Satellites
Examensarbeteutfort iReglerteknik
vidTekniskaHogskolaniLinkoping
av
Jonas Elfving
Regnr: LiTH-ISY-EX-3295-2003
Satellites
Examensarbeteutfort iReglerteknik
vidTekniskaHogskolaniLinkoping
av
Jonas Elfving
Regnr: LiTH-ISY-EX-3295-2003
Supervisors: AlbertThuswaldner
Jonas Elbornsson
Avdelning, Institution
Division, Department
Institutionen för Systemteknik
581 83 LINKÖPING
Datum
Date
2002-11-14
Språk
Language
Rapporttyp
Report category
ISBN
Svenska/Swedish
X Engelska/English
X Examensarbete
Licentiatavhandling
ISRN LITH-ISY-EX-3295-2003
C-uppsats
D-uppsats
Serietitel och serienummer
Title of series, numbering
ISSN
Övrig rapport
____
URL för elektronisk version
http://www.ep.liu.se/exjobb/isy/2003/3295/
Titel
Title
Attityd och banstyrning för små satelliter
Attitude and Orbit Control for Small Satellites
Författare
Author
Jonas Elfving
Sammanfattning
Abstract
A satellite in orbit about a planet needs some means of attitude control in order to, for instance, get
as much sun into its solar-panels as possible. It is easy to understand that, for example, a spy
satellite has to point at a certain direction without the slightest trembling to get a photo of a certain
point on the earth. This type of mission must not exceed an error in attitude of more then about
1/3600 degrees. But, since high accuracy equals high cost, it is also easy to understand why a
research satellite measuring solar particles (or radiation) in space does not need high accuracy at
all. A research vessel of this sort can probably do with less accuracy then 1 degree.
The first part of this report tries to explain some major aspects of satellite space-flight. It continues
to focus on the market for small satellites, i.e. satellites weighing less than 500 kg.
The second part of this final thesis work deals with the development of a program that simulates
the movement of a satellite about a large celestial body. The program, called AOSP, consists of
user-definable packages. Sensors and estimation filters are used to predict the satellites current
position, velocity, attitude and angular velocity. The purpose of the program, which is written in
MATLAB, is to easily determine the pointing accuracy of a satellite when using different sensors
and actuators.
Nyckelord
Keyword
satellites, attitude, orbit, control, Kalman estimation filters, quaternions, stabilization, pointing
accuracy
Asatellite in orbitaboutaplanet needssomemeans ofattitude control in order
to, forinstance, getas much sunintoits solar-panelsaspossible. The missionof
thesatellitemaybeanotherreasonforbothattitudeand orbitcontrol. Itis easy
tounderstandthat,forexample,aspysatellitehastopointat acertaindirection
withouttheslightesttremblingtogetaphotoofacertainpointontheearth. This
typeofmission must notexceedan errorin attitude ofmorethen 1
3600 Æ
. But,
sincehigh accuracyequalshighcost, itisalso easytounderstand whyaresearch
satellitemeasuring solar particles (or radiation) in space does not need high
ac-curacy at all. A research vessel of this sort can probably do with lessaccuracy
then1 Æ
.
The rstpartofthisreporttries toexplainsomemajoraspects ofsatellite
space- ight. Itcontinuestofocusonthemarket forsatellites,weighinglessthan500kg.
Thesecondpartofthis nalthesisworkdealswiththedevelopmentofaprogram
thatsimulatesthe movementof asatelliteaboutalargecelestial body. The
pro-gram,called AOSP,consists ofuser-de nablepackages. Theusercande nedata,
suchassatelliteconstantsandattitudepreferences,tosimulatetheattitudein
or-bit. Sensorsandestimation ltersareusedtopredictthesatellitescurrentposition,
velocity,attitudeandangularvelocity. Thepurposeoftheprogram,whichis
writ-tenin MATLAB,is to easily determinethepointing accuracyof asatellitewhen
usingdi erentsensorsandactuatorssothatacraftdoesnotgettooexpensivenor
toolessaccurate.
MATLAB6Release13issuesarealsobrie ydiscussedattheendofthisdocument.
Keywords: satellite,attitude, orbit,control,Kalmanestimation lters,
I would start to direct a warm thank you to the persons below, since this nal
thesisworkcouldnothavebeencompletedwithouttheirhelpandaid.
Par Degerman{whohelpedmewiththelayoutofthereportaswellasassisted
mewiththesyntaxL A
T
E
X, inwhichthis nalthesiswork iswritten.
Anders Helmersson{apart frombeingtheexaminerof this work,Anders has
alsoaided me in several otherways, includingthe quaternion representationand
pure technical support on emacs and L A
T
E
Xhandling. I have seen him as a last
resortwhenin needofhelp.
Albert Thuswaldner { for his assiduously read-through of my report, making
surethateverythinginitiswellwritten. Also,hehasbeen,inoppositetoAnders
above,my rst resort,when in needof help. Manyof thethings would nothave
beeninsidethisreportwithoutAlbert pointingoutformethat itshould.
Jonas Elbornsson { my supervisor at Linkoping Institute of Technology has
helped me with both the report and the program. Mostly, he helped with my
Englishlanguage, but he has also put some perspective to the actual work and
assistedmewithsomecontrolissues.
Apart from the mentioned people above, all of whom I owe large gratitude to,
thewholesta at SaabEricssonSpace in Linkoping,and especiallymyboss
Jan-OlofHjartstrom,havemysincerestthanksfortakingcareofwethelast7months.
Lastly,Imustthankmygirl-friendAnna Lennarthssonforhermentalsupport.
There are substantial di erences between notations in di erent textbooks. The
ones chosen in this text are stated below. Observe that a few de nitions also
canbe found in the appendices, such as the de nition of the Vernal Equinox in
AppendixC,forinstance.
Vectors and Matrices
x;X Boldfacelettersareused forvectorsandmatrices.
q TheboldfacedletterqarespeciallyreservedforQuaternions.
N Numberofsamplesusedforparameterestimation.
Parametervector.
^
y(tj) Predictor.
1 Identitymatrix.
I Momentofinertiatensor.
Standard symbols
The letter \t" in all forms are used for time or time intervals, except for the
a Semimajoraxis.
e Eccentricity.
i Inclination.
! Argumentofperigee.
Rightascensionfortheascendingnode.
P Orbitperiod.
Vectors:
L Angularmomentum.
F Torque.
A Attitudevector.
x m-dimensional statevector.
y n-dimensionalobservationvector.
Astronomical Symbols:
L Earth. J Sun. VernalEquinox. Constants
Planetarygravitationalconstant(alsoknownasGM).
G UniversalGravityconstant(GivenbyNewton).
Standard notations
rf(x) Thenablaoperatordescribingthefunction 0 B B B B @ @f @x1 @f @x 2 . . . @f @xn 1 C C C C A Subset.
O(n) FunctionwiththepropertythatO(n)=nisboundedasn!1.
E[nn T
] theexpectation valuewherenisanyvectoror matrix.
Quaternionmultiplication.
R Denotes theradiusofabody.
AOCS AttitudeandOrbitControlSystem.
AOSP AttitudeandOrbitSimulationPackage.
ASAP ArianeStructureforAuxiliaryPayloads.
CDH CommandandDataHandling.
CHAMP ChallengingMini-SatellitePayload.
COTS CommercialOfTheShelf(Products).
EELV EvolvedExpandableLaunchVehicles.
EO EarthObservation(mission).
ESPA EELVSecondaryPayload.
F 3
A Fast,Frequent,FlexibleandA ordable.
FH FigureHandle(inMATLAB).
GALILEO AEuropeanGPS.
GEO GeostationaryOrbit.
GLONASS ARussianGPS.
GTO GeoTransferOrbit.
GPS GlobalPositioningSystem.
HEO HighlyEllipticalOrbit.
ICO IntermediateCircularOrbit.
I-Cone Intelligent(adapter-)Cone.
IR InfraRed.
IT InformationTechnology.
JIT MATLABaccelerationengine.
LEO LowEarthOrbit.
LQ LinearQuadratic.
MEO MediumEarthOrbit.
MEX MATLABEternalcode(interfacebetweenMATLABandotherprogramlanguages).
NAVSTAR TheUS GPS.
PID Proportional,InductiveandDerivate.
S/C Spacecraft.
S/S SubSystem(in spacecraft).
