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19800017840.Pdf N O T I C E THIS DOCUMENT HAS BEEN REPRODUCED FROM MICROFICHE. ALTHOUGH IT IS RECOGNIZED THAT CERTAIN PORTIONS ARE ILLEGIBLE, IT IS BEING RELEASED IN THE INTEREST OF MAKING AVAILABLE AS MUCH INFORMATION AS POSSIBLE ACM Technical Report ACM-TR-121 NASA, CR- x •^ . c r aI (NASA-'CR-160702) MISSION ANALYSIS DATA FOR N80-26339 + INCLINED GROSYNC.HRONOUS ORBITS, PART 1 Analytical a.ad Computational Mathematics, Inc.) 81 p HC A05/MF A01 CSCL 22A Unclas G3/12 23607 MISSION ANALYSIS DATA FOR INCLINED GSOSYNCHRONOUS ORBITS PART 1 r r 1 t t n ANALYTICAL AND 415 16 COMPUTATIONAL ^0 e/ r..^. hi J9Qp ^' I MATHEMATICS^"^'N vt o :' a d MISSION ANALYSIS DATA FOR INCLINED GEOSYNCHRONOUS ORBITS BY OTIS F. GRAF, JR. AND K.C. WANG ANALYTICAL AND COMPUTATIONAL MATHEMATICS] INC. 1275 SPACE PARK DRIVE, SUITE 114 HOUSTON, TEXAS 77058 MAY I "E 10 This report was prepared for the NASA/Johnson Space Center under Contract NAS9-15885. A MISSION ANALYSIS DATA FOR SCLJNED OEOSYNCHRONOUS ORBITS * SECT 1ON PAGE 1.0 Introduction Background 1.2 Overview of this Report 1.3 A pp lications of Inclined Qeos,nchronous Orbits 1.4 The "Halo" Or s it Concept 1.5 Summar y of Results 2.0 Orbit Geometr y and Definitions 10 2.1 Orbital Elements and Coordinate Systems 2,2 Classification of SeosYDchrnnous Orbits 2.0 Perturbin g Effects on Geos,DchPonnus Orbits p 20 3.1 Elli ticit y of the Equator 3.2 8uD " Moon and Earth Oblateness 3.3 Solar Radiation Pressure . 4.0 Time Histories of Orbital E}emanto 24 4.1 Earth —Relative Mean Lonsitude 4.2 Motion of the Orbit Plane 4.3 Chan g e in the Eccentricit, 5.0 Velocit y Re q uirements for Orbit Maintenance 66 5.1 In —Plane Delta V 5.1.1 Mathematical Developments 5.1.2 Numerical Results 5.2 Out — of —Plane Delta V 5.2.1 Mathematical Developments 5.2.2 Numerical Results 6.8 Discussion of Multisatellite Systems 78 6.1 Problem Areas 6.2 Mission De y isD Concepts References 08 * AP peD6iX A: BibliosraphY AP p endix B: Listin g s of Com p uter Programs ` ' r_ _ _ _ MISSION ANALYSIS DATA FOR INCLINE GEOSYNCHRJNOUS ORBITS " by Otis F. Graf, Jr. and K.C. Wang 1.0 INTRODUCTION 1.1 Background _______________ The seostationar, e q uatorial orbit (GEO> has been e}tensivell, used g durin the p ast 10-15 Years. Satellites in this orbit a pp ear nearly ^ stationar y above the earth and are ideal for a pp lications in communica- tions and earth observations. g With the increasin a pp lications of the GEO, the available s pace in g the orbital arc is now bein de p leted. For exam p le, the NASA Space Trans p ortation S y stem is ex p ected to launch a pp roximatel y 160 seosta- g tionarr missions durin the next ten ,ears (Reference 1). The satellites need to be se parated b y a few des p ees in order to avoid Ph y sical and/or radio fre q uenc y interference. Because of the extensive p lanned seostationar, mission traffic and ~ the limited number of slots available, international orsanizatioOs are g over slot allocations. The U.S. has no - attem p tin to sain authorit y inherent claim to seostationar, "real estate" since it has no territory over the e q uator. The eeostationar, nrc of interest to the domestic U.S. g (55 des W. lon itude to 135 des W. lonsitude) may in the future be shared - 3 - with South American countries. Also, certain futuristic PrVJwcts (such as the solar Power satellites and s pace manufacturin g ) will re q Wire large amounts of the meAsYnchronous or g eustationar^r arc, ^ ^ For the reasons cited ab ve, it will be im p ortant in the future to Pack more satellites into useful meos-rnchronous orbits, A Promisin g Pro- p osal that has been Put forth is to use g eosYnch p onous orbits whose Planes are inclined to the e q uator. A satellite in such an orbit has a mrnund g g track that is a fi ure ei ht. If several satellites are p laced in orbits g that have the same fi ure mi g ht g round track, the y will all cross the e q uator at the same lon g itude, called the "9atema y ". The matew4, may re q uire onl y * few de g rees of the seostatiooarY arc " while accomodatiue p ossibl y 10-12 satellites in inclined orbits. As the satellites pass ~ throu g h the u pp er (or lower) latitudes, their g r0und track would a pp ear to ° be nearl y circular about a p oint on the earth^s surface~ From this Point of view, the y are called "halo" orbits. 