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7/24/2019 Satellite Orbits and Sensors
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Platformsand
Satellite
Orbits
OSTM/Jason2BoostProfile
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TypesofPlatform
Thevehicleorcarrierforremotesensorsiscalledtheplatform.Typicalplatformsaresatelliteand
aircraft,buttheycanalsoincluderadiocontrolledairplanes,balloons,kitesforlowaltituderemote
sensing,aswellasladdertrucksor"cherrypickers"forgroundinvestigations.
Platformswith
the
highest
altitude
are
geo
synchronous
satellites
such
as
the
Geosynchronous
MeteorologicalSatellite(GMS),whichhasanaltitudeof36,000kmattheEquator.
Mostoftheearthobservationsatellites,suchasLandsat,SPOT,MOSetc.areatabout900km
altitudewithasunsynchronousorbit.
Fromlower
orbit,
there
are
space
shuttle
(240
280
km),
radio
sonde
(
100km),
high
altitude
jet
plane(10km),lowormiddlealtitudeplane(0.58km),radiocontrolledplane(~0.5km)andsoon.
Thekeyfactorfortheselectionofaplatformisthealtitudewhichdeterminesthegroundresolution
IFOV(instantaneousfieldofview)ofthesensor.
Theselectionofplatformalsodependsonthepurposewhichissometimerequestedforexamplea
constantaltitudeisrequiredforaerialsurveys,whilevariousaltitudesareneededtosurveyvertical
atmosphericdistribution,forexample.
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Variousplatforms,altitudesand
objectsbeingsensed
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Atmosphericcondition
is
different
depending
on
the
altitude.
This
factor
must
be
considered
intheselectionofplatformsorsensors.Inthissection,airpressure,airdensityand
temperatureareconsidered.
AtmosphericConditionandAltitude
Theverticalstructureoftheatmosphereiscomposedofthefollowinglayers.
Troposphere:fromthegroundsurface(1017km)to11km,
Stratosphere:from1017kmtoabout50km
Mesosphere
:
from
about
50
km
to
about
90
km
Thermosphere:fromabout80kmto500km
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Exosphere
Aboveaheightofabout500kmistheexosphere,alayerwherethe
atmospheremerges
into
space.
Satellites
are
stationed
in
this
area,
500kmto1000kmfromEarth.
Thermosphere
Thethermosphereisthefourthlayerintheatmosphere,between
80kmand110kmabovetheEarth.Spaceshuttlesflyinthisareaandit
isalsowheretheauroralightsarefound.Aurorasarewispycurtainsof
lightcaused
when
the
sun
strikes
gases
in
the
atmosphere
above
the
Poles.
Mesosphere
Beyondthestratospheretheairisverythinandcold.Thisareais
knownasthemesosphere,andisfoundbetween50kmand80km
abovetheEarthssurface.
Stratosphere
Thestratosphere isthesecondlayerofairabovetheEarthssurface
andextendstoaheightof50km.Itisherethatwefindtheozone
layer.Theozonelayerabsorbsmuchofthesunsharmfulradiation
thatwouldotherwisebedangeroustoplantandanimallife.
Troposphere
ThetroposphereisthelayerclosesttotheEarth,approximately
11kmhigh.Weatheroccursonlyinthetropospherebecauseitisthis
layerthatcontainsmostofthewatervapour.Weatheristheway
waterchangesintheair,andsowithoutwatertherewouldbeno
clouds,rain,
snow
or
other
weather
features.
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Thegeometricdistortiondependsonnotonlythegeometryofthesensorbutalsotheattitudeofthe
platform.Therefore
it
is
very
important
to
measure
the
attitude
of
the
platform
for
the
consequent
geometriccorrection.
Theattitudeoftheplatformisclassifiedbythefollowingtwocomponents.
Rotationanglesaroundthethreeaxes;roll,pitchandyaw;
Random
and
unsystematic
vibration
which
cannot
be
measured.
Therotationangles;roll(),pitch()andyaw()aredefinedastherotationanglesaroundtheflightdirection,themainwingandtheverticallinerespectively,asshowninthenextslide.Thebottom
panel(nextslide)showsthesatelliteattitudeparameters.
