Astronomy 241: Foundations of Astrophysics I
16. Resonance & Stability Overview: Structure
100 AU
S
20,000 AU 5 AU
Inner system: Outer system: Oort Cloud: terrestrial planets, jovian planets and comets. asteroids. moons, “KBOs”. Belt Structure 14 August 2006
Hildas
Trojans
Mars
Jupiter Trojans
Wikipedia: Asteroid belt Belt Structure
Hildas
Trojans
Mars
Inner Belt: a < 2.5 AU Mid Belt: 2.5 AU < a < 2.8 AU Outer Belt: a > 2.8 AU
Jupiter Trojans
Wikipedia: Asteroid belt Resonances With Jupiter Inner Hildas Outer Middle Trojans
Resonances with Jupiter group asteroids by orbit period; period determines semi-major axis (Kepler III: P2 = a3). Trojan Asteroids
Hildas
L5
Mars
Jupiter L4
Wikipedia: Asteroid belt Hilda Asteroid Family
Wikipedia: Hilda family
2:3 MMR; stable since they avoid Jupiter (e ~ 0.3).
Small inclinations (i ≲ 20°).
Wikipedia: Hilda family Structure in Saturn’s Rings
Mimas
Cassini Division
Cassini’s division is due to a 2:1 resonance with Mimas:
PMimas = 2 PCassini ⇒ aMimas = ∛4 aCassini Other moons and resonances create other structures. Saturn: Ring Fine Structure
PIA08389: Expanse of Ice [movie] Saturn: “A” Ring Details
Encke gap Keeler gap
Mimas Mimas Pan Epimetheus 5:3 BW 5:3 DW 1:1 & Janus 7:6 Saturn’s Rings: “A” Ring Outskirts
Mimas Mimas Pandora Keeler gap 8:5 BW 8:5 DW 17:16 Daphnis 1:1
PIA07809: Daphnis At Work Prometheus 29:28 Prometheus 24:23 Prometheus 25:24 Prometheus 25:26 Prometheus 26:27 Prometheus 27:28 Prometheus 30:29 Prometheus 31:30 Prometheus 33:32 Prometheus 34:33 Laplace Resonance: Io, Europa, & Ganymede
2:1 Mean-Motion Resonance Pluto’s Orbit
Pluto’s orbit is highly tilted (inclination i = 17°) to the rest of the solar system.
Wikipedia: Pluto
Pluto is in a 3:2 resonance with Neptune. This is stable since Pluto avoids Neptune (cf Hildas).
Pluto’s Orbit Plutinos KBOs above this line cross Neptune’s orbit
Resonant KBOs (plutinos) avoid Neptune’s influence. 3:2
Scattered KBOs which cross Neptune’s orbit are easily perturbed.
The Resonant KBOs
These scattered KBOs may become comets.