Resonances in the Earth's Space Environment

Abstract: We study the presence of resonances in the region of space around the Earth. We consider a massless body (e.g, a dust particle or a small space debris) subject to different forces: the gravitational attraction of the geopotential, the effects of Sun and Moon. We distinguish different types of resonances: tesseral resonances are due to a commensurability involving the revolution of the particle and the rotation of the Earth, semi-secular resonances include the rates of variation of the mean anomalies of Moon and Sun, while secular resonances just depend on the rates of variation of the arguments of perigee and the longitudes of the ascending nodes of the perturbing bodies. We characterize such resonances, giving precise statements on the regions where the resonances can be found and provide examples of some specific commensurability relations.