Celestial Mechanics

Instructor: Gu, Pin-Gao (gu@asiaa.sinica.edu.tw)
Grader: Hsu, Yu-Sen (69444015@nthu.edu.tw)
Meeting place & time: Shida, 14:10-17:00, Wednesdays
Reference books (reserved in the Shida & IAA libraries): "Solar System Dynamics" by Murray & Dermott, "Galactic Dynamics" by Binney & Tremaine (BT), "Gas Dynamics" by F. Shu

2/25: introduction

3/4: homework set I distributed, Newton's universal law of gravity, Newton's laws of motion, dynamical timescale, centripetal/centrifugal force, negative heat capacity of a Keplerian orbit, reduced mass

3/11: integrals of motion (energy & angular momentum), Kepler's laws

3/18: Kepler's equation, elliptic expansion

3/25: epicycle, barycentric system, 6 orbital elements

4/1: circular restricted 3-body problems (Jacobi constant, zero velocity curves, Tisserand parameter), gravitational slingshot, planet migration in a planetesimal disk, Roche potential (Lagrangian points, Roche lobe, interacting binaries)

4/8: homework set II distributed, stability of Lagrangian points, 1:1 orbital resonance (horseshoe orbits, tadpole orbits -> Trojans)

4/15: tidal bulge (Legendre function, amplitude of equilibrium tides), potential theory for tidal/rotational deformation, quality factor Q value (phase lag, tidal dissipation, tidal torque)

4/22: Love numbers, synchronization (orbital evolution), tidal dissipation in Geophysics (Munk & Wunsch 1998; happy Earth Day!), Roche zone, orbital circularization (radial & librational tides), obliquity tides (diurnal tides & the tides with freq.=2n), dynamical tides (p & g modes), observational constraints on Q_* (cutoff periods of binaries in stellar clusters: Mathieu 1994, Mathieu et al. 2004), tidal capture

4/29: disturbing function (secular, resonant, & short-period terms), Lagrange's planetary eqns (osculating orbital elements), non-closed orbits (discrepancy between epicyclic, vertical, and mean motion under a non-Keplerian potential)

5/6: secular perturbations: on average angular momentum exchange but no energy exchange between orbits, a test particle experiences secular perturbations from planets (free + forced orbital elements), secular resonance (math: forced orbital elements blow up. physics: pericenter/nodal precession rate of the test particle is close to that of a planet. example: what determines the inner edge of asteroid belts?), sweeping secular resonance (locations of secular resonance moves as planets migrate, etc.). resonant perturbations: geometry of resonance (frequent conjunction at the same point of orbits), physics of resonance (conjunction tends to move toward pericenter), resonant arguments of a disturbing function

5/13: resonance occurs when some of the resonant arguments librate (pendulum model, width of resonance location), capture into resonance due to differential orbital migration, exoplanets

5/20: homework set III distributed, local standard of rest, relaxation time, dynamical friction, energy equipartition, evaporation, Boltzmann equation, Jeans equations

5/27: homework set IV distributed, bar in the Milky Way (Benjamin et al. 2003), one application of Jeans eqn (vertical density scale height of disk galaxy), fluid (hydrodynamical) equations, epicyclic motion & Rayleigh criterion, Jeans instability

6/3: virial theorem & negative heat capcity, Toomre Q, geometry of spiral waves (leading & trailing, constant pitch angle -> logarithmic spiral), winding problem

6/10: issue of virial theorem for dark matter halos, Lin-Shu dispersion relation, phase & group velocities, pattern angular speed (apparent angular phase speed), co-rotation (CR) & Lindblad resonances (OLR & ILR), Q-barrier (wave evanescence near CR), long & short spiral density waves, rings in disk galaxies, Toomre stability criterion for axi-symmetric perturbations (m=0)

6/17: final oral presentations (titles & abstracts): Pan, Wei-Hsiang; Yan, Chi-Hung; Tsai, An-Li; Ho, Pei-Li