1 Introduction 1
1.1 Problemformulation . . . 1
2 Satellites in general 3 2.1 Modulesin aregularsatellite . . . 3
2.1.1 Thebus . . . 3
2.1.2 Thepayload . . . 5
2.2 Movementlawsofsatellites . . . 6
2.2.1 Orbitlawsofmotion . . . 6
2.2.2 Attitudelawsofmotion . . . 8
2.2.3 Orbittimeandvelocity . . . 9
2.3 Disturbancesin orbitandattitude . . . 10
2.3.1 Solarradiationpressure . . . 10
2.3.2 Aerodynamicdrag . . . 11
2.3.3 Magneticdisturbancetorques . . . 12
2.3.4 Gravitygradienttorque . . . 13
2.3.5 Micrometeorites . . . 14
2.3.6 OblatenessoftheEarth . . . 14
2.3.7 Discussiononthemagnitudeofdisturbances . . . 14
3 Orbits and missions 17 3.1 Fromlaunchto orbit . . . 17
3.1.1 Orbits . . . 18
3.2 Missions . . . 23
4 A studyof smallsatellites 27 4.1 Previouslylaunched satellites . . . 27
4.2 Tendencyinlaunchestoday . . . 29
4.3 Customers . . . 29
4.4 Potentialuse . . . 30
4.4.1 Dispenser . . . 30
4.4.2 Mainvehicle . . . 31
4.5.1 ASAP . . . 32
4.5.2 ESPA . . . 32
4.5.3 Munin . . . 32
4.5.4 I-Cone . . . 32
4.6 Theneedforsmallsatellites . . . 36
5 Orbit and attitude stabilization 37 5.1 Redundancy . . . 37
5.2 Sensorsandactuators . . . 37
5.2.1 Sensors . . . 38
5.2.2 Actuators . . . 41
5.3 Stabilization methods . . . 44
5.3.1 Whydoweneedstabilization? . . . 45
5.3.2 Passivestabilization . . . 45
5.3.3 Activestabilization. . . 47
6 The Attitudeand Orbit SimulationPackage (AOSP) 51 6.1 Requirements . . . 51
6.2 Prerequisites . . . 52
6.2.1 Developmentenvironment . . . 52
6.2.2 Coordinateframes . . . 54
6.2.3 Modelrepresentation. . . 54
6.2.4 Di erentialequationsolvers . . . 57
6.2.5 Linearization . . . 59
6.2.6 Measurementdetermination . . . 63
6.2.7 Stabilizationstrategy . . . 64
6.2.8 Neededdata . . . 66
6.3 MATLABissues . . . 66
6.4 BehavioroftheAOSP . . . 67
6.4.1 Examplerun . . . 67
6.4.2 Program ow . . . 68
7 Conclusion and suggestionsto further work 75 7.1 Smallsatellitesstudy . . . 75
7.2 TheAOSP . . . 75
Bibliography 79 Appendix 81 A AOSP - users manual 81 A.1 Howto getstarted . . . 81
A.1.1 Whatdatacanbefound . . . 81
A.2 Inputneededto theprogram . . . 85
A.3.1 LoadandSavedata . . . 86
A.3.2 Printresultsfromsimulation . . . 87
A.3.3 Changeparameters. . . 87
A.4 Whatissavedintheoutput le . . . 87
A.5 Shortcuts . . . 87
B Orbit movements 89 B.1 KeplerianOrbitalElements . . . 89
B.2 Elliptical Orbits. . . 89
B.2.1 Orbitperiod . . . 90
B.2.2 Velocity . . . 93
C Coordinate systems 97 C.1 TheGeocentricEquatorialcoordinatesystem . . . 97
C.2 Quaternions . . . 98
C.3 Other coordinatesystems . . . 99
Introduction
Toexplorespaceisstillmanypeoplesdream. Butbeforemankindcanenterspace
themselves, investigating probes have to besent out in advance. Their missions
aremany,suchascommunication,globalsurveillanceorplanetaryresearch. With
acombinedname,theseprobesareoftencalledarti cialsatellites.
Thesatelliteindustrypossesseshugepossibilities, althoughthemarket todate is
abit slow. Of course, these crafts have to be automatic in the sense that if the
groundcontrollosescommunicationwiththesatelliteforacoupleofhours,itstill
shouldbeoperationalwhenthecommunicationlinkisreestablished. Furthermore,
the demand for accuracy and performance might be, depending on the mission,
exceptional. Thecostforsatellitestendto increaseexponentiallywiththe
perfor-mance;thusitisreallytrickytodesignacraftwithhighpointingaccuracywithout
gettingatooexpensiveone. Tokeepthecost down, expensivemeasurementand
propulsioninstrumentsmustbeassimpleaspossible;while tokeepprecisionup,
theymustbeasadvancedaspossible.
Butcomponents arenot themost expensivepartin asatellite. Thedesign, test,
veri cationandlaunchproceduresarefarmoreexpensive,sincethe rstthreetake
manyman-hoursandthelastonedemandsanexpensivelaunch-vehicle. An
exam-pleofalaunch-vehiclethatisinusetodayontheOcean'siscalledtheSea-launch,
andcanbefoundin Figure1.1.
This nalthesisbeginswithdescribingtheessentialsofspace ight(especiallyfor
smallsatellites) in Chapter2. Itcontinues to describethemarket,and trendsof smallsatellitesin Chapter4. Thedevelopmentofasimulationprogram to deter-minetheattitude variationwhen usingdi erent sensorsand actuatorsin orbitis
nallydescribedinChapter 6.
1.1 Problem formulation
This nal thesis work is actually twoaimed. The rst aim is to nd out where
Figure1.1. TheOdysseylaunchplatformwiththerocket\Sea-launch"|away
oftransportingrocketsoutontheoceanforlaunchasneartheequatoraspossible
forcountriesthatdonotownlandinthatregion(forinstanceRussiaandNorway
areparticipantsinthisproject)[25].
future, and what demands are there today? The second aim is to nd out how
goodpointingprecisioncanbeexpectedwithacertainsetofsensorsandactuators
whenthesatellitehasacertainmission? Thesequestionswillbefurtherexplained
anddealt with, but not completely answered. Thereasonfor this isthat no one
can accurately predict the future and that there was a time limit to the nal
thesiswork. Thereare, however,somesuggestionsonfurther developmentof the
Satellites in general
Asatelliteis anobjectthat movesbyitselfin orbitaboutalargercelestialbody,
accordingto [21]. In this de nition one can easily understand that moons also are satellites, in fact; even the Earth itself is oneof the Sun's satellites and the
Sunis a satellite in ourgalaxy, the Milkyway. In generalthough, when talking
about satellites, we refer to arti cial, i.e. man-made, satellites moving in orbit
around the Earth orany other planet in our solar system. In orbit means that
thesatellitehashigh enoughaltitudeand/orspeedto holdit withinthe celestial
bodies'gravitational eldwithoutfallingdownontoit. Thismayseemharderthan
itreallyis. A presentation ofthemovementlawswill bepresentedin Section2.2
which will explainthis. Butbefore that, ashort introduction to satellitesshould
beinorder.
2.1 Modules in a regular satellite
Satellitesof today can look virtuallyeverywayyoucould possibly imagine. The
satellite CHAMP, for instance, which was launched in 15th of July 2000 from
PlesetskinRussialookslikearegularelectricguitar(seeFigure2.1or[9,20]). As seentherearenorulesatallonhowtheyappearontheoutside. Theinteriorofa
satellite,however,hasafewsimilarparts,orat leastpartsthat canbeidenti ed.
Thesepartsarecalledthebus andthepayload accordingto[18].
Thepayloadisthemodulethatcompletesthemissionspeci ctasks,suchastaking
photographs,measuringradiation, relayingTV etc. Thebus,on theother hand,
consists of subsystems that work together to help the payload to complete its
mission. Thiswillbefurther explainedinthenexttwochapters.
2.1.1 The bus
Thebusinasatelliteisaninfrastructuralaidforthepayload,andishighlymission
speci c. MissionsaredescribedlaterinSection3.2. Theaidforthepayloadconsists in,forinstance, keepingthepayload atanacceptable temperature, providing the
Figure 2.1. The satellite CHAMP (Challenging Mini-Satellite Payload). An
exampleofanoddshapedspacecraft[20].
payloadwithpowerandhelpingittonavigateandpointat speci c locations.
Often, the bus is divided into subsystems, or S/S. In the chart below, the most
commonclassi cations(accordingto[18])ofS/Sareshown.
Structure: UsuallythewholestructureisconsideredtobeaS/Sofitsown. The
actual structure includes the hull and load-bearing walls in the satellites.
Sincethestructurewillbeexposedtodi erentpressures,solarradiationand
smallmeteorites,thisstructurehastobecompletelythoughtthroughsothat
itcanhandlethis harshspaceenvironment.
