Asymptotic relative dynamics for spacecraft on close hyperbolic trajectories

In this work, the problem of spacecraft relative motion in close heliocentric hyperbolic trajectories is investigated. The purpose is to obtain a description of the relative motion convenient for formation design and analysis. To handle the problem, linearized system’s solution is expressed in the asymptotic reference frame in the form of Laurent polynomials of a special angle variable or time. The truncated expansions are rather simple and can be analyzed manually. We use these expansions to determine conditions of the finite relative motion and to find out what types of relative motion are possible. The derived formulae are utilized to approximately propagate the relative motion, as well as to design a multi-spacecraft formation. The paper concludes with a numerical example of designing a formation of four spacecraft that are supposed to fly in a regular tetrahedron shape.