orbiting

OrbitalPropagation:PartII

轨道外推：第二部分

Inourlastcolumn,wecoveredthebasicsofmodelingastheyapplytopredictingthepositionof

anymodel,thecomplexityoftheorbitalmodelwechoo

dependsuponveralfactors,chiefamongthebeingtheaccuracyofthedesiredpredictions.

Atthesametime,sincewewillbecalculatingpredictionsfromthisorbitalmodelonacomputer,

unately,the

twogoalsconflict,sowewillekamodelwhichstrikesanappropriatebalancebetweenthe

model'sfidelity(accuracy)andthecomputationalburdenofproducingaprediction.

Inordertoobtaintheappropriatelevelofmodelfidelity,itwillbenecessarytodeterminethe

orbitalmodel,the

includethegravityoftheearthalongwithperturbationsduetothenonuniformmass

distributionoftheearth,gravitationalattractionofthesun,moon,andplanets,andatmospheric

ftheforcesaremostimportantwilldependnotonlyontheirrelativemagnitude

butuponwhethertheireffectsareperiodicorcular.

Aperiodiceffect,suchasyourcar'santennawhippingbackandforthasyoudrivedowntheroad,

haslittleeffectonthepositionofthetipoftheantennaovertime,eventhoughtheforces

nlyneedtoknowthepositionoftheantennatiptowithin

onemeter,r,aculareffect,onewhichconsistently

increasordecreasovertime,mayhaveaconsiderableeffecteventhoughtheforceinvolved

pleofaculareffectwouldbethatofalightwindblowingasailboat

acrossthewater.

Asfarascomputationalcomplexityisconcerned,wenotedatthecloofthelastcolumnthat

therto

startwithasatellite'spositionandvelocityandtosum,orintegrate,alloftheforcesactingon

talforceisassumedtoactonthesatelliteoversomesmalltimespan,atthe

endof

implementedonacomputer,antageof

thisapproachisthatifsufficientdetailisgiventotheforcesactinguponthesatelliteandsmall

enoughtimestepsareud,nsideto

numericalintegrationisthatwemustcalculatethesatellite'spositionandvelocityforeachtime

stepbetweenourknowninitialconditionsandourdesiredpredictiontime.

Dependinguponthesizeofthetimestepandthelengthofthetimeinterval,thecomputational

,multiplythisproblembytheapproximately

7,500objectscurrentlytrackedbyNORAD(theNorthAmericanAerospaceDefenCommand)

andyou'dprefertohaveamodel

whichprovidesananalyticalsolution,thatis,asolutionwhereinifweknowthetimeofinterest

wecandirectlycalculatethestateofthesatellite'sorbitatthattimewithouttheneedto'step'

ourcondcomputationalmethodofimplementinganorbitalmodel.

Duringthe1970s,NORADcameupwithjustsuchasolution:

thismodel,knownasSGP(forSimplifiedGeneralPerturbation),aurcancalculateasatellite's

positionandvelocityataparticulartimedirectly,

resultisaconsiderablereductionincomputationalburdentosupporttrackingthegrowing

populationofearth-orbitingsatellites.

Obviously,anymodel,

certainsimplificationshadtobemadeandthesimplificationsplacerestrictionsuponhowthe

icular,themassofthesatelliterelativetothemassoftheearthis

tion,thesatelliteisassumedtobeinalow-eccentricity,

onditionsweretrueforalarge

percentageofthesatellitepopulationatthetimeSGPwasdevelopedandallowedamodeltobe

formulatedaccountingonlyfortheprimaryperturbationsonthesatellitesduetotheearth's

nonuniformmassdistributionandatmosphericdrag.

SubquentrefinementstoSGPextendedthistheorytoincludeami-analytictreatmentof

histheorydoesdependtosomeextent

uponnumericalintegration,akat

225minutes(about6,000kmaltitude)istheresultofasomewhatnaturalgapwhichhasresulted

fromhistoricalchoicesoforbitsforvarioussatellitemissionsandacrossoverinsignificant

perturbingeffects;abovethegaptheprimaryperturbingforcesarenolongeratmosphericdrag

andtheearth'snonuniformdensity,butorbitalresonanceswiththeearth'snonuniform

gravitationalfield,solarandlunargravitationalforces,w

modelisreferredtoasSGP4andisthemodelcurrentlyinubyNORADandtheUnitedStated

SpaceCommand.

Youmaybewondering,atthispoint,nly,there

aremanyothermodels,4hasonething

goingforitthatnoneoftheothersdo:iketheadventofautomobilesrunningon

unleadedgasoline,itdidn'tmakeanydifferencehowslickanewcaryouhadifyoucouldn'tfind

herorbitalmodelsonlyprovidedataforalimitednumberofsatellites

(suchasthespaceshuttle).NORAD,ontheotherhand,isresponsiblefortrackingallsatelliteson

ansthatorbitaldataforthismodelisavailable

forallearth-orbitingobjectscapableofbeingtrackedbytheUSSpaceSurveillanceNetwork.

Butwe''tallorbitalelementts

alike?Afterall,theyallmeasurethingslikeinclinationandmi-majoraxis(termswe'lldefine

furtherinafuturecolumn)'tItaketheNORADelements

andutheminmyfavoritetrackingprogram(whichdoesn'tutheSGP4model)?Allowmeto

uacomputeranalogyheretoexplain.

ryouknowthem

bytheirformalnames,suchasrun-lengthencoding,HuffmanorLZWcompression,orbythe

termsudbysomeofthepopulararchivingpackages,suchassqueezing,imploding,crushing,

orthelike,youwouldn'tbetoohappywiththeresultifsomeonentyoudatacompresdby

,yoursoftwarewouldprobably

reportanerror,butthat'resultwillbethesame:errors.

Thetwo-lineorbitalelementtsmadeavailablebyNORAD(andredistributedbyNASA)are

nvaluesforeachelementaregeneratedusingthe

ectsofthemajorperturbingforcesareincorporatedintothemean

valuesinaveryspecificwayusingSGP4andSGP4mustbeudtogenerateaccuratepredictions.

Failuretodosowillresultinerrors,themagnitudeofwhichwilldependheavilyonthetypeof

rrorsaretypicallymanifestedaslargetimeerrorsinsatellitesignal

orvisualacquisitionorbeingunabletolocatethesatelliteatall.

youwouldn'texpectto

ension,theonlydata

distributom

othersourcesshouldneverbereformattedintothetwo-lineformatjustsoitcanbefedintoa

particularsoftwarepackageunlessyoudon'tcareabouttheaccuracyoftheresults(justasyou

wouldn'tsoyoucoulduPKUNZIP).

Manypopularcommercial,shareware,andpublicdomainsatellitetrackingpackagesimplement

SGP4andyousho

,ifyouareconcernedaboutthe

sourceofyourdata,pdatesofNORAD-generated

two-lineorbitalelementtsareavailableviaInternet(anonymousftp,gopher,ormosaic)on

hedirectorypub/spaceorontheCelestialBBSat205/409-9280[Neitherof

nnowbefoundonlyontheCelesTrakWWWsite.].

Bothrvicesareavailablefreeofchargetoallurs.

Inournextcolumn,wewillexplorehowtheNORADtwo-lineelementtsaregeneratedand

givesomenumericalexamplestoillustratethemagnitudeoftheerrorswhichcanresultfrom

orwardtoeingyouherenexttime!