tabaré gallardo · uranus satellites asteroids with jupiter, mars, earth, venus... trans neptunian...
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Resonancias orbitales
Tabaré Gallardowww.fisica.edu.uy/∼gallardo
Facultad de CienciasUniversidad de la República
Uruguay
Curso Dinámica Orbital 2018
Tabaré Gallardo Resonancias orbitales
Orbital motion
Tabaré Gallardo Resonancias orbitales
Oscillating planetary orbits
Tabaré Gallardo Resonancias orbitales
Orbital Resonances
Commensurability between frequencies associated with orbitalmotion: mean motion, nodes and pericenters
two-body resonances (λ, λp)
three-body resonances(λ, λp1, λp2)
secular resonances (Ω, $)
Kozai-Lidov mechanism (ω)
Tabaré Gallardo Resonancias orbitales
Some examples
Io-Europa-Ganymede
Saturn satellites
Saturn rings
Uranus satellites
asteroids with Jupiter, Mars, Earth, Venus...
Trans Neptunian Objects with Neptune
Pluto - Neptune
comets - Jupiter
Pluto satellites: Styx, Nix, and Hydra
Tabaré Gallardo Resonancias orbitales
Saturn rings
Lissauer and de Pater, Fundamental Planetary Science
Tabaré Gallardo Resonancias orbitales
Two-body resonance
k0n0 + k1n1 ' 0
Tabaré Gallardo Resonancias orbitales
Three-body resonance
k0n0 + k1n1 + k2n2 ' 0 only the asteroid feels the resonance
SUN asteroid
Tabaré Gallardo Resonancias orbitales
Non resonant asteroid: relative positions
Mean perturbation is radial: Sun-Jupiter
Sun Jupiter
Tabaré Gallardo Resonancias orbitales
Resonant asteroid
Mean perturbation has a transverse component.
Sun Jupiter
Tabaré Gallardo Resonancias orbitales
from Gauss equations
SUN
asteroid
R T Fperturb = (R,T,N)
dadt∝ (R,T)
<dadt>∝ T
Non resonantT = 0⇒ a = constant
ResonantT 6= 0⇒ a = oscillating
Tabaré Gallardo Resonancias orbitales
Dynamical effects: a numerical exercise
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
2.3 2.35 2.4 2.45 2.5 2.55 2.6
ecc
entr
icit
y
a (au)
final time: 1 Myrs
orbital statesinitial
Tabaré Gallardo Resonancias orbitales
1772: Lagrange equilibrium points
Tabaré Gallardo Resonancias orbitales
1906: (588) Achilles by 500 yrs
Sun Jupiter
Tabaré Gallardo Resonancias orbitales
1784: Laplacian resonance
3λEuropa−λIo−2λGanymede ' 180
3nEuropa − nIo − 2nGanymede ' 0
They are also in commensurabilityby pairs:
2nEuropa − nIo ' 0
2nGanymede − nEuropa ' 0
⇓
It must be the consequence of some physical mechanism.
Tabaré Gallardo Resonancias orbitales
1846: discovery of Neptune
quasi resonance Uranus - Neptune:
nUranus ∼ 2nNeptune
quasi resonance Saturn - Uranus:
nSaturn ∼ 3nUranus
quasi resonance: Jupiter - Saturn
2nJupiter ∼ 5nSaturn
Why the planets are close to resonance?Hint: planetary migration
Tabaré Gallardo Resonancias orbitales
1866: Kirkwood gaps
Tabaré Gallardo Resonancias orbitales
Kirkwood gaps at present
2 2.2 2.4 2.6 2.8 3 3.2 3.4
log (
Str
ength
)
a (au)
1:2
Mars
3:1
Jup
2:1
Jup
4:7
Mars
5:2
Jup
Main belt of asteroids is sculpted by resonances.
Tabaré Gallardo Resonancias orbitales
Resonance locations
k0nast = k1nJup
aast ' (k0
k1)2/3aJup
There is an infinite number of resonances...
which are the relevant ones?
