Astronomy 250: Special Topics in Astrophysics

Fall 2011

Planetary Dynamics

Gravitational dynamics of planetary bodies, both in the solar system and in extrasolar systems. To develop intuition, we will begin with classical analytic descriptions of the N-body problem. We will then introduce modern 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. The goal is to understand the literature quantitatively.

Instructor: Eugene Chiang (Departments of Astronomy and of Earth and Planetary Science )

Time & Place: Fridays 1:00-4:00 pm in 401 McCone.

Format: Weekly lectures, occasional problem sets, and eventually round-table discussions of the literature.

Class Requirements: (a) Make a reasonable attempt on at least 1 problem per problem set. (b) When discussing papers in class, be in a position to derive (at the order-of-magnitude level) equations and explain their physical significance. (c) Final project to write a numerical integrator.

Office Hours: Thursdays 2:30-3:30 pm (Hearst Field Annex D29B or adjacent conference room D29D), but also anytime I am around and am not talking with anybody else. For guaranteed meeting times, e-mail me (echiang@astro.berkeley.edu).

Text: Solar System Dynamics by Murray & Dermott (MD), plus selections from Binney & Tremaine's (BT) Galactic Dynamics, plus journal articles.

Course Outline:

I. Tour of the Mechanical Universe

II. The 2-Body Problem

A. Problem Set 1 (due Friday Sep 9; also reading assignments from MD and BT)

Solutions to PS 1

B. Chapter 3 of BT (only certain sections are relevant; see Problem Sets 1 and 2)

C. Osculating elements (Notes on osculating elements and Gauss's perturbation equations)

D. Useful relations

E. Guiding center description

F. Kicking the 2-body problem: Gauss's perturbation equations / Lecture 1 Slides on Kicking Orbits

III. The Restricted 3-Body Problem

A. Problem Set 2 (ALSO due Friday Sep 9; also reading assignments from MD and BT)

Solutions to PS 2

B. Chapter 8 of BT (only certain sections are relevant; see Problem Set 2)

C. Hill's equations and the Hill sphere (Roche lobe)

D. The Jacobi constant

E. Lagrange points

F. Horseshoes and tadpoles

G. Reading 1 (due Sep 16): "Towards a theory for the uranian rings" by Goldreich & Tremaine 1979

H. Reading 2 (ALSO due Sep 16): "On the width and shape of gaps in protoplanetary disks" by Crida et al. 2006 (read just enough to understand Figures 1, 2, 3, and 5)

I. Supplemental Reading 1 (ALSO due Sep 16): "A method for calculations of nonlinear shear flow: Application to formation of giant planets in the solar nebula " by Korycansky & Papaloizou 1996 (relevant for question 9)

J. Supplemental Reading 2 (ALSO due Sep 16): "Gas flow across gaps in protoplanetary disks" by Lubow and D'Angelo 2006

K. Supplemental Reading 3 (ALSO due Sep 16): "Dynamics of narrow rings" by Dermott 1984 (might be relevant for question 8)

L. SIGN-UP SHEET FOR HOMEWORK RELATED TO READINGS (due Sep 16)

M. Sep 23: Reading 3 (PART I): "Planet Formation by Coagulation: A Focus on Uranus and Neptune" by Goldreich, Lithwick, & Sari 2004 (PART I = Sections 1-6, everything but skim discussion surrounding equations 34-35)

N. Sep 23: SIGN-UP SHEET FOR HOMEWORK RELATED TO PART I

O. Sep 30: Reading 4 (PART II): "Planet Formation by Coagulation: A Focus on Uranus and Neptune" by Goldreich, Lithwick, & Sari 2004 (PART II = Sections 7-12)

P. Sep 30: SIGN-UP SHEET FOR HOMEWORK RELATED TO PART II

Q. Sep 30: Supplemental Reading : "The Formation of Ice Giants in a Packed Oligarchy: Instability and Aftermath " by Ford & Chiang 2007 (relevant to the onset of instability in oligarchies)

R. Sep 30: Supplemental Reading : "The largest Kuiper belt objects " by Brown 2008 ("About 10 Plutos in the Kuiper belt")

IV. The (Very) Disturbing Function

A. Strengths and arguments