MET4410RemoteSensing:RadarandSatelliteMeteorologyMET5412RemoteSensinginMeteorology

Lecture18:SatelliteObits

Outline• CircularObits• Keplerian (elliptical)Orbits• Meteorologicalsatelliteorbits:

1)geostationary2)sun-synchronous3)otherorbits

Newton’sLawofUniversalGravitation

1 22

GmmFr

=

� Where G is the universal gravitation constant

� The force of attraction between two point mass m1and m2 separated by a distance r is

CircularSatelliteOrbit

2

2eGm mmv

r r=

� Where v is the orbital velocity of the satellite. M is the mass of satellite, and me is the mass of earth. mv2/r is the centripital force required to keep the satellite in a circular orbit.

� The orbit of a satellite is independent of its mass.

� Assuming that the earth is a sphere, we can treat it as a point mass.

CalculatingtheheightofaSatelliteinGeostationaryOrbit

2Tπ

ξ =

� Where T is the period of the satellite. Therefore,

� The satellite in geostationary orbit has the same angular velocity as the earth. The angular velocity of a satellite is,

2 rTvπ

=

32eGmr

ξ=

� Inserting the angular velocity of the Earth, r=42,164 km, or 35,786 km above the Earth’s surface.

22 34

e

T rGmπ

=

� For the polar orbiting satellite with 850 km altitude, we can get its period T of about 102 min.

� However, satellite do not travel in perfect circles. Therefore we need to derive the exact form of a satellite orbit using ellipse geometry.

EllipseGeometry

2(1 )1 cosar εε θ−

=+

� Perigee:thepointwherethesatelliteisclosesttotheEarth.� Apogee::thepointwherethesatelliteisfurthestfromtheEarth.� a=Semimajoraxis;� d=thedistancefromthecenteroftheellipsetoonefocus� Eccentricity:ε=d/a(0≤ε<1)� Θ isthetrueanomalyandisalwaysmeasuredcounterclockwisefromtheperigee.

� Theequationforthepaththatthesatellitefollows:

Kepler’sLaws

� Asatelliteinacircularorbitundergoesuniformangularvelocity.ItspathcanbederivedfromNewton’slaws.

� Asatelliteinanellipticalorbitcannothaveuniformangularvelocity;itmusttravelfasterwhenitisclosertoEarth.ItspathcanbederivedfromKepler’sequation.

1.AllsatellitestravelinellipsepathswiththeEarthatonefocus.

2.TheradiusvectorfromtheEarthtoasatellitesweepsoutequalareasinequaltimes.

� BycalculatingradiusrandtrueanomalyΘattimet,wecanpositionthesatelliteintheplaneofitsorbitusingKepler’sEquation.

SatellitePosition

Thenwhatabouttheorbitalplanepositioninspace?

� Weneedtodefinea3Dcoordinatesystemfirst.� Thissystemmustbeaninertialcoordinatesystem(non-accelerating),nottheonefixedtotherotatingEarthaswehadbefore.

� Wewilladoptanastronomicalcoordinatesystem.

Theright-ascension-declination coordinateSystem

� Zaxis:Earth’sspinaxis� Xaxis:pointsfromtheEarth’scentertothesunatthemomentofthevernal(spring)equinox,whenthesuniscrossingtheequatorialplanefromtheSouthernhemispheretotheNorthernhemisphere.

� Yaxis:ischosentomakeitaright-handedcoordinatesystem.

Coordinatesusedintheright-ascension-declinationcoordinateSystem

� RightascensionΩ:istheangulardisplacement,measuredcounterclockwisefromx-axis,oftheprojectionofthepointintheequatorialplane.

� Declination(δ)ofasatelliteinspaceisitsangulardisplacementmeasurednorthwardfromtheequatorialplane.

� Radius(r) isthedistancebetweenEarthandthesatellite.

Fig.2.5Coordinates usedintheright-ascension-declinationcoordinatesystem:rightascension (Ω),declination(δ),andradius(r).

ThreeAnglestoPositionanEllipticalOrbitinSpace

� Inclination anglei:istheanglebetween theequatorialplaneandtheorbitalplane.

� Ascendingnodeisthepointwhere thesatellitecrosses theequatorialplanegoingnorth(ascends). TherightascensionofthispointΩ isthesecondangle.Itisalsotherightascensionoftheintersectionoftheorbitalplanewiththeequatorialplane.Thusitisalwaysdefined, notjustwhenthesatellite isatanascendingnode.

