Long-term analytical propagation of satellite relative motion in perturbed orbits

Many scientific applications require the implementation of satellite formation-flying in various orbits both around Earth and other planetary bodies. The design and guidance of these new formations call for relative dynamics models able to accurately and efficiently incorporate secular and long-periodic effects of all relevant perturbations. This paper leverages a quasi-nonsingular relative orbital elements state representation to devise a general methodology to model both conservative and non-conservative effects on the satellite relative motion in arbitrary eccentric orbits. By augmenting the state with force model parameters and Taylor expanding the time derivative to first order in mean space, three new plant matrices capturing the effects of solar radiation pressure, Sun and Moon third-body, and geopotential zonal harmonics up to third-order are formalized. In addition, two new effects have been discovered and modeled analytically in closed form. The first is the solar radiation pressure effect on the relative eccentricity vector of formations in near-circular orbit. The second is the lunisolar third-body effect on the relative inclination vector of formations in near-circular nearequatorial orbit. The new models are validated using numerical integration. Their accuracy and computational efficiency, combined with the novel analytical insight, can be leveraged for innovative relative orbit design and guidance.