Analytical Solution for Formation Flying Problem near Equatorial-Circular Reference Orbit

Shaheera A Altalhi,Magdy Ibrahim El Saftawy

doi:10.4236/ijaa.2019.93016

Shaheera A Altalhi, Magdy Ibrahim El Saftawy

Open Access

https://doi.org/10.4236/ijaa.2019.93016

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Abstract

The relative motion between multiple satellites is a developed technique with many applications. Formation-flying missions use the relative motion dynamics in their design. In this work, the motion in invariant relative orbits is considered under the effects of second-order zonal harmonics in an equatorial orbit. The Hamiltonian framework is used to formulate the problem. All the possible conditions of the invariant relative motion are obtained with different inclinations of the follower satellite orbits. These second-order conditions warrantee the drift rates keeping two, or more, neighboring orbits from drifting apart. The conditions have been modeled. All the possibilities of choosing mean elements of the leader satellite orbit and differences in momenta between leader and follower satellites’ orbits are presented.

Highlights

As the geostationary Earth orbits (GEO) belt becomes more crowded it is increasingly difficult to acquire slots for new satellites
All the possible conditions of the invariant relative motion are obtained with different inclinations of the follower satellite orbits
For missions which a single satellite cannot accomplish, as global position satellite system (GPS), the needed of formation flight began

Summary

Introduction

As the geostationary Earth orbits (GEO) belt becomes more crowded it is increasingly difficult to acquire slots for new satellites. The invariant relative orbits have been studied for a long time, as the earlier work of Clohessy and Wiltshire [2] in addition to the studies of Tschauner and Hempel [3] These models introduced conditions on the initial relative position and velocity so that the relative orbits result to be periodic, which are closed orbits. We extend the works of Schaub and Alfriend [2] and Abd El-Salam et al [5] model by introducing an atlas for the curves of invariant relative orbits’ conditions This atlas will be presented using Mathematica program to calculate and plot graphics of the initial conditions of invariant relative orbits. Those graphics will be shown as curves in 2D; in the case of the orbit of the leader satellite is equatorial

Hamiltonian System

The Third Solution

The Fourth Solution

Conclusions