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外文文献 > Secular dynamics of a lunar orbiter: a global exploration using Prony’s frequency analysis
Secular dynamics of a lunar orbiter: a global exploration using Prony’s frequency analysis

【DOI】
10.1007/s1056901495400

【摘要】
We study the secular dynamics of lunar orbiters, in the framework of highdegree gravity models. To achieve a global view of the dynamics, we apply a frequency analysis (FA) technique which is based o... 展开>>We study the secular dynamics of lunar orbiters, in the framework of highdegree gravity models. To achieve a global view of the dynamics, we apply a frequency analysis (FA) technique which is based on Prony’s method. This allows for an extensive exploration of the eccentricity ( $e$ )—inclination ( $i$ ) space, based on shortterm integrations ( $\sim $ 8 months) over relatively highresolution grids of initial conditions. Different gravity models are considered: 3rd, 7th and 10th degree in the spherical harmonics expansion, with the main perturbations from the Earth being added. Since the dynamics is mostly regular, each orbit is characterised by a few parameters, whose values are given by the spectral decomposition of the orbital elements time series. The resulting frequency and amplitude maps in ( $e_0,i_0$ ) are used to identify the dominant perturbations and deduce the “minimum complexity” model necessary to capture the essential features of the longterm dynamics. We find that the 7th degree zonal harmonic ( $J_7$ term) is of profound importance at low altitudes as, depending on the initial secular phases, it can lead to collision with the Moon’s surface within a few months. The 3rddegree nonaxisymmetric terms are enough to describe the deviations from the 1 degreeoffreedom zonal problem; their main effect is to modify the equilibrium value of the argument of periselenium, $\omega $ , with respect to the “frozen” solution ( $\omega =\pm 90^{\circ }, \forall \Omega $ , where $\Omega $ is the nodal longitude). Finally, we show that using FA on a fine grid of initial conditions, set around a suitably chosen ‘first guess’, one can compute an accurate approximation of the initial conditions of a periodic orbit. 收起<<

【作者】

【刊期】
Celestial Mechanics and Dynamical Astronomy
2014年4期

【语种】
eng