Astronomy 241: Foundations of Astrophysics I

16. Resonance & Stability Overview: Structure

100 AU

S

20,000 AU 5 AU

Inner system: Outer system: : terrestrial , jovian planets and . . moons, “KBOs”. Belt Structure 14 August 2006

Hildas

Trojans

Mars

Jupiter Trojans

Wikipedia: 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: Resonances With Jupiter Inner Hildas Outer Middle Trojans

Resonances with Jupiter group asteroids by period; period determines semi-major axis (Kepler III: P2 = a3). Asteroids

Hildas

L5

Mars

Jupiter L4

Wikipedia: Asteroid belt Hilda

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 .

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.