doi: 1.58/jatm.11.111 Hossin Bonyan Khamsh Shahid Bhshti Univrsity, GC Thran Iran h.bonyan@gmail.com M. Navabi * Shahid Bhshti Univrsity, GC Thran Iran navabi.du @gmail.com *author for corrspondnc On rduction of longst accssibility gap in LEO sun-synchronous satllit missions Abstract: Accssibility gaps ar inhrnt proprtis of Low Earth Orbit (LEO) sun-synchronous satllit missions. Long accssibility gaps in satllit missions imply strict in-orbit autonomy rquirmnt, mt by xpnsiv solutions. Thus, mthods to shortn accssibility gaps in satllit missions ar apprciatd by spac mission dsignrs. For that purpos, in this papr, ground sgmnt sit location is mployd as a mchanism to rduc th longst accssibility gaps in LEO sun-synchronous missions. For a givn rpatability cycl, it is shown that longitud of th ground sgmnt dos not affct th accss gaps. Simulation rsults show that incrasing th latitud of ground sgmnt rducs th longst accssibility gaps, spcially in xtrm latituds nar Polar Rgions. To avoid polar ground sgmnts du to thir practical difficultis, mission architcturs with two co-high-latitud ground sgmnts ar proposd. Slction of longitud distanc btwn th two cohigh-latitud ground sgmnts is discussd to furthr rduc th longst accssibility gap in LEO sun-synchronous missions. To show th fasibility of th proposd approach, simulation rsults ar includd for illustration. Kywords: Ground sgmnt location, LEO sun-synchronous satllit, Longst accssibility gap. INTRODUCTION During th last two dcads, thr has bn a significant incras in LEO sun-synchronous missions for various applications (Dittbrnr and McKnight, 199; Anilkumar and Sudhr Rddy, 9). Rgarding narfutur activitis, Ptrsn (1994), in his book Th road to 15, says: most of th nw growth in commrcial spac appars to b in LEO missions. An inhrnt charactristic of LEO missions is that th pattrn of ground sgmnt accss to th satllit is mad up by short and discontinuous accss vnts (Wrtz and Larson, 1999). To tak account of this pculiar accss pattrn, in our prvious paprs (Bonyan Khamsh and Navabi, 1a; 1b) w dvlopd two accss-basd mtrics namly Total Accssibility Duration (TAD) and Longst Accssibility Gap (LAG). Accssibility gaps indicat rquirmnt of autonomous opration (Chstr, 9) and in Bonyan Khamsh and Navabi (1b) it was discussd that LAG mtric is rlatd to minimum rquirmnt of in-orbit autonomy. To obtain LAG mtric in a tim-indpndnt mannr, th concpt of rpatability cycl is mployd. For a givn rpatability cycl, it is discussd that longitud variation of a ground sgmnt has ngligibl ffct on LAG mtric. Yt, our simulation rsults show that incrasing th latitud of ground sgmnt location improvs LAG mtric. It was Rcivd: 1//11 Accptd: 5//11 obsrvd that significant improvmnt in LAG mtric is only achivd for vry-high-latitud ground sgmnts, at ithr Polar Rgions. Still, stablishmnt, oprations and maintnanc of ground sgmnts at Polar Rgions brings in practical difficultis. Thus, ffctivnss of singl-ground-sgmnt architctur is qustionabl. To ovrcom this drawback, mission architcturs with two ground sgmnts ar proposd and a procdur is givn to slct ground sgmnts location with improvd LAG mtric. Th contribution of this papr is to improv LAG mtric for LEO sun-synchronous missions by mploying ground sgmnt sit location. In this mannr, singl and twoground-sgmnt architcturs ar studid. NUMERICAL METHOD OF LAG DETERMINATION Accssibility gap is dfind as th tim gap btwn any two conscutiv vnts of ground sgmnt accss to th satllit, schmatically shown in Fig. 1. Thus, to obtain accssibility gaps in a givn satllit mission, pattrn of ground sgmnt accss to th satllit must b dtrmind. For that purpos, position of th satllit in its orbit must b found. In our prvious work (Bonyan Khamsh and Navabi, 1b), Cowll s diffrntial propagation formula was mployd to obtain position of th satllit. In this papr, w mploy som altrnativ analytical J. Arosp.Tchnol. Manag., São José dos Campos, Vol., No.1, pp. 5-58, Jan. - Apr., 11 5
