EROS SYSTEM SATELLITE ORBIT AND CONSTELLATION DESIGN Dr. Mosh Bar-Lv, Dr. Lonid Shchrbina, Mr. Vola Lvin Dr. Mosh Bar-Lv, Prsidnt ImagSat Intrnational N. V. 2 Kaufman Strt, Tl-Aviv 61500 Isral. Tl: 972-3-796 0600, Fax: 972-3-516 3430 ABSTRACT Th EROS (Earth Rsourcs Obsrvation Systm) rogram conductd by ImagSat Intrnational N.V. intnds to orat a constllation of 8 commrcial imaging satllits in LEO (Low Earth Orbit). Th first satllit, EROS-A1, was succssfully launchd by a Russian START-1 launchr on Dcmbr 5 th, 2000, and is rsntly succssfully orating with 1.8 mtr to 1.0-mtr rsolution. This articl rsnts th rquirmnts and considrations rgarding th choic of th orbits for a singl- and multi-satllit imaging systm. Th main aramtrs dtrmining th orbit ar: imaging conditions, accssibility and rvisit rquirmnts. Two kinds of orbits wr comard: Sun-synchronous orbits and inclind orbits. Th altitud choic and tchniqu for th Sun-synchronous orbits, roviding rquird ground track ratability and rvisit ar analyzd. Th final aramtrs of EROS orbit and constllation ar dscribd. Finally, EROS satllits, as wll as th roosd srvics, ar rsntd. 1. INTRODUCTION Th world commrcial srvics for sac high-rsolution imagry markt facd fast growth during th last fw yars. Russia mad availabl hr archivs of high-rsolution imagry, and th Amrican authoritis lgislatd lnint rgulations, allowing th commrcial markting of sac imagry with rsolution of 1 mtr and latly 0.5 mtr. As a rsult, svral attmts wr mad by diffrnt comanis to rovid srvics of high-rsolution satllit imags. Sac Imaging Inc. succssfully launchd IKONOS-2 fw months aftr a failur in launching of IKONOS-1 (1999). EarthWatch Inc. has faild in both its launch attmts of EarlyBird (1997) and QuickBird (2000) and is lanning to launch this yar. ImagSat Intrnational s EROS-A1 was succssfully launchd in Dcmbr 2000 and bcam th scond comany to rovid high-rsolution commrcial srvics. Th comany intnds to dloy a constllation of 8 satllits with imaging rsolution, bttr than 1 m, in th nxt 6 yars. Satllit orbit is dtrmind by mission rquirmnts and may somtims b limitd by launch rstrictions. Th imaging mission dsign goal is to achiv th largst amount of imagry with th bst quality and th bst covrag of aras for a longst tim. Comromiss of ths rquirmnts dtrmin th satllit orbit. Th imaging quality is comosd of th rsolution and swath width, as wll as th illumination conditions. Th ara covrd is dfind by ithr as a rquirmnt for global worldwid covrag or a rquirmnt for frqunt rvisit of limitd scific rgions. Th bst covrag is achivd by maximizing th frquncy of imaging rvisit, imaging vlocity and th maximum swath. A constllation of imaging satllits shall incras th amount of imagry and th covrag. Th constllation dsign critria must tak into account th ror hasing of th satllits, rovision for rdundancis and th orational rstrictions of th controlling ground station and imagry rciving stations. Th orbit and constllation considrations for th lctro-otical imaging satllits, orating in th visual band ar rsntd. For othr kinds of imaging satllits, such as radar basd or infrard, som of th considrations may diffr somwhat. Most of th rincils rsntd, ar gnrally rlvant to all kinds of imaging satllits Chatr 2 blow rsnts th mission for imaging orbits. Obit dsign for a singl satllit is rsntd in Chatr 3 and considrations, rgarding satllits constllation, ar discussd in Chatr 4. Th EROS systm is rsntd in Chatr 5. 2. MISSION REQUIREMENTS FOR IMAGING SATELLITES 2.1. Orbit Rquirmnts 2.1.1. Imaging Quality Illumination Conditions Th rquird illumination conditions is a major factor in achiving high imaging quality sinc th nrgy collctd by th imaging camra in th visual band is th light rflctd from th targtd ara, Th Sun Angl, i.. th angl btwn th local rndicular and th Sun dirction, S Figur 1, dfins th illumination condition of a scific ara. Th xisting satllit camras rovid satisfactory imags at Sun Angls u to 60 80.
