Abstract
We describe the phase space structures related to the semi-major axis of Molniya-like satellites subject to tesseral and lunisolar resonances. In particular, we dissect the indirect interplay of the critical inclination resonance on the semi-geosynchronous resonance using a hierarchy of more realistic dynamical systems, thus discussing the dynamics beyond the integrable approximation. By introducing ad hoc tractable models averaged over the fast angles, we numerically demarcate the hyperbolic structures organising the long-term dynamics via the computation of finite-time variational indicators. Based on the publicly available two-line elements space orbital data, we identify two satellites, namely M1-69 and M1-87, displaying fingerprints consistent with the dynamics associated to the hyperbolic set. The computations of the associated dynamical maps highlight that the spacecraft are trapped within the hyperbolic tangle.
Dynamical properties of the Molniya satellite constellation: long-term evolution of the semi-major axis