� Argumentofperigee(ω):istheanglemeasured intheorbitalplanebetween theascendingnodeandtheperigee.

� Thesethreeanglesare:◦ Inclinationanglei,◦ RightascensionofascendingnodeΩ,◦ Argumentofperigeeω.

InclinationAngle

� Inclinationangle i:istheanglebetweentheequatorialplaneandtheorbitalplane.

� Byconvection,theinclinationangleiszero iftheorbitalplanecoincideswiththeequatorialplaneandifthesatelliterotatesinthesamedirectionastheEarth.IfthetwoplanescoincidesbutthesatelliterotatesoppositetoastheEarth,theinclinationangleis180degree.

� Prograde orbitsarethosewithinclinationanglelessthan90degree.

� Retrogradeorbitsarethosewithinclinationangle greaterthan90degree.

OrbitalElements

� Meananomaly: isrelated tothetrueanomalyθ andeccentricityε.� Epoch time:thetimewhentheseelements areobserved orare“valid”.

� Theclassicalorbital elementsareparameters forthelocationofasatellite inspace, includingsatelliteposition relativetotheEarthandtheorbitalposition.

KeplerianOrbits� Keplerianorbitsareorbitsinwhichtheclassicalelements(exceptmeananomalyM)areconstant.

� ThesatellitemovesinanellipticalpathwiththecenteroftheEarthatonefocus.

� Theellipsemaintainsaconstantsize,shape,andorientationwithrespecttotheSun.

Keplerianorbitviewedfromspace

Keplerian orbitviewedfromtheEarth

� Fororbitswithperiodlessthanadayandtheinclinationanglegreaterthanthelatitudeoftheviewingpoint,therotationoftheEarthresultsintwodailypassesofthesatelliteneartheviewingpoint.

� Onepassisdescending,andtheotherisascending.Thisusuallymeansthatonepassoccursduringdaylightandoneduringdarkness.

Fig. 2.8. The Keplerianorbitofasatelliteasviewed fromapointrotatingwiththeEarth.

MeteorologicalSatelliteOrbits� SunsynchronousOrbit:theorbitthatissynchronizedwiththesun.Thesatellitecrossestheequatoratthesamelocaltime.

� GeostationaryOrbit(GEO):synchronizedwiththeEarth.Atveryhighaltitude(~35,000kmaboveEarth).

� Nearlyallpresentmeteorologicalsatelliteareineithersunsychronousorgeostationaryorbit.

� However,sunsychronous andgeostationaryareonlytwoofinfinitepossibleorbits.

� OtherOrbitsarealsousefulandwillbecomemoreusefulformeteorologicalsatellites.Forexample,LowEarthOrbit(LEO),polarorbit(ornear-polarorbit),andequatorialorbits.

WhyusingsunsynchronousorbitsinsteadofKeplerianorbits?

TheorbitalplanisfixedwhiletheEarthrotatesaroundthesun.Thiscausesthesatellitetopassoveranareaatdifferenttimesoftheday.Forexample,ifthesatellitepassesnearnoonandmidnightinthespring,itwillpassovernear6am&6pminthewinter.Problems:1)thedatadonotfitintooperationalschedules;2)orientationofsolarcellpanelisdifficult;3)dawnorduskvisibleimagesmaynotbeasusefulasimagesmadeatothertimes.

The orbital plan rotates with the Earth so that it makes a constant angle with the Earth-Sun direction.

Keplerianorbitchangewithseason

sun-synchronousorbitchangewithseason

� Asun-synchronousorbitissynchronizedwiththesunandprovidesconsistentlightingoftheEarth-scanview.Thesatellitepassestheequatoratthesametimeeachday.

� Theorbitalplaneofasun-synchronousorbitmustalsoprecess(rotate)approximatelyonedegreeeachday,eastward,tokeeppacewiththeEarth'srevolutionaroundthesun.

� Sincesunsychronousorbitsreachhighlatitudes,theyarereferredtoasnearpolarorbits(orpolarorbitsforshort).

� PolarorbitsarealsocalledlowEarthorbits(LEOs)todistinguishfromgeostationaryorbits(GEOs).

� SunsychronousorbitsmustbepolarorbitsandLEOs,buttheconverseisnotnecessarilytrue.