Local znith Prndicular S Th bst illumination is achivd at minimal Sun Angls, i.. Sun in local znith, but this will not ncssary lad to th bst quality of acctd imags, scially for highrsolution imaging. For bttr intrrtation and distinction btwn diffrnt imags dtails, som shadow is usful. Thrfor, it is rcommndd to rform imaging for Sun Angls of about 20 40. Figur 1. Sun Angl Dfinition Wathr conditions such as haz, fog and clouds ar a vry srious obstacl in Earth imaging. Som aras, scially thos clos to th quator or to ocans, ar known for thir high cloudinss. Gnrally, th cloud covrag lvl is sasonal and has a daytim dndnc natur. Inclind orbits, for lctro-otical satllits, lads to varying illumination conditions for ach ass, as wll as to gas of svral wks in imaging ossibility (night asss only). Th us of Sun-synchronous orbit for imaging satllit, as shall b rsntd in ar. 2.3 blow, allows almost th sam illumination conditions for vry imaging ass. Th local tim of th ascnding/dscnding nods is thn dfind by rquird shadows/cloudinss conditions 2.1.2. Imaging Rsolution and Swath Width Th rsolution rquirmnt for a givn obsrvation systm is dtrmind by th orbit altitud. Th lowr th orbit, th bttr th imaging rsolution, howvr, th smallr th swath width and th shortr th satllit lifsan ar. 2.2. Covrag Rquirmnts Th covrag rquirmnts ar: Accssibl ara covrag, covrag zon of rciving ground station, ground track ratability and rvisit riod. Th Accssibl ara covrag is dfind as th Earth ara, which may b covrd by th satllit. Th covrag zon of a rciving ground station is limitd gomtrically by th Lin of Sight btwn th Ground R sr R c R α Η γ Actually, th Physical covrag ara of th satllit lis btwn th north and south mridians with latitud qual to th orbit inclination angl (s Figur 2). Th satllit may rform off-nadir imaging by ointing its camra at an angl γ to th nadir, s Figur 3. Thrfor, th actual ossibl covrag ara is dtrmind by th orbit inclination and th maximal imaging ointing angl of th camra. A olar orbit shall allow a global worldwid covrag. Figur 2. Earth Covrag Ara for Inclind Orbit of 40 Antnna and th satllit, dtrmind by th orbit altitud H, as wll as by tchnical aramtrs, lik communication link btwn th station and th satllit, minimal antnna lvation ovr th local horizon α and maximal off-nadir imaging angl s Figur 3. Figur 3. Ground Station Covrag Zon Th covrag zon radius R c is givn by th following xrssion: c R sr R + H = R arcsin( cosα ) + arcsin( sin γ ) γ R + H R R (1) whr: R - Earth radius, R sr - Slant rang radius: R sr = R sin 2 2 H H α + sin α + 2 + (2) R R
Th highr th orbit th biggr th covrag zon. For satllit systms, having no onboard rcording, th covrag ara will consist of th covrag zons of th ground stations. Th ground track ratability is dfind by th tim riod (in days) btwn th satllit rvolutions having th sam ground track. This aramtr is imortant for imaging mission rdiction and lanning. Som systms, lik SPOT, rquir th xact ratability of th ground track for long trm. This can b achivd by having rlativly high orbits (abov 600 km), which ar wakly disturbd. For lowr orbits, th ground track ratability can b maintaind for only short trms only bcaus of th highr drag ffct on th chang on th orbit hight. Th rvisit riod is dfind for a scific sit and rrsnts th minimal tim intrval (in days) btwn two imaging oortunitis of this scific sit. Th longst rvisit riod is for quator locatd sits. Th rvisit shortns, as th sit location is locatd at highr latitud. It should b also mntiond, that th lowr th orbit inclination, th bttr (shortr) th rvisit riod. This is a major disadvantag of th olar orbits. 2.3. Orbit Dfinition Th satllit orbit can b dfind by th classical st of Klrian aramtrs [1], rfrrd to th vrnal quinox inrtial coordinat axs, s Figur 4: a) a - smi-major axis b) - ccntricity c) i - inclination angl d) Ω - right ascnsion of ascnding nod ) ω - argumnt of rig f) θ - tru anomaly ra + r a = 2 ra r = r + r a Ha + H = R + 2 Ha H = 2 R + H + H a Figur 4. Orbit Dfinition Paramtrs Motion of Orbital Pan Bcaus of th nonhomognity and oblatnss of th Earth, th orbital lan dosn t rmain inrtialy fixd, but suffrs two main motions: a) orbital lan rotation around th North-South axis, charactrizd by th following xrssion: a ( 1 2 ) cos i 3.5 R 9.97 2 Ω b) in-lan rotation of th orbital llisoid, givn by: (3) (4) 3.5 2 2 2 ( 1 ) ( 5 cos i 1) [dg/day] (5) R ω 4.98 [dg/day] (6) a Ths hnomna allow som scial kinds of orbits: a) Sun-synchronous orbit, charactrizd by synchronizing th rat of chang of ascnding nod ascnsion to th rat of th Earth rotation around th Sun, i..: Ω = 360 / yar = 0.9856 / day (7) For LEO orbits, (5) and (7) lad to th orbital inclination within i 96 98 rang, i.. almost olar orbits. In this orbits th rvisit tim at any oint is at th sam tim of th day. b) Frozn orbit, i.. th orbit with constant argumnt of rig, is drivd from (6) by stting ω = 0, which lads to orbit inclination of i = 63. 43. This orbit is also known as Molniya-ty orbit, sinc it was usd for th first tim by Russian Molniya-ty communication satllits, whr th orbit high aog was constantly locatd ovr th north hmishr, lading to long duration of communication tim for th scific satllit ovr th northrn art of Russia.
