Table Of ContentINTRODUCTION TO
ORBITAL MECHANICS
T.G EYLING
FRANZ
H.R OBERTW ESTERMAN
BelTlep lheoLnaeb oratories
WhippanNye,w J ersey
A
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ADDIOSN-WESLPEUYB LINSGH CIOMPANY
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ADDISON-WESLEYA EROSPACE SERIES
ConsnugEl dtiitor.'
DANIELB ERSHADER
Copyr©i 1g9hBt7e 1Tl ell epLhaobnoere asIt,no cr.i
Philippin1es9 B7ec1Tlo elpl yerpiLhgaohbntoe r saI,tn ocr.i e
Alrli grhetsse. r vpNeaodor tfth piusb limcaabyte ri eopnr osdtuocierander ,de trsiyesvtaelm ,
ort ransmiiannt fyto erodmrb, ya nmye aenlse,c tronic, mechraenciocradli,n gp,h otocopying,
oro therwwiitshteoh,upe tr iworri tpteernm iosfts hiceoo np yrhioglhdPter ri.ni tnte hde
UnitSetdao tfAem se rPiucbal.i ssihmeudl tainnCe aonduaaLs.il byr oafCr oyn gCraetsasl og
CarNdo. 7 -7191502.
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fort heuinrf ailfianigt h,
continueonucso ugreamenta,n d
long-lapsattiinegn ce
PREFACE
Longaegtroh awnec atroer ectahlel ,oi fwd reiatt ihbniogs o wkac so nc.e ived
Ind,e egidetnsge osbeiassct kto h tei omtfeh fier ssatt ellaluinwtchehe senps e cial
isitnas p plpiheyds aincasl,yd tyincaamslit crusur,ce fltsu,im de chsa,ann idc
mathemraetgcinociscz headl lpernlogebimnbsge yotnhiden i"tsipaaalcg ee "
publ.Oi rciigtiytnhbailoslow ykab, sa soentd ht eh ouogsfhh ta rwiinctgoh,l leagues
wh,ol iokuer sealrwveie otsuha,tc adtermaiicin ndi ynnga maisctarlo tnhoem y,
appliacnaedtx itoenon sfci eolineam slet chatneicichqsnu. Te osdyta,h dee aorft h
treaotnti hssaeutjsbc e hta dsi pspareea.Sd itlnlo,no eft haev aiwloarbsklesee ms
toa im extpwolairtcdhio etb ljye wcets iefvtoeo r u rlesvsen,a menloyt, only to
derainvddei stphlpaerey t irneelinaottnb sua,tl tspoou tth eimnt thope e rspective
oft hper een.sSt incceeli eamslet chainasis cpse cwiiatlohino tefyt hleog nest
histionsr ciieefsne mcwoe dr,enc latioomr si gicnabaneml aitdiyetn h fiies.lT dhe
emphatshiwisos ri ikrsn a troh nee valutahpteei rntgmi antehnetm tartaiidocinat l
itn hlei gohcftu rraepnptli io.cn ast
Attaithniisn ge nd uhnadse rnltoiatgk. Nhe ebtneal aeryd nle yc haadpsea ssed
sintchfieer osutt loiftn hbeeo owka wsr i;tc tnoecneapntedsv aluhaatvieo ns
chanagnemdda tunroeotdn ,lb cyea uosfoe u orw ne ffobrutwtsi tthha ei odf
analaynsadip sp loincsan tubimye rcoolulesae .gsM uanya speocftt hse j cestu b
wersteu -dmioertdehca anb nei nclhuedreaedn-m da ncyo nrsaitdwieeoingsh ed
befwoerd ee cidtehdpe r eoennst agtiivioentnn h ties.x t
The dfroirvbciheenigsnt dhp irso coefrse sa pphraavies oatrlhi egitirwn os in
eveonfft usn damseingtnailtfi odc yannacmeai sctarlo enseopcmiypa,el rltyu rba
titohne :ot rhayep peaorfta hnhecih eg- spaeuetadot mcimocp utaentrdh aev ail
abiolfi" tmayn -maodbrei."tS sod eedpolt yh etswedo e veloapfmfetenhctets
sujbcetth taaotp ptlhcyel s aisncaamloe Cf e lieaMslect haninisoc atsp propriate
hecnet,ht ei atnltdeh sep iorfti htbi oso k.
