Narrow Results

We present an overview of detailed computational results for families of periodic orbits that emanate from the five libration points in the Circular Restricted 3-Body Problem, as well as for various secondary bifurcating families. Our extensive overview covers all values of the mass-ratio parameter, and includes many known families that have been studied in the past. The numerical continuation and bifurcation algorithms employed in our study are based on boundary value techniques, as implemented in the numerical continuation and bifurcation software AUTO.

We present computational results for the families of periodic orbits that emanate from the five libration points of the homogeneous gravitating triaxial ellipsoid rotating around its small axis, as well as for various secondary bifurcating families. Possible applications of our results include research on the motion of stars and clusters in elliptical galaxies, and the design of space missions to the vicinity of small bodies (asteroids) and their libration points. The numerical continuation and bifurcation algorithms employed in our study are based on boundary value techniques, as implemented in the AUTO software tool.

The massive straight segment, rotating around the axis perpendicular to its center, is a simple alternative for more precise and sophisticated models that take into account the shape and mass density of natural asteroids. In this article, we give numerical results for the families of periodic orbits that emanate from the five libration points of massive straight segment, and for some secondary bifurcating families. Possible application and extension of the results to research on the motion of satellites near small irregular-shaped celestial bodies are also discussed. The numerical continuation and bifurcation algorithms we use in our study are based on boundary value techniques, as implemented in AUTO. An extensive set of python scripts for running AUTO will be made available at http://users.encs.concordia.ca/~doedel. These scripts can be used to recompute the results in this paper, and to do a wide selection of related calculations.