Dynamical properties of the Molniya satellite constellation: long-term evolution of the semi-major axis

TL;DR

This paper investigates the long-term dynamical behavior of Molniya satellites, revealing how resonances and hyperbolic structures influence their evolution and identifying real satellites affected by these mechanisms.

Contribution

It introduces a detailed analysis of semi-major axis dynamics under resonances, combining models, numerical cartography, and real satellite data to reveal hyperbolic structures affecting satellite trajectories.

Findings

Identification of hyperbolic structures influencing satellite dynamics

Detection of Molniya satellites exhibiting resonance fingerprints

Evidence of resonance-driven trapping in satellite trajectories

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, the questions answered in this contribution are: (i) we study 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 fast angles, (ii) we numerically demarcate the hyperbolic structures organising the long-term dynamics via Fast Lyapunov Indicators cartography. Based on the publicly available two-line elements space orbital data, (iii) we identify two satellites, namely Molniya 1-69 and Molniya 1-87, displaying fingerprints consistent with the dynamics associated to the hyperbolic set. Finally, (iv) the computations of their associated dynamical maps highlight that the spacecraft are trapped within the hyperbolic tangle. This research therefore reports evidence of actual artificial satellites in the near-Earth environment whose dynamics are ruled by manifolds and resonant mechanisms. The tools, formalism and methodologies we present are exportable to other region of space subject to similar commensurabilities as the geosynchronous region.