Ast ot hceo mpuittaesbr i,tl oirt eyl itehtvehe e oorfsi tsrta ightforward
calcualnaadtn iaolhnya sysie stb eft uold leyvo epl.eI dtsi npu rseep aorfa tion
vii
Preface
V111
ephemearpipdeeaisro sub suo,tbe vffietacsswt es, h aelnld etaosv hooriw ms,o re
subtltehc eta shsuapanel c mtiagtihomtran geTi.h sea mitesr outfeh aep plication
orfo kcetwrhyih,ca bhse beonhrt ewaradnfidrn ugs ttrtoah oteri mbneigct h iaan.n ic
For fitrthsiethm eec anm odrote h panas sivoeblrsyvet eho er bniattspu rriodeve s,
buotn,t hoeht ehra nhdec, a nnol o nrgl eimhiiatsn altyons eiascr ilryca unlda r
c-oploarnbaoritr tfo so rycieesln doiKnne-gp leerffieoacafnts st rgirciattvlayt ional
nautr.Te hutshm,ee h todoydl eovogepleodv tehrle a tshtrc eeen tiunsro icteo sm
pleatpepllyi tcopa rbelspeer nomtbs; ly eettoa, p pretchfieua ltle oiftm hpea ct
copmutaenrsd p apcrero agmt,he iasr mleihteord oyml uosbgteu nrdtseoofirdts .
Thcee nttarosadfkly namaisrcntoaolmh yaa sl wbaeytesoon b ttahiseno lution
oft heeq uatpifmo ontsio oftn hh ee avbedonil.eSy si ntcheci ason tbn ed onien
clofsoerdam p,p roximmeahttoidaosrnu eas le d.f uTnwdoa mednitffeaenlrtl y
alteranraaetv iavlie:elns au bmeriinctaelg orraa tniaolrnyet pirce osneb nyt ati
seer.sTi hfeom reirns o dti scduisrseeicdntt hvlioysl u;s mueffiictteos atyh iant
cerctaasiicetnas bn em a dree ansaobalcyc ubruaitntt ee v,ge irvm euscp hh ysoirc al
mathemuantdiecraslto aftn hpderi bonlg.eO mnt hoet her thhaean nadl,y tic
apoparcothfe yni eclnodssi deirnasbbilugtethao ,tc hiaecvceua rg arcedyae,toa fl
algebraiiiscn vdlo.albv oer
Thaen almyehttoidco yal mloogsitn vareimpalboKlyeysp lemroitaiino. ne,. ,
ane lloirpbtaiiasfitc r, as ptp roxitmtoah mteoi toionaof c n e lebsdotyai raolua nd
cenmtarsa;is lm provaermteeh nestunosg hbtyv aripoeurst ursbcmahete.sIi no n
calcusluacstciiepvnsoeigs t iooafnb soy da lointKgse plerreifaetnrrj ecaentcoer y,
wefi ntdh tahtce h ooiifcn ed epveanrdieianosbgtf lr eei amotpr t.aT nhgceee otmrey
ofc oinc seacnthdie ontnchsepe os itoifaob noy di ns ucahno rbeipxtr esisne d
teromafsn gucloraodri nmaetaessfu rrotemhdf e o coutrsh c ee nottfeh fireg uarree
sipmlbeu,tt h ree labteitownteshe eansn eg uvlaarri aanbtdlh etesi me are tran
scneden;tt harilueslos u ctl oesxeepdsr sfiootrnhp seso itaisaof nu ncottfimi oen.
Nevheerltaesstsmr,eo rontsfoh e wpiattshhmte aj, ro a iompf r epeaprhienimgde ers
havuinngi ftoirmInmec rnetmcseh,o tsiema est hien depevnaidrae.bTn lhutes ,
firtts haef oremeannltgeikson,non eiw dna sntormoipcaarll aastn hcteer ue and
ecceanntormisawc,le irdeee voepledt ibsmyeei r e.Ts hetnhg er aviltp aetritounrab
infgo rscuepsoe,sr eopdnt hKee plemroidlawe,ne reex panidnte edsro mft he
angualnaorim e.aTs lhibse canmeec reyss siantchece l otsgreoidn otmreeixc
presassisioaontcwsei dt h mauttturaailcan tn ni -obynso syd smtaekmte hr ee quired
quadrraattuihrneetrsr aocttrhawiebsWleoer. k itnhtgew koi nodfssr e ies expan
sioinnset aoco ht hoenrce,o ualrdra ietvx eep srsoifto hnseso a -lcl"eddi sturbing
funicotnisnt" e romtfsi mteob, eu sfedon ru emroaunsas leoystf h seo lsaymrs .t e
Bceauosfe ltahbeio nrv oltvheisdo ,f tp haer t bweocrakam f eo cpaolio nft
attoenfn ottrihc el asst.sTs ihcebiyru oghmta niyn goeundsie vitcobe esao nri ts
rediuocpnta,r ticcaupliatroalntly his ezp ienccghi afirca cottfeh rgeir satviictsa tion
aflo rictlesaf en odnt hoer bgietot mrepireosv biynd aertdeu .
