Nominal definition of satellite constellations under the Earth gravitational potential

Abstract

This work focuses on the definition of satellite constellations whose secular relative distributions are invariant under the perturbation produced by the Earth gravitational potential. This is done by defining the satellite distribution directly in the Earth-Centered–Earth-Fixed frame of reference and using the along-track time distances between satellites to define the satellite constellation configuration. In addition, in order to expand the possibilities of application of this design methodology, a general transformation between the formulations of Flower Constellations, Walker Constellations, and a relative to Earth formulation based on along-track and cross-track distances between satellites is obtained. This allows not only for a relation between these formulations, but also for the obtainment of the relative to Earth distribution of such constellations. Finally, an example of application of these methodologies is presented for a low Earth orbit.