ASE 396: Dynamics of Planetary Systems

Course Content

Course syllabus

Lecture notes on a review of classical mechanics.
Topics covered: coordinate systems and reference frames, Newton's laws of motion, forces, torques, energy, momentum, angular momentum, the gravitational potential, Gauss law and the Poisson equation.

Lecture notes on the two-body problem.
Topics covered: the equations of motion, integrals of the motion, Kepler's laws, elliptical, parabolic, and hyperbolic motion, the orbit in space and time, epicyclic motion and the guiding center approximation.

Lecture notes on orbit evolution.
Topics covered: Gauss' planetary equations, evolution of the two-body problem over time, orbit decay due to aerodynamic drag and Poynting-Robertson drag.

Lecture notes on the three-body problem.
Topics covered: motion in a rotating reference frame, the Jacobi integral, zero velocity curves, Lagrange points, tadpole and horseshoe orbits, Hill's equations, the Hill sphere and Roche limit.

Lecture notes on epicyclic motion in an axisymmetric potential.
Topics covered: orbital precession in a non-Keplerian potential.

Lecture notes on Lindblad resonances.
Topics covered: Lindblad, mean-motion, and secular resonances, motion of a particle near a resonance, resonance trapping.

Lecture notes on tidal evolution.
Topics covered: The tidal bulge and potential, tidal quality factor and the Love number, evolution of the lunar orbit, spin evolution, tidal heating, and establishing the Laplace resonance among the Galilean satellites.