Abstract

Invited Talk - Splinter jungeAG

Tuesday, 08 September 2026, 15:00   (MW-0337)

Dynamics and stability of time-varying equilibria in a modified five-body problem

Leon Heinisch, Alexander Leukert
Jugend forscht 2026

To investigate celestial-mechanical problems, such as deriving analytical expressions for orbits in planetary systems with more than two bodies, several models have been developed in the past. Common to all of them is the use of approximations due to the general non-integrability of systems with three or more gravitationally interacting bodies. The most well-known of these is the circular restricted three-body problem (CR3BP, or its planar version, PCR3BP), which continues to be used in space mission planning. In our study, we proposed a simplified five-body model and analyzed its potential maxima. In contrast to the static Lagrange points known from the Earth-Moon system, we found that these potential maxima exhibit a periodic wandering behavior. By employing Floquet theory and the Magnus expansion as well as established results from the PCR3BP, we then derived expressions for the trajectories of small masses around these points and analyzed their stability. Finally, we demonstrated that, in its qualitative behavior, this motion can be understood as the superposition of four ellipses - a 'quadricyclic' motion - and showed that these trajectories remain stable over time. Our analytical results were further substantiated by a numerical simulation.