3. ORBIT DESIGN FOR EROS-A1 SATELLITE 3.1 Orbital Plan Orintation EROS mission rquirs rovision of th Earth imaging within 2,000 km radius covrag zons of ground rciving stations, locatd all ovr th world. Th location of xisting ground rciving stations is rsntd in Figur 5. A circular orbit clos to olar is rquird to fulfill th abov covrag rquirmnts. In ordr to rovid th bst illumination conditions during all satllit asss, as rquird for th global covrag, a Sunsynchronous orbit, which is clos to olar, was chosn. Th chosn local tim of dscnding nod was 09:45 a.m., in ordr to minimiz clouds rsnc for th Far-East rgion. Figur 5. Worldwid Ntwork of Existing EROS Ground Rciving Stations 3.2 Orbit Altitud Prliminary th orbit altitud rang of 460 500 km was drivd from th imaging rsolution/swath and th liftim rquirmnts. Th xact valu of th satllit orbit was chosn to rovid bst ground track ratability and rvisit. Th ground track ratability and rvisit calculation is basd calculating th synchronization btwn th motions of th Earth and th satllit. Ground track ratability will b achivd, if during an intgr numbr of days M th satllit has an intgr numbr of rvolutions N. For th Sun-synchronous orbit, th rvolution riod P of such orbit is givn by th following xrssion: P = T sn M / N (8) whr: T sn - solar day; T sn = 86,400sc Such an orbit will hav th ground track ratability with a riod of M days. N can acct any intgr valu within th rang: N = M Lmin M ( L min +1) (9) whr: L min - minimal intgr numbr of rvolutions r day; for th orbit altitud rang of 275 576 km: L min = 15 Th quatorial distanc D btwn two succssiv asss is givn by th following: whr: ω - Earth rotation rat; D = R ω P (10) ω = 2π / T sd, T sd - sidral (inrtial or star) day Th valu of N shall b chosn such as to rovid bst rvisit of any sit locatd on quator (worst cas), i.. bst covrag of th distanc D during M days. For EROS-A1 satllit, a 7 days ground track ratability was chosn. Th aramtrs of th ossibl orbits, dnding on th valu of N, ar rsntd in Tabl 1. δd rrsnts th daily movmnt of th ground track crossing oint at th quator: δd = L + 1 D 2πR (11) ( min ) Tabl 1. Earth Synchronizd Orbits with 7 days Ground Track Ratability M days = 7 N L P, sc a, km H, km D, km δd, km δd/d δd/d * M 105 15.00 5,760.0 6,945.0 566.9 2,671.7 2,671.7 1.00 7 106 15.14 5,705.7 6,901.3 523.1 2,646.5 2,268.4 0.86 6 107 15.29 5,652.3 6,858.2 4 80.1 2,621.7 1,872.7 0.71 5 108 15.43 5,600.0 6,815.8 437.7 2,597.5 1,484.3 0.57 4 109 15.57 5,548.6 6,774.1 395.9 2,573.6 1,103.0 0.43 3 110 15.71 5,498.2 6,732.9 354.8 2,550.2 728.6 0.29 2 111 15.86 5,448.6 6,692.4 314.3 2,527.3 361.0 0.14 1 112 16.00 5,400.0 6,652.6 274.4 2,504.7 0.0 0.00 0
Figur 6. Ma of 7 Days Passs for 480 km Sun Synchronizd Orbit For xaml, for imaging angls u to 37 th rvisit riod of 3 4 days can b rovidd vn for quatorial sits. Th sam rvisit riod can b achivd for all sits, locatd to north / south of ±41 latitud, with imaging angls u to 30. 