Sunsynchronous Orbits

Howtokeepanorbitsun-synchronized?� TheEarthmakesonecomplete revolutionaboutthesun(2π radianor

360degree) inonetropicalyear.Thus,therightascensionofthesunchangesattheaveragerateofabout1degreeperday.

� Ifwecanmake theratechangeoftherightascensionofthesatellite’sascendingnodeassameastheratechangeoftherightascensionofthesun,thentheorbitwillbesun-synchronized, whichmeans thatthesatellite crossestheequatoratthesame localtime(LT=UTC+longitude/15 degree) everyday.

� Thenonspherical gravitaionalperturbationoftheEarthactuallycausesaratechangeoftherightascensionofascendingnodeasafunctionofinclinationangle(i),semimajor axis(a),andeccentricity(ε).

� Therefore,wecanadjustiforaspecifica tomake theorbitsun-sychronized. Forexample: forasatellitewitha=7228km,ε=0,i=98.8degreewillmake itsun-synchronized.

ClassificationofSunsychronousOrbits� SunsychronoussatellitesareclassifiedbytheirEquatorcrossingtime(ECT).◦ Noonsatellites (ornoon-midnight satellites):ascend&crossequatornear

noonlocaltime(LT).Therefore, theymustdescend nearlocalmidnight.◦ Morning satellitesascendbetween06-12hLTanddescendbetween 18-24

hLT.◦ Afternoonsatellitesascendbetween12-18hLTanddescend between00-

06hLT.

CharacteristicsofSunsychronous Orbits� AdvantagesofSunsychronousorbits:

1)LowEarthorbitshavegoodgroundresolution.2)Polarorbitingat700-900kmaltitudespermitsbothalarge

groundswath,offeringadailyglobalcoverage,andagoodgroundresolution.MostoftheEarthobservingmissionsusesun-synchronoussatellitesinlownearpolarorbits.

� Limitations:Acontinuoustemporalobservationisnotpossiblewithonlyonesun-synchronoussatellite.Itpassesoverpolarregionsoneveryorbitalperiod,butmuchmorerarelyoverequatorialregions(2timesadayformostcurrentmeteorologicalsatellites;moregenerallyitdependsonthedriftandthegroundswath).Apossibilitytoeasethisdifficultycouldbetouseaconstellationofsatellites(NASAGPM,launchedinFeb.2014).

Illustration of the path of a sun-synchronous polar orbit. Image from NASA Earth Observatory.

SSMIS (microwave instrument) on DMSP satellites (sunsynchronous, 14 overpasses per day)

Observation Time (hour of day UTC)

Local Morning Passes on Mar. 24, 2011

Rain Rate (mm/hr)

SSMIS (microwave instrument) on DMSP satellites (14 overpasses per day)

Observation Time (hour of day UTC)

Local Evening Passes on Mar. 24, 2011

Rain Rate (mm/hr)

� Geosynchronous meansthatthesatelliteorbitswiththesameangularvelocityastheEarth.

� Geostationary(GEO)orbitisgeosynchronous,butitisalsorequiredtohavezeroinclinationangle(aroundequator)andzeroeccentricity(circular).

� Thegeostationarysatellites(GEOs)circletheEarthinageostationaryorbitabovetheequatorwhichmeansthattheyhovercontinuouslyoveroneplaceontheEarth’ssurface.

� Video:

GeostationaryOrbits

http://www.hurricanescience.org/science/observation/satellites/geostationary/

USGOESSatellites� GOES(geostationaryoperational environmental satellites) East:overtheUS

eastcoast.� GOESWest:oneovertheUSwestcoast.� Between themtheycanprovide imagesforthewholeU.S.� FutureGOES-R(2015):higherspatialandtemporalresolution.

Full-disc view from GOES west. Full-disc view from GOES East.

GOESUScoverage

1.Continuousobservationandhightemporalresolution:Sincethefieldofviewofasatelliteingeostationaryorbitisfixed,italwaysviewsthesamegeographicalarea,dayornight.Thisisidealformakingregularsequentialobservationsofcloudpatternsoveraregionwithvisibleandinfraredradiometers.Hightemporalresolutionandconstantviewingangles arethedefiningfeaturesofgeostationaryimagery.Goodfordiurnalvariationstudies.

2.Spatialresolution:Geostationarysatellitessensorsaremostusefulfortrackingatmosphericfeaturesovergreatdistancesbecauseoftheirhightemporalresolution(15– 30minuteintervals)andhemisphericfieldofview.However,theorbitaldistanceofthesatellitesmeansthattheirspatialresolutionislessthanoptimalfortheidentificationoffeaturessmallerthan1km.

