Solar System Models with a Selected Set of Frequencies

The purpose of this paper is to develop a methodology to generate simplified models suitable for the analysis of the motion of a small particle, such as a spacecraft or an asteroid, in the Solar System. The procedure is based on applying refined Fourier analysis methods to the time–dependent functions that appear in the differential equations of the problem. The equations of the models obtained are quasi–periodic perturbations of the Restricted Three Body Problem that depend explicitly on natural frequencies of the Solar System. Some examples of these new models are given and compared with other ones found in the literature. For one of these new models, close to the Earth–Moon system, we have computed the dynamical substitutes of the collinear libration points. The methodology developed in this paper can also be used for the analytical construction of simplified models of systems governed by differential equations which have a quasi–periodic (in time) external excitation and such that the form of the equations is rather cumbersome.