Tabaré Gallardo Resonancias orbitales
1875: resonant asteroids (153) Hilda 3:2
Sun Jupiter
2nHilda = 3nJup
aHilda = (23
)2/3aJup = 3.97ua
Tabaré Gallardo Resonancias orbitales
Hildas and Trojans
Tabaré Gallardo Resonancias orbitales
Temporary satellite capture
the most probable origin of the irregular satellites
Tabaré Gallardo Resonancias orbitales
Quasi satellite, resonance 1:1
it is not orbiting around the planet, it is synchronized 1:1 with theplanet
Tabaré Gallardo Resonancias orbitales
Quasi satellite
from Wiegert website:
Tabaré Gallardo Resonancias orbitales
2004 GU9: Earth quasi satellite, resonance 1:1
Sun Earth
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1999 ND43: Mars horseshoe, resonance 1:1
Sun Mars
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Janus - Epimetheus 1:1
Tabaré Gallardo Resonancias orbitales
(134340) Pluto in exterior resonance 2:3
Sun Neptune
Tabaré Gallardo Resonancias orbitales
Widths
Murray and Dermott in Solar System Dynamics
Chaos:at resonance borders
superposition ofresonances
Tabaré Gallardo Resonancias orbitales
350.000 asteroids (proper elements)
AstDyS database
Tabaré Gallardo Resonancias orbitales
Resonant structure (zoom)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
3 3.05 3.1 3.15 3.2 3.25 3.3
prop
er e
proper a (au)
AstDyS database
Tabaré Gallardo Resonancias orbitales
Dynamical Maps
take set of initial values (a, e)
integrate for some 10.000 yrs
surface (color) plot of ∆a(a, e)
Model: real SS. Initial i = 0
1.86 1.861 1.862 1.863 1.864 1.865 1.866 1.867 1.868 1.869 1.87
initial a
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
initi
al e
-8.5
-8
-7.5
-7
-6.5
-6
-5.5
-5
-4.5
-4
-3.5
Tabaré Gallardo Resonancias orbitales
Asteroid region
Model: real SS
1.5 2 2.5 3 3.5 4
initial a
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
initi
al e
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
Tabaré Gallardo Resonancias orbitales
Zoom
Model: real SS.
1.7 1.72 1.74 1.76 1.78 1.8 1.82 1.84 1.86 1.88 1.9
initial a
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
initi
al e
-9
-8
-7
-6
-5
-4
-3
-2
-1
Tabaré Gallardo Resonancias orbitales
Zoom
Model: real SS. Initial i = 0
1.86 1.861 1.862 1.863 1.864 1.865 1.866 1.867 1.868 1.869 1.87
initial a
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
initi
al e
-8.5
-8
-7.5
-7
-6.5
-6
-5.5
-5
-4.5
-4
-3.5
Tabaré Gallardo Resonancias orbitales
Orbital inclinations of asteroids
Tabaré Gallardo Resonancias orbitales
Atlas of resonances in the Solar System, low e
Tabaré Gallardo Resonancias orbitales
Atlas of resonances in the Solar System, high e
Tabaré Gallardo Resonancias orbitales
Atlas for DIRECT orbits
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Atlas for RETROGRADE orbits
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Atlas from 0 to 2 au
Gallardo 2006
Tabaré Gallardo Resonancias orbitales
Atlas in the asteroids region
Gallardo 2006
Tabaré Gallardo Resonancias orbitales
Atlas in the trans-Neptunian Region
Gallardo 2006
Tabaré Gallardo Resonancias orbitales
Stickiness: ability to capture particles
Gallardo et al. 2011
Tabaré Gallardo Resonancias orbitales
Bizarre worlds...