FactsforGeostationaryOrbits

Geostationary Satellite Coverages

OtherOrbits� LowEarthOrbit(LEO):theorbitthatis200to1200kmaboveEarth(todistinguishfromGEO).

� PolarOrbit(ornear-polarorbit):AnyLEOthatreacheshighlatitude.

� EquatorialOrbits:Lowinclinationangle,thusorbitsneartheequator.

� Polarorbitingsatellitesarelaunchedintoorbitsathighinclinationangles,suchthattheypassacrosshighlatitudesnearthepoles.Mostpolarorbitsarecirculartoslightlyellipticalatdistancesrangingfrom700to1700km(435- 1056mi)fromtheEarth.Atdifferentaltitudestheytravelatdifferentspeeds.

PolarOrbits:i≈90º

Fig. 1. Example of a Near-Polar Orbit.

The ground track of a polar orbiting satellite is displaced to the west after each orbital period, due to the rotation of the Earth. This displacement of longitude is a function of the orbital period (often less than 2 hours for low altitude orbits).

Fig. 2. Map of the ground path of one revolution of a typical near-polar orbiting satellite.

Fig. 3. The orbit of a near polar satellite as viewed from a point rotating with the Earth.

Fig. 4. The ground paths of the multiple orbital revolutions during one day for a near-polar orbiting satellite.

Depending on the ground swath of the satellite, it is possible to adjust the period (by varying the altitude), and thus the longitudinal displacement, in such a way as to ensure the observation of any point on the Earth within a certain time period. Most of the near polar meteorological satellites ensure complete global coverage of the Earth, during one day, thanks to a ground swath of about 3300 km.

EquatorialOrbits:Lowinclinationangle,thusorbitsneartheequator.

Ø LaunchedinDec.1997.

Ø 16+years(1998-current)ofdataavailable, veryuniquedatasetforprecipitationandconvectionstudiesintropics

Ø TRMMsatelliteorbit:LEO,equatorial,circular,Non-Sunsynchronous)

Ø Altitude: 350km(402kmsinceAug.2001)

Ø Inclination: 35degree.

Ø Observation frequency: 16timesperday.

Ø TRMMfliesovereachpositionontheEarth'ssurfaceatadifferent localtimeeachday.Soitisgoodfordiurnalvariationstudies.

NASA’sTropicalRainfallMeasurementMission(TRMM)Satellite

Blue: Inclination ~65º (GPM core) Green: Inclination ~35º (TRMM)

� TRMMMovie� -- AnimationofTRMMorbithttp://earthobservatory.nasa.gov/Library/TRMM/

Ø TheA-train (fromAfternoon Train) isasatelliteconstellationofsixsatellites insun-synchronous orbitatanaltitudeof690kilometersabove theEarth.Theorbit,ataninclinationof98.14°,crosses theequatoreachdayataround1:30pmsolartime,andcrosses theequatoragainonthenightsideoftheEarth,ataround1:30am.Theyarespacedafewminutesapart fromeachothersotheircollectiveobservationsmaybeusedtobuild3DimagesoftheEarth'satmosphere andsurface.

Ø Aqua,launched in2002.;landcover, landcoverchange,andatmosphericconstituents

Ø Aura,2004;Ozone,airquality,etc.Ø CloudSAT,CALIPSOandPARABOL :2006;cloudsandaerosolsØ OCO-1,failurein2009;OCO-2launchinJuly2014;measureCO2

NASA’sA-TrainSatellites

� AnimationofA-Trainorbithttp://sci.gallaudet.edu/MSSDScience/a-trainanimation.mpg

Satellite InstrumentsInstruments are sensors on board satellites. Meteorological observations are taken by instruments.

For example,

Instrument Satellite

PR TRMM (Equatorial orbit) TMI TRMMSSM/I DMSP F14 (sun-syn.)SSM/I DMSP F15 (sun-syn. )CPR CloudSat (sun-syn. circular, 705km )MODIS Terra (sun-syn. circular, 705km )MODIS Aqua (sun-syn. 1:30pm ECT)SeaWinds QuikSCAT (Sun-syn., 803 km, 98.6° inclination orbit)NSCAT/SeaWinds ADEOS (Sun-syn.)