Inthe
case
of
satellites,
the
variation
of
the
positionand
the
attitude
will
be
continuous,
Incaseofaircraft,thevariationwillnotalwaysbesmooth,whichmakesthegeometriccorrection
moredifficult.
Thetypicalattitudesensorsforaircraftareasfollows.
Speedometer
Altimeter
Gyrocompass(forattitudemeasurement)
Dopplerradar(formeasurementofaltitude)
GPS(forpositioning)
Gyrohorizon
TV
camera
Flightrecorder
AttitudeofPlatform
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Theaircraftandsatelliteattitudeparameters.
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OrbitalElementsofSatellite
Asetofnumericalvaluestodefineanorbitofasatelliteorplanetarecalledorbitalelements.The
independentorbitalelementsoftheearthobservationsatellitearesixelementsoftheKeplerianorbit(satellitesorbitinanellipseofconstantshapeandorientation).
Asatellitecanbeconsideredtorotatearoundtheearthinaplane,calledtheorbitalplane,because
theinfluenceofgravityofthemoonandthesuncanbeneglectedascomparedwiththegravityof
theearth.
Apointinspacecanbeexpressedintheequatorialcoordinatesystemasfollows.Theoriginof
equatorialcoordinatesystemisthecenteroftheearth.
Thereferencegreatcircle:theequatorialplane
Theorigin
of
astronomical
longitude
(right
ascension)
:the
vernal
equinox
Theastronomicallongitude(rightascension):024hourstotheeastfromthevernalequinox
Theastronomicallatitude(declination):anglefromtheequatorialplane(+90degreeinthenorth
pole;90degreeinthesouthpole)
The
six
elements
of
Keplerian
orbit
are
;(1)Thesemimajoraxis(A):
(2)Eccentricityoforbit(e):
(3)Inclinationangle(i):
(4)Rightascensionofascendingnode(h)
(5)Argumentofperigee(g)
(6)Time
of
passage
of
the
perigee
(v)
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Figure(below)showstheaboveelements.Theshapeandsizeofanorbitcanbedefinedby
Aande,whiletheorbitplanecanbedefinedbyiandh.Thelongeraxisoftheorbitellipse
canbe
determined
by
g.
The
positionof
asatellite
can
be
located
by
T.
OrbitalelementofKeplerArgumentofPerigee(g): Theanglebetweenthe
ascendingnodeandperigee,measuredcounter
clockwisealongtheplaneoftheorbit.
Apogee(A):Pointinanorbitwhenthesatelliteis
farthestfromtheEarth
Perigee(P):
The
point
in
an
orbit
when
the
satellite
isclosesttotheEarth.
Eccentricity(e):Halfofthedistancebetweenthe
fociofanellipsedividedbythesemimajoraxis.
Inclination(i):Theanglebetweentheplaneofthe
orbitandtheplaneofthecelestialequatorforEarth
orbitingsatellites(ortheplaneoftheeclipticforsun
orbitingsatellites).
RightAscension
of
the
Ascending
Node
(h):
AnothertermforLongitudeoftheAscendingNode,
ItistheangleoftheascendingnodemeasuredEAST
ofthevernalequinoxalongthecelestialequator.
SemiMajorAxis(A):Thehalfofthelongerofthe
twoaxesoftheorbitalellipse
VernalEquinox:Oneoftwopointswherethe
ellipticcrosses
the
celestial
equator,
the
other
being
theAutumnalEquinox.
CelestialEquator:TheplaneoftheEarth'sequator
projectedontothecelestialsphere.Thecelestial
equatoristilted23.5degreesinrelationtothe
planeoftheEarth'sorbit(theelliptic).
Ecliptic:TheplaneoftheEarth'sorbitaroundthe
sun.
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Satelliteorbits
Thepath
followed
by
asatellite
is
referred
to
as
its
orbit.
Orbitselectioncanvaryintermsofaltitude(theirheight
abovetheEarth'ssurface)andtheirorientationand
rotationrelativetotheEarth.
Threeprincipally
employed
types
of
Earth
observation
orbitsare(1)geosynchronous, (2)sunsynchronousand
(3)nearpolarorbits.