Tabaré Gallardo Resonancias orbitales
Coorbital retrograde
heliocentric motion
SUN
asteroid
planet
relative motion
Morais and Namouni 2013
Tabaré Gallardo Resonancias orbitales
2015 BZ509: discovered in January 2015
a = 5.12 au, e = 0.38, i = 163
Sun Jupiter
Tabaré Gallardo Resonancias orbitales
Bizarre extreme: fictitious particle in resonant polar orbit
0
2
4
6
8
2.04 2.06 2.08 2.1 2.12 2.14 2.16 2.18
q,a
(au
)
0
90
180
270
360
2.04 2.06 2.08 2.1 2.12 2.14 2.16 2.18
i,ω (
degr
ees)
time (Myr)
0
90
180
270
360
2.04 2.06 2.08 2.1 2.12 2.14 2.16 2.18λ J
- λ
Tabaré Gallardo Resonancias orbitales
Bizarre extreme: fictitious particle in resonant polar orbit
collision with the Sun in the rotating frame
-2.5
-2
-1.5
-1
-0.5
0
0.5
-1.5 -1 -0.5 0 0.5 1 1.5
Z
X
Sun Jupiter
Tabaré Gallardo Resonancias orbitales
Resonances of Long Period Comets
Fernandez et al. 2016
Tabaré Gallardo Resonancias orbitales
Resonances of Long Period Comets
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
0 10 20 30 40 50
orbi
tal s
tate
s
<a> (au)
1:1
1:6
1:7
1:8
1:2
1:9
1:10
1:11
1:5
1:3
1:4
2:5
2:11
2:7
2:3
2:9
1:12
1:13
1:14
1:15
1:16
1:17
1:18
1:19
1:20
1:21
1:22
1:24
2:13
2:15 2:
17
Fernandez et al. 2016
Tabaré Gallardo Resonancias orbitales
Three-body resonance
k0n0 + k1n1 + k2n2 ' 0 only the asteroid feels the resonance
SUN asteroid
Tabaré Gallardo Resonancias orbitales
Atlas of TBRs: global view (for e = 0.15)
1e-005
0.0001
0.001
0.01
0.1
1
0.1 1 10 100 1000
Str
en
gth
∆ρ
a (au)
Gallardo 2014
Tabaré Gallardo Resonancias orbitales
Effects on the distribution of asteroids
2 2.2 2.4 2.6 2.8 3 3.2 3.4
log (
Str
ength
)
a (au)
1-4
J+
2S
1-4
J+
3S
2-7
J+
4S
1-3
J+
1S
2-7
J+
5S
2-6
J+
3S
1-3
J+
2S
3-8
J+
4S
2-5
J+
2S
3-7
J+
2S
3-8
J+
5S
2-1
M
Gallardo 2014
Tabaré Gallardo Resonancias orbitales
Density of resonances versus density of asteroids
0
50
100
150
200
250
1 1.5 2 2.5 3 3.5 4 4.5
dens
ity o
f 3-b
ody
and
2-bo
dy r
eson
ance
s
a (au)
3BRs2BRs
asteroids
Tabaré Gallardo Resonancias orbitales
Galilean satellites
Tabaré Gallardo Resonancias orbitales
Europa: dynamical map
0.00435 0.0044 0.00445 0.0045 0.00455
initial a (au)
0
0.02
0.04
0.06
0.08
0.1
initi
al e
-8.5
-8
-7.5
-7
-6.5
-6
-5.5
-5
-4.5
-4
E
∆a
Gallardo 2016
Tabaré Gallardo Resonancias orbitales
Chronology
1772: Lagrange equilibrium points1799: Lagrange planetary equations, stability of the SS1784: Laplacian resonance 3λE − λI − 2λG ' 180
Laplace quasi resonances: great inequality 2λJup − 5λSat
1846: Neptune discovered1866 Kirkwood gaps1875: first resonant asteroid (153) Hilda 3:21882: secular resonances (Tisserand, ν6)1906: first Trojan asteroid (588) Achilles1930: Pluto and exterior resonance 2:3 Neptune-Pluto1962: Lidov-Kozai mechanism1993: resonant TNOs (2:3 plutino)planetary systems in 2BRs and 3BRsminor bodies in 3BRshigh inclination resonant orbitsretrograde resonances
Tabaré Gallardo Resonancias orbitales
Bibliografía
Efectos dinámicos de las resonancias orbitales en el SistemaSolar. Gallardo 2016, BAAA 58, 291.
Resonances in the asteroid and TNO belts: a brief review.Gallardo 2018, Planetary and Space Science 157, 96.
http://www.fisica.edu.uy/~gallardo/atlas/
Tabaré Gallardo Resonancias orbitales