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Celestial Mechanics: from Asteroids to Extrasolar Planets
23.06.2010 :: Florian Freistetter :: OATS
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Orbital Dynamics: Order and Chaos
since Poincaré (1889) we know that the n-body problem (n>2) can not be solved analytically and can give chaotic solutions
Part I: Chaotic Orbits of Near Earth Asteroids during the last 15 years ~450 extrasolar systems were
discovered – but it is still almost impossible to detect terrestrial planets
Part II: Stability of potential terrestrial planets in extrasolar systems
Part III: Planets and Asteroids in the disk of Beta Pictoris
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Asteroids
0
5 0
1 0 0
1 5 0
2 0 0
1 2 3 4 5
num
be
r o
f ast
ero
ids
s e m i m a j o r a x i s [ A U ]
M e r c u r y V e n u s E a r t h M a r s J u p i t e r
3 : 1 8 : 3
5 : 2
1 : 1
3 : 2H i l d a s
T r o j a n s
2 : 1
4 : 1
H u n g a r i a s
A T E N s A M O R sA P O L L O s
N E A s
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Chaotic Motion of NEAs
Close encounters -> Chaos!10563 Izdhubar
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Chaotic Motion of NEAs
Longterm evolution of chaotic orbits
gives no meaningful results for single objects !
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NEA Groups
2 important classifications: Shoemaker et al. (1973):
Aten :: Apollo :: Amor a, e (crossing behaviour)
Milani et al (1989) 7 classes Dynamical behaviour (encounters, etc)
How does Chaos effect the groups?
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Mixing!
Chaos + Long Timescales = Problems!
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Mixing
Object ↔ Group
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Mixing
How much time does a NEA spend in its initial group?
• 69.86 % (Shoemaker et al. classification) (Dvorak & Freistetter 2001, Freistetter 2009)
• 65.72 % (Milani et al. classification) (Dvorak & Freistetter 2001, Freistetter 2009)
Need a new way of classification: Fuzzy Logic!
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Fuzzy LogicAge: 32 years
•very young: 25%
• young: 50%
• not very young: 75%
• more or less old: 2%
• old: 0%
• very old: 0%
It is possible to be a member
of multiple groups with a
different degree!
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Fuzzy Classification
Comparison with Milanis Classification
http://www.celestialmechanics.eu/neas/
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Fuzzy Classification
• compare the classification data with the Spaceguard classes
Geographos group
• many close approaches with Earth
• some close approaches with Venus
• semimajor axis almost constant
(1620) Geographos:
• G1 (no mixing): 1
• G2 (Venus): 0.03
• G3 (Earth): 0.76
Oljato group
• chaotic orbits
• large eccentricities
• close encounters with all planets
(2201) Oljato:
• G1 (no mixing): 0.04
• G2 (Venus): 0.38
• G3 (Earth): 0.36
• G4 (Mars): 0.28
Fuzzy Classification works!
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Extrasolar Planets
Observation of terrestrial planets? -> Theoretic simulations Stability in the habitable Zone
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HD 41004 A
Star 1Mstar1 = 0.7 MSun
Planetm sin i = 2.3 Mjup
a = 1.31 AUe = 0.39 + 0.17ω ≈ 114o
Star 2m = 0.4 MSun
a = 21 AUe = 0.1
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Influence of the companion
ebin=0.1 epl=0.22 no secondary epl=0.22
4:1 7:2 3:18:3
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Different Methods
epl=0.22MEM FLI
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Importance of observationsepl=0.24 epl=0.26 epl=0.28 epl=0.30
epl=0.32 epl=0.34 epl=0.36 epl=0.38
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b Pictoris
spectral type: A5 V star age: ~20 Myrs mass: 1.75 MSUN
1984: debris disk!
Smith & Terrile 1984
first debris disk some 100 articles
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The disk of b Pictoris
many interesting structures:
warp: → inclined planet? Mouillet et al.:
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The disk of b Pictoris “Falling Evaporating Bodies (FEBs)”: variations in spectral lines → small bodies fall onto the star → planet has to disturb these bodies
Beust et al. 1990
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The disk of b Pictoris clumps in the disk
Telesco et al. (2005) Okamoto et al. (2004)
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Belt structures in the b Pic-disk A: ~6.4 AU [2] B: ~16 AU [1,2,4] C: ~32 AU [1,2,4] D: ~52 AU [1,3,4] structures in the outer disk
[1] Wahhaj et al 2003 [2] Okamoto et al. 2004[3] Telesco et al. 2005 [4] Golimowski et al. 2006
Can these clumps be caused by planetesimal belts? What planets are needed to con- fine such belts?
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Planetesimal belts objects from 0.15 m – 7 km M
tot = 0.3MEARTH
a = 6 - 7 AU e = 0 - 0.1 → evolution of dust particles → Brightness
→ observed peaks can be due to planetesimal belts!
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Planets
belts are confined by planets What are the parameter of the planet(s) so
that the perturbations cause the observed clumps?
simulations with 1 – 3 planets parameters (M, a, e, i) very varied
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One Planet
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Two Planets
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Three Planets
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Summary Confirmation of
previous results Additional
restrictions for planetary parameters
At least 3 planets are needed to explain observations
The planetary system could be resonant
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Beta Pictoris b Do the planets
exist?
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Beta Pictoris b
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E N D