Wec an sneomewo rsep eciwfihceamrloeldr yenc odniotnhisa vwer ouag ht
cha.n gTelhiete epxraanls oifco lnsasis cdails tufrubnicnatgrii eon naisp cpalble
Preface
IX
tom anoyft hpere turbinegn cfoournwctieetasrhr etdic fiecliieaabslloit deasn d
ot heoirrbg iemtoe traiswe e.slM loerovtehrte,r anscernedleabntetitaowlne se n
t
thaen guvlaiararb alnetdsi maern eom oraew kwatrohd a ndblyae u tomatic
computtheatrnhs" e d irreeclta"st uoigohbntysc lsaiscaaslto rmoe.nrH sence,
botthhc eh obiectew aeletne rfnoaurtlmiavtoeift o hpnees r tufrobraicnntedgh e
resupletriatnitugorm nbeh todasws,e a lstl h ceh ooific ned epevnadreihnaatbv lee
becomeq uoeipsoeotnnns c e moarrete.hb eaT shiecsw eedi issssicsutnu eh sti es.x t
Weh avter iteod makbeok ou tshetifotsu hloe sneg iannesdec riises wnthts,o
fovra oruirsae sohnasvm,eo rteh apna ssaii nngt eirnoe rsbtmi etcahilac. Tns he
matesrhioabuleal cdc etsasoni ybolneae s ewnioitrfiohr r s tg-ryaedaura te-school
backgirpno huynsdoi rec nsg inweheor idntegous n idreersts htaeas ntdmr iocnaol
teromliyona gntdh weor kidnegt oafiv alirso puesr turtbeactuhien.oTsi nhuq s,
thmea themdaveteilcoaplam resent trsa igh(taefliolbtra wbaorradin fodoum rsal)
inn at:uS rienmcaen pyr loebmosf" spaacgeea "s trooncocmiuynsr e veral
alterfnomarsta,in vsdei nmcaeno yft htee chnairqseuo ewmshe aitvn ovle,d
numoeurisl lautsietvxreap mlaerspe r oevdiI.dn stphieor f"i etv ailounwa,et"
haivne seorctcenadasc lio omparbiestowdneiseff nef rroemnutln a.sCt oinosriidneg
thmeu ltioplfpi ucbiltiyci antt hifiioesnl sd ,r eeavdweeinrts sho msep ecialist
backgrmoauyfin ntddh ecsoem mehnetulslpi f,of ln yt os timiunldaetpee ndent
thouognsh utcc ho mrpias.Io nna sddiatnie offnoh,ra tbs e emna dteoi nterpret
thmea ifne atoufsrv eeesrp aelr turtbhaetoiirntoi ener osmf fs u ndampernitnal
ciplmeesc hosafT.n h iircesv tihvpeeh sy siincsawilhg ihhctah os ft ebne elnoi snt
clacsaaslci couunndtteshrb e u rdoefrun ot ianseto rmoinccaallci uo.ln ast
Thteh outghhatt tmhiisgs hetwr aovsraet k e xotohbka osc ucrrteotd h e
auhtorasn,cd o nrsaitdhieaobsne egni vteopn r acptriomcbeslA .es t hree ader
musbtea wabryne o we,x telnasbiiovcsreo n necwtietndho ntreixvaimaoplfl es
perattuirobni ;sia dnneaetldyy,pso inceasl swreovauetsl e dpr rmjoc etrsa tthhearn
homewaossrikg ntmsFe.on r rtehaistsohi ned, oe fae xceirsfeotsrhs et udent has
beeanb aonnd.eA dsa p artsiuabls titudteietl,ade edsv oemleo wphmiecnht s
