Analysis of Petal Rotation Trajectory Characteristics

In this study, the characteristics of petal rotation trajectories are explored in both the two-body problem and the circular restricted three-body problem (CRTBP). Petal rotation trajectories alternate long- and short-period nonresonant transfers between one or more gravity assist bodies to rotate the line of apsides relative to the central body. These petal rotation trajectories are typically computed using the patched-conic model, and they have been used in a number of different missions and mission concepts, including Cassini, JUICE, and planned Europa missions. Petal rotation trajectories are first analyzed here using the patched-conic model to quantify their characteristics and search for cases with fast rotation of the line of apsides. When petal rotation trajectories are computed in the CRTBP, they are unstable periodic orbits with corresponding stable and unstable manifolds. The characteristics of these orbits are explored from a dynamical systems perspective in the second phase of the study, and differences with patched-conic results are analyzed.