Thermal: Inthedesignofspacecrafts,thermalcontrolisneededinorderto
main-tainstructure and equipment integrityoverlongperiods of time, according
to [18]. It has been recognized since theconception and design of the rst spacevehiclesthataprimeengineeringrequirementisasystemfor
tempera-turecontrolthatpermitsoptimumperformanceofmanycomponents. Infact,
ifit waspossibleto operateequipmentat anytemperature, there would be
noneedforthermalcontrol. Normaloperationtemperaturesmustbewithin
20 Æ
C to+50 Æ
CDH: (Command and Data Handling) This is the brain of the satellite. Here,
all calculations and control of other S/S are done. CDH also works as a
communicationhandlerbetweendi erentS/S.Incomputertermsthiswould
becalled amaster unit,and theotherstructuresforslave units.
AOCS: (Attitudeand Orbit Control System)This S/S couldbecompared with
thehumaninnerear,i.e. fromsensorsthisS/Sdetermineswherethesatellite
isand how itis oriented. With thisinformation theAOCSdetermineshow
to navigate (in case its position orattitude is wrong). To summarize, the
AOCS consists of three parts; one that operatessensors, another one that
calculateswhattodoandathird onethatoperatesactuatorswithwhathas
beencalculated.
Propulsion: Everysatelliteneedssomemeansoftransportationandsomemeans
ofattitudeadjustment. ThesemeansarecalledthepropulsionS/S.It
main-tainsthefuelconsumptionandcontroltheoutputgivenby,forinstance, the
AOCSabove.
ElectricalPower: Thissubstructuremanages thepowersupplyin the satellite.
ItprovidesalltheotherS/Swithelectricalpower,andrechargesthebackup
batteries, when the satellite is not within an eclipse. Otherwise, this S/S
makessurethat thesatellitestopsoperatingandmovesintoa\wait"mode
topreservepower. Thispower-savingmodeoperatesonthebackupbatteries
untilthesatellitehascomeoutoftheeclipseagain.
Communication: Itwouldberatherpointlesstosendsomethingintospacethat
cannot communicate. All satellites should have this S/S, although there
mightbespecialcaseswhenthissubsystemisnot needed. Oneoftheearliest
satellites,forinstance,wasmadeofare ectivematerial. Insteadofactively
receivingandrelayingasignal,astodayscommunicationssatelliteswork,it
re ectedsignalsbackdownagainto theEarth,thusnotneedinganysortof
communicationdevice.
2.1.2 The payload
Apart from the subsystems in the previous section that constitutes the bus, a
payload isalsoneeded. Thepayloadiswherethemissionspeci ctoolsarelocated.
Therecouldbecamerasthat takesatellitephotos oftheEarth,orcommunication
equipmentwhich enableus tosee satelliteTV andsoon. These di erent eldsof
applicationforpayloadsarecalleddi erentmissions,andwillbediscussedlaterin
Section3.2.
When constructing the payload, the manufacturer has to consider many things,
suchaskeepingpowerconsumptionandweightdown. Thereasonforthisisthata
higherdemand onthebusmakesthewholesatellitelargerandheavier. Themore
2.2 Movement laws of satellites
A man-made satellite has to be stabilized due to many disturbance forces. For
instancethepressurefromtheSun'sphotons,thesolarwind,othercelestialbodies,
spacedust and other factorsmay play amajorpartin howthe satelliteactually
moves in space. In addition, the owner of the satellite may want to adjust the
orientation,orattitude,to acertainmissionspeci ctask(takephotographsof,or
broadcastTVto, thecorrectlocation). Tobeabletomeettheserequirementsthe
satellitecontrol systemsmust consist ofat least twoseparate parts. Onecontrol
systemthat keepsthesatelliteinacorrectorbit,sincethedisturbancesdescribed
inthischapterwill tendtodegeneratethesatellitesorbit(i.e. decreaseitsspeed).
Theother control system keeps theattitude correct. The control needed for the
lattertask doesnot haveto be activecontrol |passivestabilization techniques
mightbejustasuseful. TheactualcontrolsystemisdiscussedinChapter5. To be able to control the satellite, we have to know its movement laws. The
following sections will deal with orbit and attitude movement laws, as well as
di erentdisturbances.
The orbit and the attitude movement are however not uncorrelated, as implied
earlier. Thisisdueto thefact thatdisturbancetorquesdependsonwhereweare.
Forexample, weonly get adisturbancefrom theSun ifthe satelliteis notin an
eclipse. Thiswillbefurther discussedinSection2.3.
2.2.1 Orbit laws of motion
Accordingto[19,21],therearemainlysixlawsgoverningthemotionofasatellite. ThreearefromKeplerandtherestfromNewton. Thesetwowelknownphysicists
theorem'saredescribedbelow.
Theorem2.1(Kepler's Laws)
I: Theorbit of eachplanet isanellipse, withthe Sunasfocus.
II: Thelinejoining the planettothe Sunsweepsoutequal areasin equal times.
III: The square of the period of a planet is proportional to the cube of its mean
distancefrom theSun.
Theorem2.2(Newton's Laws)
I: Every body continues in itsstate of rest or of uniform motion in astraight line
unlessitiscompelledtochange that stateby forcesimpressedupon it.
II: The rate of change of momentum isproportional to the force impressed and is
inthe samedirection asthatforce.
III: Toeveryaction thereisalways opposedanequal reaction.
constitutesawaytocalculatetheforceactingbetweentwobodiesduetogravity 1 : F g = Gm 1 m 2 r 2 r r (2.1)
The Equation (2.1) states that the force attracting two bodies to each other is proportionalto theirmasses (m
1 andm
2
)and inverse proportionalto thesquare
ofthedistancebetweenthem(r). Gistheuniversalgravityconstantderivedfrom
theterm,oftenreferedto asGM, whereM themassoftheplanet
2
. The term
=GM iscalled theplanetarygravitationalconstant(withunit m
3
s 2
),where Gis
theuniversalgravityconstant,withthevalueG6:6710 11 Nm 2 kg 2 .
InEquation(2.2),the Newtonforce described in Equation(2.1)isgeneralizedto anequationofnbodies: F g = Gm i n X j=1;j6=i m j r 3 ji (r ji ) (2.2)
Thisforcealoneconstitutesthegreatestforceactingonasatelliteinorbitatalow
to medium height abovethe Earth's surface. But there are other forces as well,
suchasthesolarpressure,thenonsphericalsymmetryoftheEarth,aerodynamic
drag due to the Earth's atmosphere and, of course, induced forces like thruster
burnsetc. Tosummarize,wehave:
F TOTAL = F g +F DRAG +F THRUST +F SOLARPRESSURE + +F OBLATEEARTH +::: (2.3)
Ifwedi erentiateNewton'ssecondlaw(Theorem2.2)and ndthedistance r i we get: d dt (m i v i )=F TOTAL (2.4)
Keepinginmindthat wemightusethrustersthat expelmatter(which makesthe
satellite'smasstimedependent),Equation(2.4)evaluatesto:
r i = F TOTAL m i _ r i _ m i m i (2.5)
These equations combined (Equation(2.3) and Equation (2.5))can be solved to ndanysatellite'smovementintime.
1
Observethattheinnernatureofgravity,i.e.whatgravityreallyisandhowitactuallyworks,
stillisapuzzlefortodaysscientists.
2
SinceGisderivedfromforall planets,it isbothmorecommonand accuratetousethe
2.2.2 Attitude laws of motion
Depending onthecoordinateframe usedtorepresenttheattitude, themovement
equationsdescribingtheattitude willlookdi erent. Forexplanationsofdi erent
coordinatesystems,studyAppendixC. Themovementequationsforthedi erent coordinate frames haveonething in commonthough. Theyare all derived from
theequationofangularmomentum (from[27,4]):
_ h A =r P=A ma+ _ r P=A mv (2.6)
wherea=v_ is theacceleration,r
P=A
is thevectorfrom point A topointP and
h
A
isas inDe nition 2.1.
Whenutilizing Newton'ssecondlaw(F =ma,where F istheresultingforce) on
thesecond term,weget:
r P=A ma=r P=A F =M A (2.7)
Wherethe last step is the de nition of the moment of a force F about point A,
denotedM
A
,asin [4].
Whenweapplythis, Equation(2.6)evaluatesto:
M A = _ h A _ r P=A mv (2.8)
Accordingto[12]theangularaccelerationofasatellitecanbederivedfrom Equa-tion(2.8)andfromthefact that:
De nition2.1 (Angularmomentum)
h
A
I! (2.9)
WhereI isthe momentofinertia tensorand ! istheangular velocity. The nal
angularaccelerationbecomes:
_ !=I 1 (M _ h ) I 1 (I!+h ) (2.10)
WhereM istheapplied torque, andh istheinternal angular momentumvector
from,forinstance,thedi erentreactionwheels. hisinotherwordsnottheangular
momentumfromthesatelliteitself,asinEquation(2.8)(i.e. h A
=I!+h
Others ).