paraelalredllei meorrn asttihoavnbese eonm iet.dTt hree aderb eas bhtlooeu ld
sintghlees feo hroi ust p orwacnce* tB. iy t hsea mteo kaef ne,tw u rtiosaelc tions
arien cltuaods estdih rseet a wdheiorss t dielvle lhoibpsai cnkgg irdnoy unnadsm .i c
Thbeo ockot naians seo tfm ethsoedlse acntedev da lubaytt haeeud t hors
duringy esaeorvntse hb reaa solitf sh eoiwarne rosepxapcecereT i.he sinesl ection
diffferrotsmh t er adistciooopfcne ae tlli emaselc hatneixbctyoss m isstiobo en s
disscspuerde s.eF rnisthtlo,yew veabr r,is ekfeo tfeca hcc hha pmtaebyre h el.p ful
Chaptaen2rdcs o vtehiren teogpfra arltmsio ictolfneom, ru lfaoKsre plerian
1
orb,di etfisonniostfe i lemaennsdte sr,ei pxeasn sfioovrnai sro us lciams.i etsing
Thiissst anmdaaetrrd;i atolhnoe t hhearni dto,sm iswsoiuohlnad vr ee suilant ed
seiroluasc ck omopf leestse.n
*W ea lrseoft eotr hc ea urles feleocfbt aisoeinxc e ricnJiM .s. e sD anbFyu,nd ameonft als
CelesMteicahla nMiaccsm,i NlelwYa onr,1k 69,2 . A.
Preface
x
Chaptgeirv esi notadrnu cttiba osnt mriocnraoelf erfernacmaeen sd
3
epheermeistd,h eajidurms etnftov ra rieoffueascn tadsd ,i scuosafss itomrnio cnaol
crhoneotm.rW yhitlhemi ast ecrnoitaalni ona sn alcyhtailcil steu nmgmea rizes
thbesa ifca crtesq ubiyar yneodni en voilncv oemdp uotritbnsaig,ni dis n cluded
becatuhrseae nt aibloeeh aisntdmr iocntaoelr omliyoni gnso atl wsaeylsf e-n.et vid
InC hap4tw eeer x aminael gterhbeerl aaiptcei rotntisoon rebdniteet tr mina
tiforno vmao ruisso rotfms e asuresmuecanhsst isga,hnl tge rsag,ne asn,rd a nge
ra.tT ehsgeo ver(ndientge remqiuniaioatsnrtsdei e cr)ia vntedhd er,ie rl atttoih oen
clasfsomiruclaalto ifLo anpsl Laacmeb,ae nrGdta ,u scso sniids.e S ratetdistical
daptraco ensgs iaapncpdal itoifno unm ermiectahalor dneso t tr e;ah toewdever,
thceno ceopoftr bdiett etrimioiesnnx a tetniodn ecdlfi urdset -"osrednesri tivities"
needeodr bsfieotlr e acnttdirj ocaent odreiysg. n
Chap5tb geeirwn isat d hi scuosvfsa iiroopunhs y sdiicsatlu rebnacnocuenst er
edb ys pavceeh iacnildle lsu tshtferuianrtd easm eeffneitctnate lsr o mefsl ementary
partdiycnlasemT. ih bcesa ipcre turbaapptraiocothnos o ldvyinnagem uqiact ions
isp reseanntsdep dec fiomfirucl atairdoein ssc .uT shseiesndec ltuhEdene c ke
mehtoadn sde vefromaruallt iionsn psh ecroirocdailn saotmeoesft , h efmr om
recyeena.tr s
Thcel saiscmaelt hoofvd a rioaftp iaorna mietstr eeraistnC e hda ptIetrs
6.
