Download Neptune`s Resonances With Kuiper Belt Objects and What It Tells

Neptune’s Resonances With Kuiper Belt Objects
and What It Tells Us About the Early Solar System
The Origin of Pluto’s Orbit: Implications for the Solar
System Beyond Neptune
Renu Malhotra
A signature of Planetary Migration: The Origin of
Asymmetric Capture in the 2:1 Resonance
Ruth A. Murray-Clay & Eugene I. Chiang
On the Plutinos and Twotinos of the Kuiper Belt
E.I. Chiang & A.B. Jordan
Resonant and Secular Families of the Kuiper Belt
E.I. Chiang
The Effect of Neptune’s Accretion on Pluto and the Plutinos
Paul Wiegert
Horseshoe Orbit
Stationary frame | Rotating frame
Janus & Epimetheus
The Migration of the Planets
» Initial orbit (AU)
•
•
•
•
Jupiter
Saturn
Uranus
Neptune
5.4
8.7
16.3
23.2
Migration
Final orbit
-0.2
0.8
3.0
7.0
5.2
9.5
19.3
30.2
Pluto migrates out as a result of
being in resonance with Neptune
Eccentricity final from Eccentricity initial, resonance, and
initial and final semi-major axes of the migrating planet
e
2
final
e
2
initial
aN , final
1

ln
j  1 aN , initial
j is a resonance value ( j  1: j )
e final  e
2
initial
e final
aN , final
1

ln
j  1 aN , initial
1
30
 0 
ln
 0.25
2  1 25
2
Groupings of the test particles
Semi-major axis, eccentricity, and inclination over
the period 0 to 108 years
Ф – resonance angle
ω – argument of perihelion
Cold
Hot
e=0.001, sini=e/2
e=0.1, sini=e/2
Eccentricity and inclination of the known Plutinos, and of
the simulated particles under hot conditions
Different distributions reveal the rate of migration
107 yrs
106 yrs
Known Plutinos
Simulated Particles
Dione
A Jupiter-mass planet spends 50,000 years of migrating from 1 AU to 4
AU. As its exterior resonances swept through a group of planetesimals,
it excited their orbits and captured them into resonances.
Rotating Frame images of the orbits of the
captured particles.
Ratio
P2 : P1
Decimal Form
P2 / P1
1 :
1
1
17 :
16
0.941176
Semi-Major Axis
a1
a2 
2
 P1  3
 
1
 P2 
1.041244
16 :
15
0.9375
1.043965
15 :
14
0.933333
1.047069
14 :
13
0.928571
1.050646
13 :
12
0.923077
1.054811
12 :
11
0.916667
1.059723
11 :
10
0.909091
1.065602
10 :
9
0.9
1.072766
9 :
8
0.888889
1.081687
17 :
15
0.882353
1.087022
8 :
7
0.875
1.093104
15 :
13
0.866667
1.100099
7 :
6
0.857143
1.108233
13 :
11
0.846154
1.117808
6 :
5
0.833333
1.129243
17 :
14
0.823529
1.138188
11 :
9
0.818182
1.143142
16 :
13
0.8125
1.148465
5 :
4
0.8
1.160397
14 :
11
0.785714
1.17442
9 :
7
0.777778
1.182396
13 :
10
0.769231
1.191138
17 :
13
0.764706
1.195833
4 :
3
0.75
1.211414
15 :
11
0.733333
1.2297