Equation(2.10)ishowevernotauniversalone,sinceittakesforgrantedthat the principal and the inertial axes are the same, i.e. it is a symmetric body with
regardto the mass and the shape. Because this evidently seldom is the case, a
moregeneralequationthat workswith any kindofinertia matrixis(alsoderived
in[12]): _ ! x = J x T x +P xy T y +P xz T z _ ! y = P yx T x +J y T y +P yz T z _ ! = P T +P T +J T (2.11)
where T x = h (M x _ h x ) ! z ! y (I z I y ) (! y h z ! z h y ) DX i T y = h (M y _ h y ) ! x ! z (I x I z ) (! z h x ! x h z ) DY i T z = h (M z _ h z ) ! y ! x (I y I x ) (! x h y ! y h x ) DZ i (2.12) where DX = D zy ! 2 y D yz ! 2 z +! x (D zx ! y Dyx! z ) DY = D xz ! 2 z D zx ! 2 x +! y (D xy ! z Dzy! x ) DZ = D yx ! 2 x D xy ! 2 y +! z (D yz ! x Dxz! y ) (2.13)
Thegeneralinertiamatrixisdescribedby:
I= 0 @ I x D xy D xz D yx I y D yz D zx D zy I z 1 A (2.14)
andtheinverseby:
I 1 = 0 @ J x P xy P xz P yx J y P yz P zx P zy J z 1 A =J (2.15)
Again, h is the totalangular momentum due to reaction wheels etc. within the
satellite.
2.2.3 Orbit time and velocity
FromKepler's Theorems (2.1)andNewton's Theorems (2.2)theorbitperiod, P, and the velocity, v, at perigee
3
can be calculated. Since the velocity changes
during one lap, a satellite has its maximum speed at perigee and its minimum
speedatapogee,onlythevelocityinperigeeorapogeeisreallysimpletocalculate
inadvance.
Theseequationsareasfollows:
P = 2 p a 3 2 (2.16) v = s 2 r 1 a (2.17)
Wherea isthe semi-majoraxisasin Appendix B, and the velocity expressionis givenforperigee.
2.3 Disturbances in orbit and attitude
Disturbances in space could be a rather extensive chapter, since virtually every
existing objectwill act uponthe satellitewithgravitationalforces and moments.
Tokeepthischaptertoareasonablelevel,somesmallerdisturbanceswilltherefore
beneglected.
How much torques actually will act upon the satellite'sattitude depends on the
size-to-massratio. If, for instance, the satellite looks likea perfect sphere, there
willprobablybeonlysmall(notsigni cant)disturbancestothesatelliteinattitude
fromoutere ects. Butontheotherhand,ifthesatellitelookslikealong atrod
wewill gete ectsto theattitude fromdisturbancetorques.
ThemaincausetothesedisturbancesmightbetheSun,theEarth'satmosphereor
thegravitational eldsofdi erentcelestialbodies,buttheyhaveasimilarimpact
onanon-symmetricspacecraft.
Example1
IfweusetheSunasanexample,wecanseethatthesolarwind fromtheSunwill
putan evenlydistributed pressureonthesatellite. This pressurewillbeuniform
on each part that is exposed to the Sun. You could therefore replace all these
smallforceswiththesumofthoseonthegeometricalmiddlepointexposed tothe
Sun, called the center-of-pressure. If this center-of-pressure is not on the same
spot as the center-of-mass, there will bean additionalmoment. The size of this
moment,ortorque,istheforcetimesthedistancebetweenthecenter-of-massand
thecenter-of-pressure. Inother words,itisnotthesymmetry oftheshapealone,
ratherthedisplacementrelativetothemassdistributionsymmetry,thatwillcause
thisdisturbance.
Similarthingsasin Example1happenswhendealingwithaerodynamicdrag. Gravitygradient,however,isadi erentstory. Thisisaforcethatwilltrytoalign
thesatellite with the Earth's magnetic eld. If this seem interesting, the reader
shouldstudy[27].
Allofthesedisturbancescanbemodeled,andabriefexplanationonhowisgiven
inthenextfewsections. Foramoreinvestigativeexaminationofthesedisturbance
models,[19]wouldbetoprefer.
The reader should note that the oblateness of the Earth is no real disturbance
torque since it can be modeled with agood accuracy. Instead of regarding this
anomalyasadisturbance,itshouldbeconsideredtobeanupdatetothemovement
equation,i.e. Equation(2.1).
2.3.1 Solar radiation pressure
ThesolarradiationpressureisduetophotonsfromtheSunconstitutingapressure
moreenergythenthecolorsilver(whichre ectsmostenergy).
Ifweusethegeocentricequatorialcoordinates(whichareexplainedinAppendixC), radiationpressurecanbemodeled. Thisisdonein[19],buttheretheyhavetaken forgrantedthat it isablackbody
4
that travelsin space. Whilethis is not
com-pletelytrue,agoodapproximationof thetorquedue tosolarradiationis:
x = fcosA y = fcosi sinA z = fcosi sinA (2.18) Where f = 4:510 10A m [ m s 2 ]:
A = Crosssectionofvehicleexposedto theSun[m]:
m = Massofvehicle[kg]:
A
= MeanrightascensionoftheSunduringcomputation.
i
= Inclinationofequatortoecliptic(=23:4349):
Observethatthe andthesignsarecommonsymbolsusedfortheSunandthe
Earthrespectively.
Thesolarradiatione ectsboththeattitudeandtheorbitofthespacecraft,since
theresultofapressureat apointapartfrom thecenter-of-masswill constitutea
torque. The e ect on orbit is normallynegligible (if the satellite hasnot got an
extremelyhighaltitude)sinceitisrathersmallcomparedtootherforces.
Ontheotherhand,thisis thedominantdisturbanceforceonveryhigh altitudes.
Additionallythisforce isindependentofthedistancefrom theEarth(althoughit
obviouslyis dependentonthedistancefrom theSun).
2.3.2 Aerodynamic drag
Aerodynamic drag is a disturbance that arises when the satellite move through
theEarth'satmosphere,which(althoughitisnotdense)isenoughforatorqueto
appear.
Accelerationscaused byaerodynamicdrag canbedescribedasfollows:
r = 1 2 C D A m V a _ r a (2.19) 4
where
C
D
= DimensionlessdragcoeÆcientassociatedwithA.
A = Crosssectionalareaofvehicleperpendicular
tothedirectionofmotion[m]:
m = Massofvehicle[kg]:
= Atmosphericdensityatthevehicle'saltitude[ k g m 3 ]: V a = jr_ a
j=Speedofvehiclerelativetotherotating
atmosphere[ m s ]: _ r a = 0 @ _ x + _ y _ y _ x _ z 1 A _ r = 0 @ _ x _ y _ z 1 A
=Theinertialvelocity.
_
= RateoftheEarth'srotation[ rad
s ]:
Tosimplifytheequations,youcouldusetheballisticcoeÆcientforthevehicle,,
whichisde ned by:
= C
D A
mg
Obviouslyg isaltitudedependent.
This force both slows the craft down as well asit starts to spin the craft if the
center-of-pressureisapartfrom thecenter-of-mass.
Theaerodynamicdisturbanceisthedominantdisturbancebeneath500km
alti-tudefromtheEarth,anditdependsonthedistancefromtheEarthase r
,where
isaconstant.
2.3.3 Magnetic disturbance torques
Themagneticdisturbancetorqueisaresultfromtheinteractionbetweenthe
space-craft residual magnetic eld and the geomagnetic eld. There are three main
sourcesin thesatellitefordisturbancetorquesof thissort,andtheyare:
1: Spacecraftmagneticmomentums
2: Eddycurrents(due tospinningmotionofcraft)
3: Hysteresis(duetospinningmotionofcraft)
Depending on the material, construction technique and mission, the two latter
sourcesfordisturbancecanbemadenegligible. Thisleavesthespacecraftmagnetic
momentum as the largestsource of disturbance,and theinstantaneousmagnetic
disturbance, N
mag
, due to the spacecraft e ective magnetic momentum, m, is
givenby:
whereBisthegeocentricmagnetic ux.
Thisdisturbanceisdominantintheregionbetween500kmtoabout35000km,
anditdependsonthedistanceformtheEarthasr 3
. Togetacompletediscussion
onhowthis disturbancetorquecanbemodeled,please referto[27].
2.3.4 Gravity gradient torque
The gravity gradient torque is a torque that wants to align the craft with the
Earth'sgravitationalforce eld. Sincethe force eldwill notbeconstantoverall
non-symmetricalobjectsinorbit,di erentforceswillacton di erentpartsof the
satellite. Ifthe gravitationalforce- eldwould be uniform,this disturbancewould
vanish.
