16. Resonance & Stability

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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 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 Prometheus 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..

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Asteroid Shape and Spin Statistics from Convex Models J
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