Date of Award


Degree Type


Degree Name

Master of Science in Aeronautics and Astronautics


Aeronautics and Astronautics

First Advisor

Kathleen C. Howell

Committee Chair

Kathleen C. Howell

Committee Member 1

Carolin E. Frueh

Committee Member 2

James M. Longuski


The equations of motion in the Circular Restricted Three-Body Problem (CR3BP) allow five equilibrium solutions, that is, the Lagrange or libration points. Two of the five equilibrium solutions are the triangular or equilateral libration points, L4 and L 5. As the secondary gravitational body moves in its orbit about the larger mass, L4 and L5 lead and trail the secondary by 60 degrees, respectively. This investigation focuses on periodic solutions in the vicinity of the triangular libration points, specifically horseshoe and tadpole orbits. Horseshoe orbits are symmetric periodic solutions in the plane of primary motion encompassing both triangular points, as well as one of the collinear libration points, L 3. As a result of these known properties, it is possible to identify regions bounding the motion of horseshoe orbits. Also planar, tadpole orbits represent stable oscillations about the triangular points, combining a long-period librational motion and a short-period epicyclic motion reflecting the period of the two large gravitational bodies about their barycenter. Different strategies are developed to effectively construct tadpole orbits numerically, since the motion is not symmetrical and cannot be bounded to a limiting region as accomplished with horseshoe orbits. The relationship between tadpole orbits and other periodic orbits in the vicinity of L4 and L 5 is examined to explore the natural dynamical evolution of motion and produce useful insight for applications.