ResultsOblatenessTrendsAsimulationwasrunfor25orbits,giventhefollowinginitialorbitalelements:

Oncethesimulationswerecomplete,orbitalelementswerecalculatedfromthepositionandvelocitytimehistories.

Above:Changeininitialorbitduetooblatenessperturbation.Below:Animationofchangeinorbitovertime.

Secular Trends of Perturbations Explored NumericallyKyle Litzer CU Boulder ASEN 5050

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Above:Timehistoryofsemimajoraxis,eccentricity,radiusofperigee,andradiusofapogee.Below:Timehistoryofinclination,rightascensionoftheascendingnode,andargumentofperiapse.

Asseenabove,semimajoraxis,eccentricity,radiusofapogee,radiusofperigeeandinclinationareallunaffectedsecularlybyoblateness.Thereisauniquetradeoffwitnessedbetweenradiusatapogeeandperigee.Whenoneisataminimum,theotherisatamaximum.

Aspredictedanalytically,thetimehistoriesshowaseculartrendinbothrightascensionoftheascendingnode(RAAN)andduringtheapproximately65hoursimulationtimespan.RAANdecreasesbyapprox.7.5,whileargumentofperiapserisesbyapprox.13.

Asmentionedbefore,inhistextValladogivesanalyticalexpressionsfortheseculartrendsintheorbitalelementsduetotheoblatenessofEarth.ItisshownthattheonlyorbitalelementsaffectedinasecularwayaretheRAAN,theargumentofperiapseandthereference(initial)meananomaly.

Comparingtheseequationstothebehaviorwitnessedabove,thenetchangeinRAANandargumentofperiapseagreewiththeanalyticalexpressions.

DragTrendsAsimulationwasrunfor100orbits,giventhefollowinginitialorbitalelements:

Oncethesimulationswerecomplete,orbitalelementswerecalculatedfromthepositionandvelocitytimehistories.

Above:Changeininitialorbitduetodragperturbation.Below:Animationofchangeinorbitovertime.

Above:Timehistoryofsemimajoraxis,eccentricity,radiusofperigee,andradiusofapogee.Below:Timehistoryofinclination,rightascensionoftheascendingnode,andargumentofperiapse.

Above:Detailoftimehistoryofsemimajoraxis,eccentricity,radiusofperigee,andradiusofapogee.Below:Detailoftimehistoryofinclination,rightascensionoftheascendingnode,andargumentofperiapse.

Theperturbationsduetodragyieldquiteinterestingresults.Allsevenelementsplottedfollowadefiniteseculartrend.Allsixelementsasidefromargumentofperiapseshowadownwardtrend.ItalmostappearsasiftheorbitistryingtoalignitsperigeedirectiontobecomeparallelwithtotheEarth/Sundirection.Themagnitudeofchangeinradiusofapogeeversusperigeeshouldalsobenoted.Thenetchangeinapogeeisontheorderof30km,whilethenetchangeinperigeeisontheorderof200m.Thiscanbeconceptuallyverifiedifwecomparethelossofspeedduetodragwithacircularizingantivelocitydirectionburnperformedatperiapse.Sinceperiapseisthemostefficientplacetoperformorbitchangingmaneuvers(duetohighspeeds),smallerchangesinvelocityatperigeebecomelargerchangesintheorbit,especiallyatapogee.

Uponcloserinspection(referringtothezoomedinplots),itcanbeseenthattheelementsallremainrelativelyunchanging.Sincethisorbitiseccentric,andasareasonablylowperigeealtitudethatdipssignificantlyintotheEarthsatmosphere,theeffectsofdragareonlywitnessedduringshortspurtsoftimeneartheorbitsperigee.Curiously,theargumentofperiapsetimehistoryshowssharpspikeseverytimethespacecraftiswithintheatmosphere.Furtherinvestigationwouldneedtobeperformedtofindthereasonforsuchhighrateofchange.

SolarRadiationPressureTrends

Asimulationwasrunfor100orbits,giventhefollowinginitialorbitalelements:

Oncethesimulationswerecomplete,orbitalelementswerecalculatedfromthepositionandvelocitytimehistories.

Above:ChangeininitialorbitduetoSRPperturbation.Below:Animationofchangeinorbitovertime.

Above:Timehistoryofsemimajoraxis,eccentricity,radiusofperigee,andradiusofapogee.Below:Timehistoryofinclination,rightascensionoftheascendingnode,andargumentofperiapse.

Theonlyoftheorbitalelementsinduringthissimulationthatshowsnoseculartrendisthesemimajoraxis.Itisverypeculiarthateventhougheccentricity,radiusofapogeeandperigeechange,thesemimajoraxisremainsrelativelyconstant.Furtherinvestigationwouldbenecessarytounderstandthisrelationship.

ItcanalsobeseenthatthetrendsforRAANandargumentofperiapsemirrorthatoftheoblatenessperturbation.

Finally,itshouldbetakenintoconsiderationthatthemagnitudeofsecularchangeintheorbitalelementsduetoSRPismuchsmallerinmagnitudethanthesecularchangesduetoEarthsoblateness.