4. ORBITAL CONSTELLATION DESIGN Th orbit, corrsonding to N =107, was chosn, with th quatorial distanc btwn two succssiv asss D = 2,622 km and daily mov of th quator cross of δd = 5/7 D (or quivalntly 2/7 D). Th 7 days ground track ma is shown in Figur 6. Th ga btwn th two nighbor quatorial crosss is 375 km, which can b covrd for th worst-cas rvisit riod of days by offnadir imaging with imaging angls u to 21. Th us of highr imaging angls or/and for sits locations with highr latitud maningfully imrovs (rducs) th rvisit riod. A constllation of satllits has th following bnfits: a) Incras th amount of imagry rcivd. b) Allows daily rvisit for any oint with highst with minimal imaging angl. As shown in ar. 3.2, on satllit in th EROS constllation has a 7 days rvisit riod at low imaging angls at th quatorial ara (worst cas). Us of a constllation of 7 satllits, rorly hasd will lad to a daily rvisit of any sit all ovr th world at th almost highst rsolution. Th EROS systm lans to us an 8 satllits constllation, out of which on sar satllit. c) Achiv imaging oortunitis for aras, with high cloudinss, by allowing imaging oortunitis during clar or artially clar hours. This rquirs distributing th satllits orbits into diffrnt orbital lans with a wid rang of local tims of th dscnding nods, varying from morning hours till aftrnoon. Th 8 satllits constllation will b lacd into 8 sarat Sun-synchronous orbital lans with th following local tims: 9:45 a.m., 10:00 a.m., 10:30 a.m., 11:00 a.m., 1:00.m., 1:30.m., 2:00.m., 2:15.m. EROS constllation orbital lans ar rsntd in Figur 7. d) Orational constraints of th ground stations shall b takn into account: a minimal tim intrval of 10 min. is rquird btwn any two succssiv satllit aaranc at th communication rang of ach ground station. Sinc a singl satllit ass within th communication rang of a ground station lasts u to 10 min., th minimal hasing of 20 min. (75 ) btwn any 2 satllits in 2 nighbor lans is rquird, s Figur 8. 75 0 Figur 7. Orbital Plans of EROS Constllation Figur 8. 75 Phasing btwn Two Satllits in Nighbor Plans
5. EROS PROGRAM 5.1 Gnral Th EROS rogram aimd to suly commrcial high-rsolution imags and srvics using a constllation of Sunsynchronous satllits launchd and oratd by ImagSat. 5.2 EROS Satllits EROS-A1 satllit (s Figur 9), th first satllit of th constllation, was succssfully launchd on Dcmbr 5, 2000 from th Russian Cosmodrom Svobodny, locatd in southast Sibria. Th satllit has assd th IOT (In-Orbit Tsts) rogram and is in commrcially orational. Th scond satllit, EROS-B1, is lannd to b launchd in 2003 Figur 9. EROS-A1 Satllit Th main aramtrs of EROS-A1 and EROS-B1 satllits ar rsntd in Tabl 2. Tabl 2. Main Orational Paramtrs of EROS-A1 and EROS-B1 Satllits Paramtr EROS-A1 EROS-B1 Wight 250 kg 350 kg Dimnsions (Launch) 1,210 * 2,235 mm 1,210 * 2,255 mm Orbit Altitud 480 km 600 km Liftim Ovr 6 yars Ovr 10 yars Imaging Snsor CCD Lin,> 7,000 ixls CCD TDI, 32 stags, > 15,000 ixls Panchromatic Imaging Rsolution (GSD) at Nadir 1.8 m 0.87 m (@ 600 km) Swath 12 km 13 km Samling Dth 11 bits 10 bits Multisctral Imaging Non 4 bands Rsolution (GSD) at Nadir 3.5 m Swath 13 km Vido Transmission Rat 70 Mbit/sc. 280 Mbit/sc. 5.3 EROS Srvics EROS systm rooss th following srvics: Satllit Orating Partnr (SOP) Programs: rovid th customr with xclusivity for full lanning and tasking and acquisition ability within th footrint of th customr s ground station. Acquisition, Archiving and Distribution (AAD) Programs:. Existing ground stations, (s figur 5) adatd for rction of EROS imags, suorts this srvic. Th imaging tasking is rformd by EROS cntral ground station. Th ground stations articiat in satllit imagry rction, archiving and distribution orations to suort worldwid commrcial imagry and drivativ roduct sals. Washington D.C Paris Rfrncs: [1] Marcl J. Sidi Saccraft Dynamics and Control, Cambridg Univrsity Prss, 1997. [2] Jams R. Wrtz & Wily J. Larson Sac mission analysis and dsign, Third Edition, Sac Tchnology Library 1999