devraitiigsoi nvi entn e romfasd iusrtbfiunnigco atnsw ealsld ias tufrobricneg,
i.beyw. a,oy fL a grbarnagceak neidtn sfi nitiemspsiue.Tmls hadeli scussion treats
orbwiitltsohe w c cenatnridin ccilotinayn as as tpieccai;sta ehle cohifon idceep en
devnatr iaanbtdlh meee roifrt esc tiafirceeax taimo;ifin nr esdt-roersdauerlret s
givfeoanrv arioefpt hyy seiffcceta.s l
Thger oundfwocorar nnkiop ce rturmbeatthiiodsode nsv elioCnph eadp7 t,e r
wheLraeg greaa'nnsHd a mlitoenq'usa tairdoeen rsib vyaed di rmeecttdh ,ao s
wealslb y v ariaatrigounsmaT.elh n uets oefH itlylep-qeu atiiislo lnuss itnr ated
derifivrisndtge- croo rdoirnpaetret urfboamrto itoiinontsn h nee ioghrhobod
ofa nu npertourr.bb ietd
InC hap8wt eea rpp raocthht eh eoocfra yn otnriacn sfobryvm aiarattiioonnsa l
argeunm.tS separaobfti hHleai mtliyt on-eJqaucaoitbisiil o lnu sftotrrha et ed
Keplperrlo ebm faonordb tleanpeesrst uribnas tpihoenrcsoo idodiranel.as t
Thereiatfetreaarppt,ri ovaetc oth heneso npsaeraHbalmleit on-ieJ qauicaootnb
ares icdo,enl reeaddtpioen rgt uribtnah gteei noenrsfa utnicantcgirc odonit ntogh e
voZne ippreolcr eed.u
Fin,ai lnCl hyap9tw,ee gr i vei noatudnrc ttioHo ann 'smesen tdhS.oi ntchei s
technuisqeausc e o mbinoafot riboeinlt e maennpdtso si tcioodonir naatse s
depenvdaebrniltaie otscc ,u pais eoswm heastp epcosiiatlai moonpn egr attuirobn
metdhsIo.tm sa nipualradeti uisoscdnsi sens omdee taaniadlr i el luswtirtaht ed
partialrleys fueolxortpb sll iactpieretnt euisrosb.n a st
Sveertaolpa ircpesa n ttemliys sfirnogm outth.li isEn waeocuhrl edq uaitr e
leaacs hta pftoperrr o rcp oeverbauagtc e ru,s yot rreatwmoeubnltedo lnya
usegleessttsou awrraedb roasdceoOrpn ese.u chi tsah ureseo eacf a nomneitch ods
Prefaxcie
ind eripveirnatgtu irobotfnh sceo o rdeisnw,ah terei nstoiemnrerge e sstaurloetn s
reocrAdn.to hietsrh eo afss eytm pmteotthwiohcdi hsca hbv eeu esnse eodff ectively
inr ecyeenaftro osrr bibti-lssitttua.ydN ieextsth,ei rtseh s eu mmaroirfze isnugl ts
frosmy msatteaincdd e taniulmeedra incadan la lcyotmirpcoia snosft hbete ter
known permtehutor.dbB sayetointodhnp e r ionvcoefs altlemiottei loitneh e
mulotdipybr bole,im nsclmuoddirenneg ff oirntt osp iocldaoylgn asmH.ie croen e
mayc ofindenptonlitty o s everaaln ddre eficneipntutib vlieio c*nAas nt.o ther
subojfeicm optr taintsch reee pnrteoasntoe ifp oewred fliogfah ttms opahnedr ic
ree;nt threnysaet ulreaialndltt yhoa e r oeftar j caetoorpytz iamtiwihoinic,wsh e ll
dcoumenetlweshdee. Sr mieila,rt lhsyet attirsmeteaintcotafo l r bdiett eromni nati
irse ceaimvpialntegt einnt ictouhnre rl eintte raalttuhtroheuve,ga hr,p ireadctical
experwiietnrhce eaislm t-ertj caetyoc rompiuotnsastt aiwlalci otm prehensive
dcoumetni.toI anna ddittoti hoents oepi inpc rast idcylneas mt,ih sceuj bceto f
attisttbuaizdlaeit iidsou nfe o dre findiotuicmveeni to.an t
Let thissu jbcaetrosru atyst ihsodecfe o o pfe btohoipksu tc ointtsie nnttos
prorpp eersipv.eSe vceetroaftl h easree asbi enaegrpx el obryet dha eu otrhs'
coluleewsah,gso ien terwaictothuiw rro inte iffnohgrap tsr ovvaeldu iamnba lney
wa.yI siths o ptehdta hteo iwwrno rmka byep ubliasnhde tdh fianttd h btiohsoe ky
au seffouulni doant.
WhippanNye,w J ersey F.T.G.
Novembe1r9 70 H.R.W.
*F oerx amplSez,e beThheeolroyyfO, r biTthesR ;e sttrePidrc obloefTm hr eBeo dies,
AcadePmrieVNcs.e swY, o r1k69,7 .
