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Astrodynamics

Article Title

Dynamical models for secular evolution of navigation satellites

Keywords

navigation satellites, disturbing function, secular resonances, double-averaging approach

Abstract

In this work, two dynamical models are formulated to describe the secular dynamics ofnavigation satellites moving in the medium Earth orbit (MEO) and geosynchronous orbit(GSO) regions. In the dynamical models, the leading terms of the Earth’s oblateness and theluni-solar gravitational perturbations are considered. For convenience, the orbits of the Sunand the Moon are described in the geocentric ecliptic reference frame, where the regressionof nodal line and precession of apsidal line of the lunar orbit can be approximated as linearfunctions of time. The disturbing function acting on navigation satellites is analyticallyaveraged over the mean motions of both the satellite and the third body (the Sun orthe Moon). Explicit expressions of the averaged disturbing function are provided in thegeocentric ecliptic and equatorial reference frames, corresponding to averaged model 1 andaveraged model 2, respectively. It is found that there are seven resonant arguments inaveraged model 1, while there are thirty-two resonant arguments in averaged model 2.The associated resonance curves corresponding to these resonant arguments in each modelform the dynamical backbone in the phase space, organizing secular behavior of navigationsatellites. At last, the averaged models are numerically compared to the associated non-averaged model, and simulation results indicate that (a) the averaged models formulated inthe geocentric ecliptic and equatorial reference frames are identical, and * both of thesetwo averaged models are applicable in predicting secular behavior of navigation satellites.

Publisher

Tsinghua University Press

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