Investigation on a Doubly-Averaged Model for the Molniya Satellites Orbits

Abstract

The aim of this work is to investigate the lunisolar perturbations affecting the long-term dynamics of a Molniya satellite. Some numerical experiments on the doubly-averaged model, including the expansion of the lunisolar disturbing functions up to the third order, are carried out in order to detect the terms dominating the long-term evolution. The analysis focuses on the following significant indicators: the amplitude of the harmonic coefficients, the periods of the arguments involved and, in particular, the ratio between the amplitudesand the corresponding frequency. The results show that the second-order lunisolar perturbation gives the dominant contribution to the long-term dynamics. The second part of this work aims to study the resonant regions associated to the dominant terms identified so far by using both the ideal resonance model and an alternative approach. The results obtained show when the standard method does not catch the main features of the dynamical structure of the resonant regions. Finally, the maximum overlapping region is identified in the proximity of the Molniya orbital environment. KeywordsMolniya orbits • Luni-solar perturbation • Luni-solar resonances • Resonances overlapping • Third-body effect 1 Introduction On April 23, 1965 the first Molniya-1 spacecraft was launched by the former Soviet Union [3].After that many others were set in orbit until 2004. These satellites were initially designed for Russian communication networks and their orbits form a class of special orbits around the Earth: the Molniya orbits. The main dynamical features of Molniya orbits are: an eccentricity e ≥ 0.7, an inclination i ≈ 63.4 deg and an orbital

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

“…They compared orbits generated using this model against TLEs data on several cases and were able to reproduce qualitatively the time evolution of the argument of perigee on several decades. More recently, [29] advocated that the cos h term produces a significant contribution to the dynamics of ω, where the reader is referred to Appendix A for further details. We adopt the following 2-DoF Hamiltonian system…”

“…This paper is part of a recent series of papers dedicated to properties and dynamics of Molniya spacecraft [1,6,29] with emphasis on the long-term evolution of the semi-major axis. We approach the problem by studying the long-term and drag-free motion of a test-particle subject to the nonspherical geometry of the Earth and third-body perturbations due to the Sun and the Moon.…”

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

“…They compared orbits generated using this model against TLEs data on several cases and were able to reproduce qualitatively the time evolution of the argument of perigee on several decades. More recently, [28] advocated that the cos h term produces a significant contribution to the dynamics of ω, where the reader is referred to Appendix A for further details. We adopt the following 2-DoF Hamiltonian system…”

“…This paper is part of a recent series of papers dedicated to properties and dynamics of Molniya spacecraft [1,5,28] with emphasis on the long-term evolution of the semi-major axis. We approach the problem by studying the long-term and drag-free motion of a test-particle subject to the nonspherical geometry of the Earth and third-body perturbations due to the Sun and the Moon.…”