Fall 2002
Planetary Dynamics
Fall 2002
Planetary Dynamics
|
Gravitational dynamics of planetary bodies.
The goal will be to understand the orbital motions
of planets and satellites, both in extrasolar systems
and in the solar system. To develop intuition, we will begin
with classical analytic descriptions of
the N-body problem. We will then introduce modern, powerful
numerical integration techniques.
Having developed an understanding of point-mass interactions,
we will impart shapes to planetary bodies to study
tides and spin-orbit coupling.
We will achieve a quantitative understanding
of celebrated case studies in planetary
dynamics, including resonant dynamics in
the extrasolar planetary systems Upsilon
Andromedae and GJ 876; the chaotic obliquity of Mars;
the origin of Plutinos in the Kuiper Belt;
and
the sculpting of planetary rings by shepherd moons. |
Instructor: Eugene
Chiang
(Departments of Astronomy and of Earth and Planetary Science )
Time & Place: Tuesdays and Thursdays 2:00 - 3:30 in 501 Campbell Hall
Format: Weekly lectures and problem sets. Each problem set will contain 3 problems. For registered students, a reasonable attempt at 1 problem of your choice out of every 3 will be required. As the course progresses, we may interleave the lectures
with round-table discussions of famous journal articles.
Office Hours: Anytime I am around and am not talking with anybody else. For guaranteed meeting
times, e-mail me (echiang@astron.berkeley.edu).
Text: Solar System Dynamics by Murray & Dermott. Supplemental journal articles.
Course Outline: Click on the hyperlink to find readings and problems.
| I. Tour of the Mechanical Universe |
| II. The 2-Body Problem PDF version |
| A. Osculating elements of the Keplerian ellipse |
| B. Useful relations |
| C. Guiding center description |
| D. Kicking the 2-body problem: Gauss's perturbation equations |
| E. Hamiltonian description and changing canonical variables |
| Solutions to PS 1 PDF version |
| III. The Restricted 3-Body Problem PDF version |
| A. Hill's equations |
| B. The Jacobi constant |
| C. Lagrange points |
| D. Horseshoes, tadpoles, and Trojan extrasolar planets |
| Solutions to PS 2 PDF version |
| IV. The (Very) Disturbing Function PDF version |
| A. Strengths and arguments |
| B. Secular, resonant, and short-period terms |
| C. Lagrange's potential equations |
| Solutions to PS 3 PDF version |
| V. Secular Theory PDF version |
| A. Wires |
| B. Laplace-Lagrange theory for eccentricities and inclinations |
| 1. Extrasolar planets: Upsilon Andromedae |
| 2. Kuiper Belt collisional families |
| C. Secular resonances |
| 1. Kozai and Extrasolar Planets: 16 Cyg AB |
| 2. Planetary Rings: Uranian Epsilon Ring |
| Solutions to PS 4 PDF version |
| VI. Resonance Theory PDF version |
| A. Good and bad phasing |
| B. Metronome model |
| C. Resonant widths |
| D. Resonance encounters |
| 1. Capture: Extrasolar system GJ 876 and planetary satellites |
| 2. Passage: Divergent crossings and eccentricity excitation of extrasolar planets |
| E. Reading for Tuesday October 1: Resonant Capture by Inward-Migrating Planets, |
| by Yu & Tremaine (2001) |
| F. Reading for Thursday October 17: Structure in the Dusty Debris around Vega, |
| by Wilner et al. (2002) |
| G. OPTIONAL SUPPLEMENTAL Reading for Thursday October 17: |
| The Geometry of Resonant Signatures in Debris Disks with Planets |
| by Kuchner & Holman (2002) |
| Solutions to PS 5 PDF version |
| VII. Chaos, Integration Techniques, and Long-Term Evolution |
| A. Lyapunov exponent |
| B. Resonance overlap criterion |
| C. Chaotic orbit of Pluto |
| D. Wisdom's Resonance Map and the Kirkwood Gap of Asteroids |
| E. Wisdom-Holman N-Body Symplectic Map |
| F. Reading for Thursday November 7: Dynamical Stability in the Outer Solar System |
| by Holman & Wisdom (1993) |
| G. Reading for Thursday November 7: Dynamical Structure of the Kuiper Belt |
| by Duncan, Levison, & Budd (1995) |
| **Color figures of DLB here** |
| H. Reading for Thursday November 14: Origin of Chaos in the Outer Solar System |
| by Murray & Holman (1999) |
| VIII. Tides and Spin-Orbit Coupling PDF version |
| A. Damped spring model and tidal Qs |
| B. Tidal migration |
| C. Eccentricity damping of hot Jupiters |
| D. Evolution to synchronicity |
| E. Chaotic obliquity of Mars |
| Solutions to PS 6 PDF version |