High Precision Integration Methods for Orbit Propagation
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High Precision Integration Methods for Orbit Propagation P.L. PalmerI, S.J. Aarsetlr', S. Mikkola 3 and Yoshi Hashida 1 Abstract We present four integration methods which exploit efficient numerical techniques for orbit propagation. The methods have been selected to compare the strategy of using first order differential equations, required by the use of regularization, to integrating the equations of motion directly so that second order integrators can be used. All the methods have demonstrated high levels of orbital accuracy as well as very short integration times in astronomical simulations of long term dynamical evolution. We outline the bases of these techniques and illustrate their accuracy by comparing the orbital predictions with data from a GPS receiver on board a satellite in Sun synchronous LEO orbit.
Introduction One of the most fundamental problems to be addressed in satellite engineering is the prediction for the motion of the satellite in time. Virtually all applications of satellites require the correct timing for switching on and off equipment: for downloading data to a ground station when it is overhead; taking remotely sensed images; monitoring equipment for the ionosphere or magnetosphere or just reducing power load during times of eclipse. We need good orbital predictions when performing satellite maneuvers such as transferring satellites to target orbits or for interplanetary travel. Sending satellites even to the Moon requires a very high precision in the prediction of the motion of the satellite [2]. To counteract errors in orbit prediction satellites must carry large amounts of fuel on-board for orbit correction. This adds to the mass of the satellite and reduces the amount of space and mass for experiments, thus reducing the costeffectiveness of the mission. Satellite constellations are useful for the telecommunications industry [12] as well as regional monitoring [6]. They require accurate orbital predictions to ensure long 'Center for Satellite Engineering Research, School of Electronic Engineering, Information Theory & Mathematics, University of Surrey, Guildford GU2 5XH, England. 2 Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 OHA, England. 3 Tuorla Observatory, University of Turku, 21500 Piikkio, Finland.
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term coverage. Also geodesy and monitoring the Earth's gravitational variations requires accurate predictions based upon current models. In this paper, we compare a number of methods for the accurate propagation of satellite orbits, including highly eccentric orbits. The focus of this study is on whether direct integration methods outperform transformation methods (such as regularization) in computational time for a given accuracy requirement. We first discuss merits of direct integration approaches and transformation methods. Secondly, we describe the four methods that we have implemented for this study and present the theoretical basis of each. Next, we present some orbital integrations we have perf
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