Aconceptualexpressionof thegravitygradienttorquecanbeexpressedas:
N gg = Z r i dF i = Z (+r 0 i ) R i R 3 i dm i (2.21)
InFigure2.2, thede nitions ofthecoordinateframecanbefound.
r
R
S
R
i
r
i
Center
of mass
r
i
'
dm
i
Geometric
center
Body
reference
frame
Figure 2.2. CoordinateSystemfor theCalculationofGravityGradient Torque
de nedinEquation(2.21)
Thistorqueis,likethemagnetic disturbancetorque,dominantbetween500km
and35000km. ItdependsonthedistancefromtheEarthasr 3
.
2.3.5 Micrometeorites
Disturbance torque from small fragments in space are rare, and often not taken
intoaccountatall. Thistextwillnotbebotheredwithsuchrandomevents.
2.3.6 Oblateness of the Earth
Accelerationscausedby theasymmetryof theEarth,i.e. thefact that theEarth
is slightly attened by its poles, is rather diÆcult to model. The force in
Equa-tion(2.1)will actuallynot bedirectedat thecenteroftheEarthasstatedbefore whenassumingEarthtobeaperfectsphere,ratherslightlymoreagainstthe
equa-torsincetheEarthhasmoremassin thatregion.
Thereforethis anomalyis regardedasan update to Equation(2.1) ratherthen a perturbationofitsown.
Themain resultingupdate acceleration,still accordingto [19], to Equation (2.1) becomes: a = r (2.22) = r " 1 1 X n=2 J n r r n P n sinL # (2.23) where
= GM (Theplanetarygravitationalconstant).
J
n
= CoeÆcientstobedeterminedbyexperimental observation.
r
= EquatorialradiusoftheEarth.
P n = Legendrepolynomials. L = Geocentriclatitude. sinL = z r : Forn=2ton=4thetermsofJ n
areexperimentallydeterminedto:
J 2 = (1082:640:03)10 6 J 3 = ( 2:50:1)10 6 J 4 = ( 1:60:5)10 6
It is fairly easyto see that these equations, printedin theirrespective direction,
willberatherlarge. Thereforetheywill notbeprintedhere. Toseethecomplete
expressions,consult[19], whereonealsocan ndthree moretermsofJ n
.
Thedisturbance due to theoblateness of theEarth is adisturbance that canbe
completelymodeled,andisnotonecompletelyconsistingofwhitenoise. Therefore
itseldomisregardedasadisturbanceat all,butratherasamodelingerror.
2.3.7 Discussion on the magnitude of disturbances
Disturbance Regionofdominance Distance dependence
Aerodynamic .500km e
r
fromtheEarth
GravityGradient 500kmto 35000km r 3
fromtheEarth
Magnetictorques 500kmto 35000km r 3
fromtheEarth
Micrometeorites Normallynegligible
Solarradiation &20000km r 3
fromtheSun
OblateEarth Consideredamodelerror
Table2.1. Anestimateofdisturbancesinspace
altitudes,wheretheEarth'satmosphereislessdens,theforceandtorquecausedby
solarpressuredominates. Eventhemoonsgravitationalforcevaryin time. When
thesatelliteisnearthemoon,itwillobviouslybesubjecttoalargermagnitudeof
forcefromthemooncompared towhenthesatelliteisontheoppositesideof the
Earth.
Every other force, such as gravitational forces from the other planets and the
re ected solar pressure from the Earth and the moon, acting on a satellite are
small enough to be completely discarded. The reason for this is that they will
vanishinthesystemsnoise.
To sumthis chapter up, a simpletable where magnitude of disturbancescan be
foundisgivenin Table2.1. Observethat these guresarerepresentativeand not necessarilycompletelycorrect. Forfurtherreading,thereadershouldlookinto[27].
Orbits and missions
Beforeconducting amorethorough investigation onhowtostabilize aspacecraft
whenit isoperationalin orbit,somethingshould besaidabouthow asatelliteis
putintoorbitandwhat kindoforbitsthereare. Thisiswhatthischaptercontains
alongwithdi erentmission de nitions.
3.1 From launch to orbit
There are but one way to get a satellite into the correct orbit that we know of
today. And that is by launching it with a rocket, which is separatedat agiven
altitude. Afterthat,aseriesofthrusterburnshastobemadetoreachthedesired
orbit.
Forlargesatellitesthisisprettymuchwhathappens. Anadapterconeisboltedto
thecarrierrocketandthesatelliteismountedontopofit. Thereasonforusingan
adapterconeis boththeneedforaseparationsystembetweentherocket andthe
satelliteand thefactthatcarrierrocketsaremanufacturedinparticulardiameters,
and the satelliteoften has other dimensions. The adapter cone supplies both of
thesefunctionalities.
For small satellites, however, other launch possibilities may be used. If it is
re-ally small, it can use abig satellite as a transport, i.e. alarge craft has many
smallsatellitesinside,anddeploythem attheirdestined position. Anothermean
to travelinto spaceis by hitchhiking with alargersatellite. This is similar with
theprevious transport method, except that it does notuse the main satellite at
all. Insteaditisattachedtotherocket,inonewayoranother,andseparatesafter
themainsatellitehasseparated. Thisis agoodsolutiontokeepcostdown, since
carrierrocketsoftenhasacapacitytotakemoreweightthenitoftendoes. Ashort
presentationofthesedi erentmethodswill bepresentedinChapter4.
Oftenlaunches happen neartheequator,this isdue to theEarth'soblateness. It
issimplynotasmuchgravityneartheequatorcomparedto thepoles,thusnotas
sitecalledPlesetskinnorthernRussia,forinstance. There,thecarrierrocketslook
verydi erent. Insteadofonlyonemainrocket,theyhaveattachedseveralbooster
rocketsto thesideofthemain onetobeableto put thesatelliteinto thewanted
orbit,thusmakingtheselaunchvehiclesoneofthemostpowerfulin theworld.
Thereareother waystolaunchsmall satellitesintospacethantheprevious
men-tioned. Thereare, forinstance, oldintercontinental rocketsthat hasbeenrebuild
totakesmallcrafts intospaceinsteadofdumpingdestructivepower. Theseother
methodswillnot bementionedanymorein thisdocument.
3.1.1 Orbits
Whenthe satellite is positioned into space by its rocket, it sometimes is parked
in thecorrect orbitdirectly. Butsince thisseldom is thecase, thesatelliteoften
hasto makea series of thruster burnsto get into the right position. When this
isthecase,the satelliteisparkedinto anotherorbitcalled aGTO (GeoTransfer
Orbit). Thisisanorbitthat willintersectwitheither thecorrectorbitor another
GTO,althoughthelatterisseldomthecase. Thereasonforthisisthatthesekind
of maneuversare fairly expensive to do, thereforeis it pro table to separate the
satellitein asgood position aspossible.
Whenmakingatransferbetweentwodi erentorbitsaHohmann transfer isoften
If you get your velocity
boost here, you'll go from
a circular orbit to an
elliptical orbit
If you give your velocity a
boost here, you can
change your orbit from an
ellipse to a larger circle
Assume that we
begin with a
circular orbit
Figure3.1. AHohmanntransferfromonecircularorbittoanotherinthesame
used. A Hohmanntransferusesthe minimum energypath betweenthe orbitsin
thesameorbitplane,andisdonein twostages. Firstathrusterburnchangesthe
currentorbit into aGTO, whose apogee (the orbitsmaximumdistance from the
orbitedobject) isexactlyinthewantedorbitspath. Then,when thesatellitehas
reached theorbitsapogee, anotherthrust is made, andthe neworbit isattained
(seeFigure3.1).
Todoatransferbetween orbitsin di erent planes, aHohmanntransfermay not
betheoptimalone,butitwill stillwork.
Therearefour di erentkindsoforbitsthat areoftenreferredtoaccordingto[3], GEO(GeostationaryOrbit),LEO(LowEarthOrbit),MEO(MediumEarthOrbit)
andHEO (HighlyEllipticalOrbit). Thefollowingsectionswilldescribethesetypes
oforbitsinmoredetail.
Figure3.2. GeostationaryorbitaswellastwoLowEarthOrbits;APolarOrbit
andanordinaryLEO[3].
GEO
GeostationaryorbitsarecircularorbitsthatareorientedintheplaneoftheEarth's
equator. In thisorbit, thesatelliteappearsstationary,i.e. ina xedposition,to
an observer on the Earth. More technically speaking, a geostationary orbit is a
circularprograde
1
orbitin theequatorialplanewithanorbitperiodequaltothat
oftheEarth;thisisachievedwithanorbitradiusof6:6107(equatorial)Earthradii,
oranorbitheightof35786km. Asatelliteinageostationaryorbitwillappear xed
abovethesurfaceoftheEarth,i.e. at a xedlatitudeandlongitude.
Thefootprint
2
,ofageostationarysatellitecoversalmost1/3oftheEarth'ssurface.
