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

• Published in: Nonlinear dynamics Vol. 105; no. 3; pp. 2081 - 2103
• Main Authors: Daquin, Jérôme, Alessi, Elisa Maria, O’Leary, Joseph, Lemaitre, Anne, Buzzoni, Alberto
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.08.2021; Springer Nature B.V
• Subjects: Aerospace environments; Artificial satellites; Automotive Engineering; Cartography; Classical Mechanics; Control; Dynamical Systems; Dynamics; Engineering; Mechanical Engineering; Molniya satellites; Orbital resonances (celestial mechanics); Original Paper; Satellite constellations; Spacecraft structures; Vibration; Tesseral resonance; Molniya orbit; Hyperbolic manifolds; Lunisolar resonance; Fast Lyapunov indicator; Space situational awareness
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-021-06708-5

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: (1) 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, (2) 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, (3) we identify two satellites, namely Molniya 1-69 and Molniya 1-87, displaying fingerprints consistent with the dynamics associated to the hyperbolic set. Finally, (4) 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 hyperbolic 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.