A guide to hunting periodic three-body orbits

The recent discovery of thirteen new and distinct three-body periodic planar orbits suggests that many more such orbits remain undiscovered. Searches in two-dimensional subspaces of the full four-dimensional space of initial conditions require computing resources that are available to many students, and the required level of computational and numerical expertise is also at the advanced undergraduate level. We discuss the methods for solving the planar three-body equations of motion, as well as some basic strategies and tactics for searches of periodic orbits. Our discussion should allow interested undergraduates to start their own searches. Users can submit new three-body orbits to a wiki-based website.