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Typescript. / Thesis (Ph. D.)--University of Hawaii, 1967. / Bibliography: leaves [91]-103. / ix, 103 l illus., maps, tables

Thesis (MScEng)--Stellenbosch University, 2003. / ENGLISH ABSTRACT: This study investigates the theory of precision satellite orbit propagation and satellite lifetime prediction and lead to the development of two necessary software tools for analysis in these fields. Precision propagation was achieved through the implementation of Cowell's method of special perturbations, considering perturbations due to a 70x70 asymmetrical gravity field, atmospheric drag, Luni-Solar attraction and Solar radiation pressure. The satellite's perturbed equations of motion were integrated utilizing a seveneighth order Runge-Kutta-Fehlberg numerical integration procedure, limiting error propagation by employing adaptive step size control. The MSlS-90 atmospheric density model, providing for diurnal and semi-annual variations, was employed to determine atmospheric density. Care was taken in the precision modelling of the motion of the 12000 equator and equinox. Propagation results for this test case proved to be superior to the SGP4 propagator and a commercial package. The long-term effects of Earth oblateness and atmospheric drag on a satellite's orbital elements were investigated and applied to the orbit decay prediction problem. Orbit decay was predicted by integrating the rates of change of the orbital elements due to Earth oblateness and atmospheric drag. A semi-analytical technique involving Runge-Kutta and Gauss-Legendre quadrature was employed in the solution process. Relevant software was developed to implement the decay theory. Optimum drag coefficients, estimated from drag analysis using precision propagation, were used in decay prediction. Two test cases of observed decayed satellites were used to evaluate the theory. Results for both test cases indicated that the theory fitted observational data well within acceptable limits. / AFRIKAANSE OPSOMMING: 'n Ondersoek is gedoen oor die teorie van presiesie satelliet-wentelbaan vooruitskatting en satelliet-wentelbaanleeftyd afskatting en het gelei tot die ontwikkeling van twee analiseprogramme vir gebruik in hierdie vakgebiede. Presiesie vooruitskatting is bereik deur die gebruik van Cowell se metode van spesiale perturbasies, wat die invloed van 'n nie-simmetriese 70x070 gravitasieveld, atmosferiese sleur, Son-Maan aantrekkingskragte en druk van sonradiasie, in ag neem. Die satelliet se versteurde bewegingsvergelykings is numeries ge-ïntegreer deur gebruik te maak van die sewe-agste orde Runge-Kutta- Fehlberg metode wat fout-voortplanting inhibeer deur gebruik te maak van 'n aanpasbare integrasiestaplengte. Die MSIS-90 atmosferies model, wat voorsiening maak vir dag-nag en half-jaarlikse atmosferiese variasies, is gebruik vir die berekening van atmosferiese digtheid. Sorg is gedra by die presiesie modellering van die beweging van die J2000 ekwator en ekwinokse. Resultate vir hierdie toetsgeval toon meer voortreflik te wees as die SPG4 - en 'n kommersieël-beskikbare vooruitskatter. Die langtermyn effekte van aard-afplatting en atmosferiese sleur op wentelbaanleeftyd is ondersoek en toegepas op die wentelbaanverval-afskattingsprobleem. Wentelbaanverval is bereken deur die integrasie van die tydsafgeleides van die wentelbaanelement onder invloed van aard-afplatting en atmosferiese sleur. Vir die doel is 'n semi-analitiese tegniek, wat gebruik maak van Gauss-Legendre kwadratuur en Runge-Kutta numeriese integrasie, gebruik gemaak. Nodige rekenaar programmatuur is ontwi kkeI om die vervalteorie te implimenteer. Optimale sleur-koëffisiënte is afgeskat deur van presiesie wentelbaananalise gebruik te maak. Twee gevallestudies van bekende vervalde satelliete is gebruik om die vervalteorie te evalueer. Resultate vir beide gevallestudies toon aan dat eksperimentele resultate werklike vervaltye binne aanvaarbare limiete navolg.

The effect of the atmosphere on near-earth satellites is evaluated by consideration of the drag perturbation and the associated dispersion parameters. Recommendations are made for each of these dispersion parameters. The recommendation concerning the density is that a dynamic density model be utilized instead of a static model. Included are numerical comparisons which quantify the error in predicted satellite positions which can occur due to an inferior density model alone. These comparisons are made for a variety of satellite orbits. / Master of Science

Dr. Schumacher can be emailed at paul.schumacher@us.af.mil / Presented herein are some analytical results available from regularization of the differential equations of satellite motion. True-anomaly regularization is developed as a special case of a more general Sundman-type transformation of the independent variable (time) in the equations of motion. Constants of the unperturbed motion are introduced as extra state variables, and regularization with several types of coordinates is considered. Because analytical results are sought, those regularizing transformations which produce rigorously linear governing equations are of main interest. When solutions of the linear regular equations in the true-anomaly domain are examined, it is found that the initial value and boundary value problems of unperturbed motion, typically requiring iterative solutions of the time equation, can be solved with only a single transcendental function evaluation per iteration cycle. Various means are described which can accelerate the evaluation of this function. The time equation developed in this study is a new universal relation between time of flight and true anomaly, and applies uniformly to all types of orbits, including rectilinear ones. It is a well-behaved function, the zero of which can be found reliably by Newton's method or other typical iteration methods. Once this time equation has been solved, the initial and final state vector on the transfer arc can be related to each other by rational algebraic formulae; no other transcendental function is needed. When the two problems are generalized by variation of parameters to the case of oblate-gravity perturbed motion, it is found that, to first order, the corrections of the unperturbed solution can be obtained by direct, noniterative formulae valid for all types of orbits. Moreover, it is possible to compute these corrections with only a single extra evaluation of the same transcendental function used in the unperturbed problem. Additional results are also presented, including exact solutions of the first-order averaged differential equations governing secular variations of the regular orbital elements in the true-anomaly domain. Complete universal expressions are given for the Keplerian state transition matrix in terms of the orbital transfer angle, and a simple midcourse guidance scheme is rederived in terms of universal variables valid for all non-rectilinear transfer orbits. / Ph. D. / incomplete_metadata

Thesis. 1979. M.S.--Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERONAUTICS. / Includes bibliographical references. / M.S.