1.2 Overview of this Report ----------------------------- Most of the earlier studies of inclined seos,nchronous orbits have concerned seumet p ical relationshi p s with idealized (un p erturbed) orbits, g In p ractice, however,the orbits will be p erturbed b y ravitational and non-sravitational forces. The result is that the orbits will be altered, ^ and corrective maneuvers must be executed b y on-board control systems. - Principal orbit Perturbations are due to earth oblateness " earth e q uato- rial elli p iticr, sun and moon g ravit y , and solar radiation pressure. - 4 - ­ _­ 1 ­ .1______'____'_ . I For e q uatorial eeosynchronous ( g eostationar y ) orbits, the effects of these Perturbations are well known. However, for inclined seosynr_hronous orbits, less information is known about the orbit Perturbations or the orbit maintenance delta-V re4uirements. The Pur p ose of this re p ort, therefore,is to Provide certain data that is needed for Preliminar y desi g n of inclined seos'rnchronous missions. In Particular, the objectives are try: • Study the Perturbatians on circular orbits with inclinations UP to 60 deQr•ees. • Determine the time histories of the orbital elements for Periods of u p to twirl Years. • Determine the velocit y mana g ement re q uirements needed to cancel the major Perturb as effects. • Present a com p ilation of data on inclined circular• weos •v'nchr•onous orbit characteristics. :section I of this re p ort introduces the Problem and saves the scope and Purose of the stud y . A summar y of the Princi p le results is also given. Section 2 describes the inertial and earth-fixed (rotatin g ) co- ordinate s y stems, as well as orbit Parameters and elements. The complete famil y of seas y nchr• onous+ orbits is discussed. It is shown that circular, inclined eeos` nchronous orbits com p rise onl y one set in this family. Section 3 g ives a discussion of the ma j or orbit Perturbations, and their se parate effects on the seosy nchronous orbit. ORIGINAL, PAPI I 09 PDOR QUALM - 5 - - -----'---------r----- ----------'--------------^---^' ^~ Section 4 mives detailed information on the orbit p erturbations of inclioed, circular eeos\^nchronous orbits. The 0aJV p emp hasis is to Pro-- vide time histor y data of certain orbital elements. Section 5 Provides a detirmination of orbit maintenance delta veloc- it y re q uirements to counteraot the ma j or orbit p erturbatiums " The v"uppose is to Pro y idw order of masnitude estimates, and to show the effects of orbit inclination on delta-V. g Section 6 discusses some of the considerations in mission desi n for a multisatellite s,stem, i.e. a "halo" orbit constellation. Section 7 Presents some conclusions and recommendations based on this study. A pp endix A sives a biblio g ra p h y of pa p ers and re p orts on the subject ° of seosYnchronous orbits. There is a wide bod y of literature on this , subject, The biblio g ra p h y includes p ap ers of interest to this studY, as well as back g round pa p ers concerned with the fundamentals of orbital ' ute p g ' Appendix u contains a /istznm of all the com p p ro rams that were g develo p ed for this stud y . These Pro rams are on the Interdata 8/32 com- p uter at the NASA Johnson S p ace Center. All routines are throushly documented with comment cards. ^ ' ' 6 ' 1.3 A pp lications of Inclined Geos y nchronous Orbits Several authors have discussed the Possible ,a pp lications of Inclined Geos •rnchronous Orbits (IGO) . Generall y these orbits are useful for a pp lications where there must be a Ions viewin g time from the earth. How- ever it is not necessar y that the satellite be fixed relative to the surface of the earth. The followin g a pp lications have keen Pro p osed for IGO orbits: • Earth observation • Solar Power Satellite • Communication, • Militar y applications A pp lications and ground tracks are discussed by Akin (Reference 2), If Bielkowir_z (Reference 3) and Graf (Reference 4). 1.4 The "Halo" Orbit Concept These is an additional a pp lication of IGO that has been Pro p osed NO, Fielder (Reference 5). His su gg estion is to establish a constellation of satellites in inclined circular g eos y nchronous orbits, such that each satellite in the constellation follows the same fi g ure ei g ht g round track: g (see. Fi g ure 1). At the hi her latitudes (which are of interest for the U.S.) , the satellites would app ear to rotate in a nearl y circular orbit relative to the earth, hence the term "Halo" orbits.
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