This means that near global coverage canbe achieved with a minimum of three
1
WiththesamerotationaldirectionastheEarth.
satellitesin orbit.
Thisorbitshouldnotbemistakenforthegeosynchronous orbit. Thede nitionfor
thiskindoforbitis:
De nition3.1 (Geosynchronousorbit) A geosynchronousorbit means that a
satellite makes one orbit every 24hso that it is \synchronized" with the rotation
periodof theEarth.
Thiswillhappenatanaltitudeofapproximately36000kmabovetheEarth's
sur-face.
Thisde nitiondoesnot sayanythingabouttheorbitsposition,thusgeostationary
orbitisasynchronousorbit,butnotnecessarilytheotherwayaround. Thereason
forthisisthatthegeostationarymustbeinorbitintheEarth'sequatorialplane,
thusbeingasmallsubsetofthegeosynchronousones.
Theorbitlocationofgeostationary satellitesiscalled theClarkeBelt in honorof
Arthur CClarkewho rstpublished thetheory oflocatinggeosynchronous
satel-litesin theEarth'sequatorialplaneforusein xedcommunicationspurposes[6]. SeealsoFigure3.2or Figure3.3.
LEO
LEOs (Low Earth Orbits) are either elliptical or (more usual) circular orbits at
aheight of less than 2000km above the surface of the Earth. The orbit period
atthese altitudesvariesbetween90minand 2h. Theradius ofthefootprintof a
communicationssatellitein LEOvaries from3000kmto 4000km. The maximum
timeduringwhichasatelliteinLEOorbitisabovethelocalhorizonforanobserver
ontheEarthisupto 20min.
Inthis category,which isthemostcommonorbittype,thereareseveralsubtypes
of orbits. For instance there is a Polar orbit where the orbit almost has a 90 Æ
inclination
3
,andaSunsynchronous orbitwherethesatelliteneverisshadedfrom
theSunbytheEarth.
Mostsmall LEO systemsemploy polar, ornear polar, orbits. A complete global
coveragesystemusingLEOorbitsrequiresalargenumberofsatellites,inmultiple
orbitplanes,invariedinclinedorbits. Seeexamplebelow.
Example1
Thecurrently in operation Iridium(Motorola) system, utilizes 66satellites (plus
sixinorbitspares)insixorbitplanesinclinedat86:4 Æ
atanorbitheightof780km
withanorbitperiod P =100min;28sec. Global coveragewiththis singlesystem
isanastounding5:910 6
miles 2
persatellite.
SeealsoFigure3.2orFigure3.3,wheredi erentexamplesofLEOsaregiven.
3
Figure 3.3. Usualorbitde nitionsfromtheEarth'scenterandout;LowEarth
Orbit, Medium Earth Orbit, Geostationary Orbit and Highly Elliptical Orbit.
AlsotwoexamplesofRussianHEOisgiven(thecommunicationsatellitesystems
Molnya andTundra)[3].
MEO
MEOs(MediumEarthOrbits),alsoknownasICOs(IntermediateCircularOrbits),
arecircularorbitsatanaltitudeofaround10000km. Theirorbitperiodmeasures
about 6h. The maximum time during which a satellite in MEO orbit is above
thelocal horizon foran observeron the Earthis in theorder of a few hours. A
globalcommunicationssystemusingthis typeof orbit,requiresamodestnumber
ofsatellitesin 2to3orbitplanesto achieveglobal coverage. SeealsoFigure 3.3.
Example2
TheUS NavstarGlobal PositioningSystem(GPS)isaprime exampleofaMEO
Figure 3.4. TheUSNavstarGlobalPositioningSystemsnominalconstellation.
Using24satellitesin6orbitplaneswith4satellitesineachplane. Thealtitude
being20200kmandtheinclination55 Æ
,thuslayinginaMEOorbit[3].
HEO
HEOs(HighlyEllipticalOrbits)forEarthapplications wereinitially exploited by
theRussiansto providecommunicationstotheir northernregions notcoveredby
at63:4 Æ
inordertoprovidecommunicationsservicestolocationsathighnorthern
latitudes.
Theparticularinclinationvalueisselectedinordertoavoidrotationoftheapses,
i.e. theintersectionofalinefromtheEarthcentertoapogee,andtheEarthsurface
will alwaysoccurat alatitudeof 63:4 Æ
North. Orbit period varies from eightto
24h.
Owingtothehigheccentricityoftheorbit,asatellitewillspendabouttwothirds
of the orbit period near apogee, and during that time it appears to be almost
stationary foran observeronthe the Earth(this is referredto asapogee dwell).
A well designed HEO systemplaces each apogee to correspond to aservice area
ofinterest, i.e. which would coveramajorpopulationcenter, forexamplein the
RussianMolnyasatellitesystemdesignedtocoverSiberia,seeExample3.
Aftertheapogeeperiodoforbit,aswitch-overneedstooccurtoanothersatellitein
thesameorbitinordertoavoidlossofcommunicationstotheuser. Freespaceloss
andpropagationdelayforthistypeoforbitiscomparabletothatofgeostationary
satellites. However,duetotherelativelylargemovementofasatelliteinHEOwith
respecttoanobserverontheEarth,satellitesystemsusingthistypeoforbitneed
tobeabletocopewith largedopplershifts.
Example3
OneHEO systemsis the Russian Molnya system, which employs3 satellites in
three 12h orbits separated by 120 Æ
around the Earth, with apogee distance at
39354km andperigeeat 1000km. With these three satellites, theRussians have
completecoveragewithcommunicationsoverthewholearcticarea,includingtheir
owncountry.
AnotherexampleistheRussianTundrasystem,whichemploys2satellitesintwo
24horbitsseparatedby180 Æ
aroundtheEarth,withapogeedistanceat53622km
andperigeeat17951km.
InFigure3.3 twoHEOsareshown.
3.2 Missions
Thereareavarietyofmissions possibleforsatellites. Afewof themhavealready
beenmentioned, butwill bediscussed alittlemorein detailin this chapter.
Ob-servethatallofthebelowmissionclassi cationsarestrictlysubjectivetomyown
opinion,andaredrawnfromobservationofpreviouslylaunchedsatellitesmissions
presentedin[14]. Otherbooksmaythereforehaveotherclassi cations,butinthis texttheseonesareused:
Communication: If acommercial companiy owna satellite,it probably belong
1.7 %
Education
11.0 %
Tech Demo
2.3 %
Military
69.2 %
Commercial
14.4 %
Science
1.4 %
EO
Figure 3.5. Di erent market shares of missions calculated to the year 2000.
(Sourceis[14]).
EarthObservation: Inthiscategoryyoucan ndweathermonitoringsatellites
aswellas environmentmonitoringsatellites. Commerciallysomecompanies
sellphotographsoftheEarthtakenfromsatellites. Also,mapsarenowadays
drawn from satellitephotos,andlastly tracking airplanesand certainboats
isalsoa eld ofusebelongingin thiscategory.
Military: Thesesatellitesarefor defenseando enseuse. Forinstance thereare
spysatellites, taking high resolution picturesof theEarth. A few satellites
belonging in this mission pro le could also be Earth surveillance satellites,
suchasweathersatellites, orglobalpositioning satellites. Yet another may
alsobesomesortofcommunicationsatellites. Thecommonground,however
isthatallareusedin militarypurposes.
Education: Someuniversitieshavecoursesthatbuildsatellitestosendintospace.
Techdemo: Companies that want to trytheir components, and show the
con-sumersthattheyactuallywork,sendthesekindsofsatellitesintospace. They
sometimesalsohavesecondarymissions.
Science: This is by far the widest and the most diverse category. These
satel-litesdoeverythingfromobserving(suchastheHubbleSpace Telescope)via
researchonsolarphenomenatoresearchonotherplanets(suchasthe
Mars-lander).
GlobalPositioning: This is, in contrastto thepreviousitem, themostnarrow
category. Allofthesatelliteswiththesemissionsactuallyhasthesamekind
oforbit,aMEOorbit.
TheNAVSTAR GPSisaUSvariantofthissystem. AEuropeanone,called
GALILEO,isonthe way,but willprobablytakeat leastafewyearsbefore
operational(See[8]). TherealsoexistaRussianvariantofglobalpositioning, calledGLONASS(Global'nayaNavigationnayaSputnikovayaSistemaGlobal
Navigation SatelliteSystem), which isthe mostaccurate globalpositioning
systemonthemarket today. See[22]forfurtherinformation.
0
10
20
30
40
50
60
70
80
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
EO
Education
Science
Tech Demo
Military
Communications
Figure 3.6. Di erentmissions marketsharedividedperyearsince 1980to the
year2000. Sourceis[14].
