The purpose of the lecture is to discuss basic issues of classical and celestial mechanics centered on the theory of two-body orbits, in the context of the N-body problem and its restricted variants (e.g., the restricted elliptic three-body problem). Modeling observations of binary stars and planetary systems is an important application in the field of astrophysics. Numerical techniques for solving equations of motion and qualitative analysis of simple models, such as the three-body perturbation problem, address basic concepts in dynamical systems theory.

The material is intended to be understood by undergraduate students with an elementary background in differential calculus, linear and vector algebra and vector calculus.