
0.029
30.38
60.93
55 Cnc
(1.03)
b
c
0.784
0.217
0.115
0.24
0.02
0.44
14.67
43.93
HD82942
(1.15)
b
c
1.7
1.8
0.75
1.18
0.39
0.15
219.5
436.2
17.5
2.41
0.83
2.44
0.433 256.2
0.284 1296.8
HD202206 b
(1.15)
c
a_P
[AU]
e_P Period
[days]
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
[M_Sun]
47Uma
(1.03)
Planet
b
c
mass_P a_P
[M_Jup] [AU]
2.9
1.1
2.1
4.0
e_P Period
[days]
0.05
0.0
1079.2
2845.0
habitable zone
Terrestrial planet
is possible!
Unstable orbits
2:1 1.3 AU
3:1 1 AU
SR 0.8 – 0.9 AU
4:1 0.82 AU
Stable orbits
Between resonances
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.
Star
Planet
[M_Sun]
55 Cnc
(1.03)
mass_P
[M_Jup]
a_P
e_P Period
[AU]
[days]
e
b
0.045
0.784
0.038
0.115
0.17
0.02
HD169830 b
(1.4)
c
2.88
4.04
0.81
3.6
0.31 225.62
0.33 2102
HD37124 b
(0.91)
c?
0.72
1.3
0.54
2.5
0.1 153
0.7 1595
(Ups And, HD12661, HD160691)
2.808
14.67
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.
Star
Planet mass_P
[M_Sun]
a_P
[M_Jup]
[AU]
e_P
Period
[days]
HD168443
(1.01)
b
c
7.7
16.9
0.29
2.85
0.529
58.116
0.228 1739.5
HD74156
(1.27)
c
b
1.86
6.17
0.294
3.40
0.636
0.583
51.643
2025.0
HD38529
(1.39)
b
c
0.78
12.7
0.129
3.68
0.29
0.36
14.309
2174.3
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.
Motivation
A study of
Extra-solar planetary systems
similar to
our solar system
Initial Conditions and Computations
Jupiter: on its orbit
Mercury 6 (J. Chambers)
Saturn: a_sat = 8 ..... 11 AU
Integration time:
20 mio years
m_sat = 1 .... 30xm_Sat
Testplanets in the HZ:
a_tp = 0.6 ..... 1.6 AU
HZ: maximum ecc.
HZ im Sonnensystem:
Kasting: 0.93 – 1.3 AU
Mischna: 0.93 – 1.7 AU
Forget: 0.93 – 2 AU
a< 0.93 AU  H2O becomes a major atmospheric compound and is
rapidly lost to space after UV photolysis
a>1.3 AU  CO2 condensates in the atmosphere producing CO2clouds, that can affect significantly the T-CO2 coupling
Sun – Jupiter – Saturn
Sun – Jupiter – Saturn
Influence of a third giant planet
Jupiter – Saturn -Uranus
Jupiter -- Saturn
Influence of a third giant planet
Jupiter – Saturn -Uranus
Jupiter -- Saturn
Sun-Jupiter-Saturn-Uranus
Influence on an Earth-like planet at 1 AU
Earth-like planets in
inclined multi-planetary systems
similar to the Solar system
Motivation
The discovery of
the planetary system
OGLE 06-109l
Initial Conditions and Computations
Jupiter: on its orbit
Mercury 6 (J. Chambers)
Saturn: a_sat = 8 ..... 11 AU
Integration time:
20 mio years
i_sat = 10 .... 60 deg
Testplanets in the HZ:
a_tp = 0.6 ..... 1.6 AU
HZ: maximum ecc.
Sun – Jupiter – Saturn
Increase of iSaturn = 10 deg
Orbits of Venus, Earth and Mars
iSaturn = 20deg
Escape of Saturn for a_Sat = 8.2 AU
iSaturn = 30deg
iSaturn = 40 deg
iSaturn = 50 deg
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