Global positioning does not really make up a category by itself, rather it is a
combinationbetweenEarth observationand military. Butfor simplicitytheyget
andin Figure 3.6 ahistorical aspect ofdi erent missions are given(observethat EOstandsforEarthObservation). Thesechartsarederivedfrom[14].
Itwouldbeaneasyguessthattherearemostlycommunicationsatellitesinspace,
buttechdemohasasurprisinglylargeshare. Theprobablecauseofthiscouldbe
thatthespaceindustryisextremelyconservative,andnoonewillspendanymoney
onasatellitethathasnotbeentestedinrealityatleastafewtimes(exceptmaybe
governmentsor the military). This has lead to a most peculiar phenomena; old
proventechnologyispreferredovernewandadvanced (i.e. a386computerwould
A study of small satellites
Nowadays there areseveralsatellites in orbit. Most commonare communication
andEarth surveillance satellites, but these arefairly big satellites. Smaller ones,
i.e. witha weight.500kg arecalled smallsatellites. These are historicallyfew,
buttheyaregrowinginnumbersaswewillseeinthis chapter.
4.1 Previously launched satellites
Figure4.1. Smallsatellites(i.e. mass.500kgplottedpermonthsince1980. A
Thehistoryof actualspace ightis, asalmost everyoneof youprobably already
know,extremelyshort. But,onthecontrary,thelongroadfrom discoveringblack
powderto the actual rstlaunch isabit moreextensive,and isbrie y described
inAppendix D.
Ifwejustlookatsmallsatellites,themainmissionsusuallyareglobalpositioning,
weathersurveillanceandofsciencenature. Ifwedividesmallsatellitesevenmore,
intomini(<500kg), micro(<100kg)and nano(<10kg)satellites,wecan
com-pare the numberof launches that have been historically (that we know of) with
theweightof thelaunched satellite. This comparison hasbeendone in [14], and theresultisshownin Figure4.1.
From gures4.1and4.2,onecanseethatbetween1997-1999,whentheinformation technology haditspeak, theincreaseoflaunchedsmall satelliteswassubstantial.
0
10
20
30
40
50
60
70
80
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
Mini
Micro
Nano
Figure4.2. Massdistributionoflaunchedsmallsatellitesdividedperyear.
4.2 Tendency in launches today
Toguess the future in this areais rather diÆcult. There is notmuch happening
rightnow,butin thefuture therewillprobablybeanew\boom". Thereasonfor
thisisthelifetimeofsatellites. Mostsatelliteshavesomekindofsolarpanels,which
meansthattheycanrestoreitspowerresources. Thereisoneproblemthough. To
change orbit, or just adjust it, the satellite needs to use thrusters of somekind,
andtheyallusesresourcesthatarenot renewable. Therefore,thesatellitewillrun
outoffuelatacertainage(whichrangesfromanythingbetweenacoupleofyears
toacoupleofdecadesdepending onthepropellingsystem,size and missionetc).
Whenit runs out of fuel, it will use its last propellant to do agraveyardburn
1
,
andburnup.
Thisproblemwithfuelrunningoutcanbesolvedinafewways. Either,theowner
couldjustreplacethesatellitewithanewone,ortheycansendarefuelandrepair
team to it. There are a lot of communication, weather and positioning satellites
in space now, that are growingvery old, thereforethere will probablybeseveral
launchesinthefuture,withtheaimonrenewingthepopulation.
Sincetheactuallaunchisamongthemostexpensivepartsofasatellite,therewill
probablybealotofcompanies/scientiststhatwilltryto takeadvantageofothers
thatwantto renewtheirsatellitesin space. Becausewithsmallercrafts thereisa
possibilityto\hitchhike"into space,thusreducingcosttremendously.
4.3 Customers
Themarketforsatellitescanbedevidedinto vemaincategories(accordingto[14]):
Military(exampletype: spyorweathersatellite)
Amateur(exampletype: radio relaysatellite)
University(exampletype: studentresearchprojects)
Commercial(exampletype: TVbroadcastorGPS)
Government(exampletype: researchorweathersatellites)
Historicallythegovernmenthasbeenthecustomersthathasbeenthelongesttime
inthebusiness(forsmallsatellites),seeFigure4.3. Buthistorically,thecommercial grouphaveincreasedtheirmarketshareconsiderably,aswecansee inFigure4.4.
1
Awaytopreventthespacetobe lledwithtrash. Theprocedureissimplyto rea series
5.1 %
Amateur
35.1 %
Military
5.4 %
University
37.1 %
Commercial
17.3 %
Government
Figure 4.3. Di erent customers marketshare for historically launched small
satellites. (Source[14].)
4.4 Potential use
Thissectionwilldiscusshowand towhatsmallsatellitescouldbe,andare,used.
Thereare probablymorewaysto usethem thanthese, and theinterested reader
couldlookinto[14,27].
4.4.1 Dispenser
Onewaytousethese smallsatellitesisastransportationand deploymentofeven
smallerones,for instancenanosatellites. This kindofsatelliteis usuallycalled a
dispenser,sinceitdispensesmallercraftsin space. Theadvantagewithdoingthis
isthat manysmall satellitescanshare onelaunch. Since, asstated severaltimes
inthistext,thelaunchisthefarmostexpensivepartofasatellitestotalcost,this
wouldlowerthecostpersatellitetremendously.
The use of many small satellites can be motivated by the obvious reason of
re-dundancy. Ifonelargesatellite malfunctions,youare smoked, but ifasmall one
malfunctions,thereareothersthat still work.
Dispensers are increasing in number especially in space research missions, since
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999
Government
Commercial
University
Amateur
Military
Figure4.4. Marketsharebetweendi erentcustomersforsmallsatellitesdivided
peryear. Noticethetrendthatmilitaryisdecreasingandcommercialisincreasing
theirmarketshare. (Dataderivedfrom[14].)
4.4.2 Main vehicle
As a main vehicle there are some limitations when speaking of small satellites.
Since they are just that, much of the interior will be aimed at controlling the
vehicle, which leavesa\not sobig"space left forthe payload. Thebudgets
2
for
thepayloadarealsomuch smaller.
2
4.5 Ways to launch small satellites
Assaidbefore,themainadvantageofsendingasmallsatelliteintospaceisthatit
can\share"thelaunch vehiclewith othersatellites,thusreducingthelaunchcost
foreachsatellite. Therearebut afew waystohitchhikeintospaceonthemarket
today,and thesewaysarebrie ydiscussedinthenextcoupleofsections.
4.5.1 ASAP
The ASAP, Ariane Structure for Auxiliary Payloads,is a way to launch several
smallsatellitesatthetime, bymountingthem ona\rig". Therigismountedon
theadaptercone,andin spacethemain satelliteseparatesbeforethehitchhiking
satellitesdoes. See Figure 4.5. ASAP is meant to besent by the carrierrocket Ariane.
ASAPisafullyworkingsysteminuse. Themaindrawbackistheadditionalwork
before launch thatmustbedone. Test and rocketparametershas to be changed
forthis towork.
Furtherinformationcanbefoundat[14,23]
4.5.2 ESPA
Lockheed Martin, Boeing and Alliant Techsystems, three manufacturers of the
launch vehicles calledAtlas,Delta andTitan respectively, havedevelopeda
stan-dardtogetherfortheUS government,calledEELV (EvolvedExpandableLaunch
Vehicles) according to [7]. This standard implies that a satellite that can be mountedon top of oneof these carrier rocket alsocan be mounted on theother
ones.TogethertheyhavealsodevelopedtheSecondaryPayloadAdapterforEELV,
calledESPA. Here,thesmallsatellitesaremountedasinFigure4.6.
Themain drawback with this kind of satellitetransport is the placement. Most
oftheforcesacting onthelauncherare inthe vericalplane, which coincideswith
theseparation plane for all of these small satellites. This is not good, since the
separationsystemsis theweakest pointand should notbe exposed toanystress.
Forfurther informationaboutESPA,consult[9].
4.5.3 Munin
Muninis anexample onhowto have but oneother satellitehitchhiking. Inthis
concept,asmallsatelliteresidesontopof themainsatellite. Thesetwosatellites
areseparatedwith asmall separationsystem. Forfurther information about the
Muninproject,consult[2].
4.5.4 I-Cone
I-Conestandsforintelligentcone, andisaconcepttousetheactualadapter-cone
Secondary
small
satellites
The rig
Adapter-cone
Primary
satellite
Figure4.5.HowsmallsatellitesaremountedonacarrierrocketwiththeASAP
system. Aringisboltedtotheadapter-conebeneaththepayload. Onthisring,
EELV
Standard
Interface
Plane
ESPA
Small
Secondary
Space-craft
Large
Secondary
Space-craft
Separation plane of
Secondary Spacecraft
Small Secondary
Space-craft
Primary
Space-craft
EELV
upper
stage
Figure4.6. SchematicofESPAmountedtoEELVupperstagewithoneprimary
payloadandsixsmallsatellites. (Referenceis[1].)
at take o , the structure of the cone must be very stern. Thus resulting in a
heavyconstruction, which actually isthe main limitation to the I-Coneconcept.
