Dynamics of spacecraft formation flight

Abstract

In recent years, the need for spacecraft flying formation has increased significantly.  Its diverse applications range from synthetic aperture radar systems, like TechSat-21 to science missions such as EO-1 or LISA.  Correspondingly, many studies have been performed on the relative motion of a spacecraft with respect to a reference orbit.  Much of the literature, building on the early work of Clohessy and Wiltshire, is focused on solving the relative motion between spacecraft in two closely placed earlier orbits.

Their solution works fairly well for low eccentricity missions.  Recently, however, several missions have been proposed, designed or flown that need spacecraft flying in formation about a highly elliptical reference orbit.  Most of these missions, such as the Cluster, have space physics science objectives, which involve at least four spacecraft moving in a “tetrahedron” configuration at apogee.  The shape and the separation of the configuration are designed to resolve spatial and temporal variations.  In order to be able to analyze the relative motion of such missions, a novel approach of analyzing spacecraft relative motion is proposed in this thesis.  The new approach deals with the derivation of the relative coordinates of a deputy satellite with respect to a master satellite by a series of Euler transformations and a translation from the Earth-centred inertial frame to the spacecraft-centred rotating frame.  The equations of relative coordinates derived in this thesis are precise and can be used to analyze orbits at any eccentricity and of any initial separation with or without the inclusion of orbit perturbations.  For perturbed relative orbits, a modified version of the Gauss perturbation equations using equinoctial variables are used to model the dynamics.  Several initial conditions are simulated using the developed mathematical model including practical cases like spacecraft having differential drag effects.  Based on the simulation results, the amount of fuel required for formation and station keeping is estimated for different formation patterns.

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