(1)Satellitesatveryhighaltitudes,whichviewthesame
portion
of
the
Earth's
surface
at
all
times
have
geostationaryorbits(ataltitudesofapproximately36,000
km).
Thesesatellitesrevolveatspeedswhichmatchthe
rotationoftheEarth,sotheyseemstationary,relativeto
theEarth's
surface.
This
allows
the
satellites
to
observe
andcollectinformationcontinuouslyoverspecificareas.
Examplesareweatherandcommunicationssatellitesthat
commonlyhavethesetypesoforbits.
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(2)Manyremotesensingplatformsaredesignedtofollowan
orbit(basicallynorthsouth)which,inconjunctionwiththe
Earth'srotation
(west
east),
allows
them
to
cover
most
of
the
Earth'ssurfaceoveracertainperiodoftime.Thesearenear
polarorbits.
(3)Manyofthesesatelliteorbitsarealsosunsynchronous such
thattheycovereachareaoftheworldataconstantlocaltimeof
daycalled
local
sun
time.
If
asatellite
is
in
polar
orbit
at
an
altitudeof800km,itwillbetravellingataspeedof
approximately7.5kmpersecond.
Atanygivenlatitude,thepositionofthesunintheskyasthe
satellite
passes
overhead
will
be
the
same
within
the
same
season.Thisensuresconsistentilluminationconditionswhen
acquiringimagesinaspecificseasonoversuccessiveyears,or
overaparticularareaoveraseriesofdays.Thisisanimportant
factorformonitoringchangesonthesurface.
Mostof
the
remote
sensing
satellite
platforms
today
are
in
near
polarorbits,whichmeansthatthesatellitetravelsnorthwards
ononesideoftheEarthandthentowardthesouthernpoleon
thesecondhalfofitsorbit.Thesearecalledascendingand
descendingpasses,respectively.
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AsasatelliterevolvesaroundtheEarth,thesensor
"sees"acertain
portion
of
the
Earth's
surface.
The
areaimagedonthesurface,isreferredtoasthe
swath.
Imagingswathsforspacebornesensorsgenerally
vary
between
tens
and
hundreds
of
kilometres
wide.
AsthesatelliteorbitstheEarthfrompoletopole,its
eastwestpositionwouldn'tchangeiftheEarth
didn'trotate.However,asseenfromtheEarth,it
seemsthatthesatelliteisshiftingwestwardbecause
theEarth
is
rotating
(from
west
to
east)
beneath
it.
Thisapparentmovementallowsthesatelliteswath
tocoveranewareawitheachconsecutivepass.
Thesatellite'sorbitandtherotationoftheEarth
worktogethertoallowcompletecoverageofthe
Earth'ssurface,afterithascompletedonecomplete
cycleoforbits.
Mercatormap
of
the
satellite
ground
track
for
the
orbit
for(a)nonrotatingEarth,and(b)rotatingEarth.
swath
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Orbitalvelocitiesandperiods
Tocalculate
the
velocity
and
orbital
period
of
the
sensor,
we
equate
the
gravitational
andcentripetalforcesonthesatelliteattheorbitalaltitudeofinterest,
Where,
G
=gravitational
constant
=6.671011 Nm2 kg2
=massofthesatellite
=massoftheearth=5.9761024 kgr =meanradiusoftheearth=6.371106mH =orbitalaltitudeinmeters(h=a(1e2)/1+ecos)
=
velocity
of
the
satellite
Wederivethe asfollows,
Thesubsatellite velocityattheground,vg,isgivenby
Hr
vm
Hr
mGm sses
2
2)(
sm
em
sv
1
2/1
ms
Hr
Gmv es
Hr
rvv sg
Therefore,
Usingthisequation,wecancalculatevg forvarious
satellites.Forexample,vg andvs forLandsatTM
having
an
the
Earth
orbit
altitude
of
705103
m
is
6.76and7.51kms1 respectively.
2/3
2/1
)(
)(
Hr
Gmrv eg
1
2/36
11
)10371.6(10272.1
kms
Hvg
sv
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