In Figure 4.7, a suggestion of how an I-Cone satellite could look like is shown. F
3
A is aSESpace used \slogan"for I-Cone. Itstands forfour di erent positive
characteristicsofthesatellite:
Fast: Thetimeto developanI-Conefrom theconceptto thecompleteproduct
isshort.
Frequent: SinceaI-Conecan be launched withany kindoflaunch vehicle,the
satellitecangainafrequentaccess intospace.
Flexible: TheI-Coneis builtinsuchawaythat it tsmanydi erentmissions,
suchasTechDemo,CommercialorMilitaryforinstance. Furthermoreisthe
I-Coneindependentofthemainsatellite.
A ordable: The most expensive part of a satellite is the launch cost, assaid
before. This concept could however dramatically decrease this cost. By
Figure4.7. SuggestionhowanI-Conecouldlooklikeasasmallsatellite
con gu-ration. Noticethenon-symmetricmassdistributionovertheareaofthesatellite.
BycourtesyofSaabEricssonSpace[24].
Thereareseveral potentialmissions forI-Cone. Butin general,certainorbitsare
toprefer. It allcomesdowntotheweightofI-Cone. Sinceitis heavy, relativeto
itssize, it is diÆcultto movethe satellitearound to much, thus excluding GEO
orbitswhich needs a lot of thrusterburns to reach. Buton the other hand,due
to theweight italso becomes morestable which makesit an excellentchoice for
LEO-missionsandMEO-missionswithhighaccuracypreferences.
Communication satellite
Thiscouldbea eldofinteresfortheI-ConeunlesstheorbitisaGEO.Thereason
forthisisitsweight. TogetintoaGEO,aseriesofthrusterburnshastobedone
inordertogettherightaltitudeandspeedinthecircularorbit,andwhenacraftis
asheavyasI-Cone,itwillconsumetoomuchenergytomakeitasoundalternative.
Positioningsystems
position andattitude isimportantfor thesatellites,much fuelisconsumed. This
way,ifanI-conewasto beused,allfouroftheF 3
A atributesareutilizedinfull.
Mainvehicle
The prospect of making I-Cone into a satellite of its own seems to be the most
probable. Then thebusinside I-Conewould take 3
4
ofthespace, leavingtherest
forthepayload.
Dispenser
This isa highly interesting areafor theI-Cone concept, since noother company
asyet hascome forth with a good solution how to attach small satellitesonto a
rocket in agood manner. I-Cone could be the rstreal good solution, since the
mainstructureisnota ectedbythematall.
4.6 The need for small satellites
Smallsatellitesis agrowingmarket. But this market could groweven moreif a
solutiontohowtheycouldbelaunchedintospaceinaneasierandcheaperwaywas
solved. Therearefourpossiblewaysto hitchhikeintospacepresentatthemarket
today, but all of them have some drawbacks. Since no good solution has been
found,companieslaunchinglargesatellites(communicationsatellitesforinstance)
arenothappytohavehitchhikers. SESpacesolution,however,mightchangethis,
since the actual small satellites are almost invisible to the main satellite. This
concept,calledI-Cone,couldthereforehaveapromisingfuture.
Ifwelookhistoricallyonthesmallsatellitesdevelopment,onecanclearlyseethat
moresmallsatellitesarebeingsentupeveryyear. Butwhenlookingatthemissions
andcostumers, therehavebeenbigchanges fromyearto year. Attheend of the
periodresearchedinthisarticle,themostusualsatelliteslaunchedintospacewere
commercial communicationsatellites, compared to just afew years earlier when
research and government was in top of the list \most launched". Since the IT
businessisbadrightnow,thishasprobablychangedbacktothepreviousscenario
withscienceasprimefocusof spacemissions.
Inthefuturehoweverthiswillprobablychangeagain. Thereasonwhythismight
beistheexpected life-timeofsatellites. Sincetheyeventuallywillrunoutoffuel
andheadtowardstheEarthandburnup,theymustbereplaced. Thismeansthat
satellitelaunchesofcommunicationsatellitesprobablywillincreaseagaininanot
toodistantfuture.
What this means for thesmall satelliteindustry is diÆcult to predict, but since
Orbit and attitude
stabilization
Inordertointeractwithotherbodiesinspaceinone wayoranother,thesatellite
musthaveknowledgeofafewthings. Itmustknowhowitis,andhowitshould be
oriented. This chapterdealswith aspectsofthis matter,and especiallyit focuses
ontheAOCSusedtocontrolaspacecraft.Itstartsbydescribingwaystodetermine
iftheattitudeiscorrectinSection5.2.1,andcontinueswithdiscussingthemeans tomakechangestoasatellite'sorientationinSection5.2.2.
ActualstabilizationmethodsaredescribedinSection5.3,but rstashortnoteon redundancymeasureswouldbeinorder.
5.1 Redundancy
Sinceitisexpensivetolaunchasatellite,ssstatedaboveinChapter3,itwouldbe catastrophicifsomethinginthesatellite,suchassensorsoractuatorsforinstance,
malfunctions. Twothingsaredonetoensurethatthisneverhappens. First,allof
theequipmentenduresheavytests,andsecond,manyofthesensorsandactuators
havea\spare",i.e. ifforinstancethreesensorsofonesortisneeded,fourareused
insteadsothatifonebreaks,theotheroneswillstillbeabletocompletethetask.
Forlargernetworksofsatellites,suchasGPSforinstance,sparesatellitesarealso
orbitingthe planet. This kindofredundancy isneededincase oneormoreof the
satellitesmalfunctionsin one way oranother. Then thespare satellitecould fast
andeasyreplacethe aseone.
5.2 Sensors and actuators
Tocontrolaspacecraft,weneedto knowthreefundamentalthings;whereweare,
hastobesolvedwithsomesortofsensors. Thesecondhastobegiveninadvance
(the user has to know where the satellite should point, which orbitthe satellite
should haveand what themaximumallowederror is). Themeans by which the
satellitewill be controlled are called actuators. All of these three things will be
dealtwithinthis chapter,startingwithsensorsandactuators.
Thesensorsandactuatorsareveryexpensivepartsonsatellites,sincetheprecision,
aswell asthe durability, of these instrumentsmight beveryhigh (depending on
themission). Since they haveto be ableto withstand the climate in space even
the cheapest sensors and actuators must have a certain standard. To keepcost
down,companiesthat manufacturessatellitestries touse COTS
1
in asfarextent
aspossible. Speci cations,andashortdescription,forafewoftheseCOTScanbe
foundforsensorsinTable5.1andforactuatorsinTable5.2. Mostofthesesensors canbemodeled,andalthoughthatwillnotbedoneinthistext, amorethorough
explanationwill be given in the next few chapters. If the readeris interested in
howtomodelthem, [27,18]ispreferable.
5.2.1 Sensors
Asensor is adevice that bysomemean candeterminesomething aboutthe
sur-roundingenvironment. It could beathermometer measuringthe temperature, a
Geiger-meter that measures the activity on isotopes or a hydrometer measuring
thedampnessin theairetc. Inthesatellite'sbus,actuatorsareusedtodirect the
spacecraftiftheattitude iserroneous. Henceit needssensorsthat candetermine
thecurrentattitude. There aremanywaysto dothis, thenextfew sections
con-stitutes alist of afew ofthese sensors, and asummary of these canbefound in
Table5.1.
Earthsensors
AnEarthsensormeasureswheretheedgeoftheEarth'satmosphereis. Therefore
this kind of sensors sometimes also are called horizon sensors. Since the
atmo-sphereis warmerthen thesurroundingspace,anIR-sensor
2
ndswherethisedge
is.
Byitselfthisdoesnotgivemuchinformation,sincethiskindofsensoronlyknowsif
itpointstowardtheEarthornot. Butwithadditionalsensorsitmightbepossible
to determine more about the attitude for the spacecraft. Especially when using
spinningstabilization
3
withthespacecraft,thissensorissuitableaccordingto[18]. AnEarthsensorisrelativelycheap,and hasincreasingprecisionthefurtheraway
fromtheEarthitis. Thereforethissensoroftenisused asacomplementtoother
sensors,for instance asunsensor. With asun sensor and twoEarthsensors, the
completeattitudecanbedetermined.
TheEarthsensorscanalsobeusedas\moonsensors",butthisisseldomthecase
1
CommercialO TheShelfproducts,i.e. cheapstandardproducts
2
Asensormeasuringheatradiation,i.e. temperature