Khamsh, H.B., Navabi, M. Figur 1: Gaps in ground sgmnt accss to a satllit. rlationships to obtain position vctor of th satllit. In this mthod, Lagrang plantary quations ar mployd with th scond-dgr gravitational potntial function. Lagrang plantary quations can b found in rfrncs such as Capdrou (5) and ar givn by Eq. 1: da 1 R dt na M d 1 1 1 R R dt na 1 M di 1 R R i dt na i cos 1 sin d 1 R dt na i i 1 sin d 1 1 R cos i R dt na 1 i i sin dm 1 n a R 1 R dt na a (1) In Eq. 1, ai,,,,, M is th Kplrian st of orbital lmnts namly smi-major axis, ccntricity, inclination, Right Ascnsion of Ascnding Nod (RAAN), argumnt of prig and man anomaly, rspctivly. Also n is a th man motion, µ is Earth gravitational paramtr and R is prturbing Gopotntial. A scond-dgr prturbing Gopotntial taks account of J ffct i.. dominant prturbation of LEO rgion and thus is mployd in this study. If w only tak account of th scular variations of orbital lmnts, w may obtain an lgant rlationship for th avrag scond-dgr gravitational prturbing function, i.. RJ. Th procdur to obtain RJ is givn by Capdrou (5) and th rsult is givn by Eq. : R J a R 1 J 1 sin 1 i () Whr R is Earth s quatorial radius and J =.186 is a constant rlatd to Earth s oblatnss. Substituting Eq. in Eq. 1 and noting that RJ a a R J, RJ R RJ sin i cos i J, RJ 1 i 1 1 sin i s and RJ R R J J, w obtain th following M analytical rlationships for orbital lmnts of th satllit: a a() t a ct () t ct i i() t i ct R () t nj cos i t t ( ) a 1 R () t nj 5 1 cos i t t 41 ( ) a M() t M n( t t ) Whr n M n 1 41 ( ) R J a cos i 1 (). With th orbital lmnts dtrmind at any tim t, satllit position, i.. r S, may b dtrmind in th gocntric inrtial fram as: È coswcosw - sin Wsinw cos i a r ( t ) ( 1- ) Í = S Í sin Wcosw + coswsinw cosi 1+ cos J ( t) Î Í (4) sin isinw -coswsinw - sin Wcosw cosi sin Wsin i È cos J( t) Í - sin Wsinw + coswcosw cosi -coswsin i Í sin J( t) sin icosw cosi Í Î And ϑ(t), i.. satllit tru anomaly, is dtrmind from Kplr s quation by itrativ mthods such as Nwton- Raphson. In cas of circular orbits, simply ϑ(t)=m(t). With th satllit position dtrmind at any tim t, now ground sgmnt position vctor in th inrtial fram must b dtrmind. Basd on W84 modl, Fig. shows a 54 J. Arosp.Tchnol. Manag., São José dos Campos, Vol., No.1, pp. 5-58, Jan. - Apr., 11
On rduction of longst accssibility gap in LEO sun-synchronous satllit missions ground sgmnt () on th Earth s surfac in th inrtial gocntric quatorial fram. commrcial communication hardwar. From Eq. 7, ris/st tims of th satllit with rspct to a givn ground sgmnt may b dtrmind. Duration of ach accssibility gap is computd by subtracting th accss trmination tim from nxt accss initiation tim. r : ground sgmnt position; θ: local sidral tim of ground sgmnt (in dgrs); R: Earth s quatorial radius; Rφ: radius of curvatur in prim vrtical (Polar axis); Rp: Earth s polar radius; θ G : Grnwich sidral tim (in dgrs). Figur : A ground sgmnt () on th surfac of oblat Earth. At a givn tim t, th ground sgmnt position vctor r () t in th inrtial fram is givn by: r ( t) R cos cos t c ( ) R cos sin ( t) c R sin S Whr φ is ground sgmnt latitud, R = R + Alt, c φ R = ( 1- f ) R, R R φ = S φ 1- ( f - f )sin φ and f =.5 is th Earth flattning factor. Also, Alt is th altitud of ground sgmnt abov th llipsoidal surfac and θ (t) is th instantanous angular distanc btwn th ground sgmnt location and th Vrnal Equinox, masurd in th quatorial plan. With r () t dtrmind, position vctor of th satllit rlativ to th ground sgmnt r () t S_ rl _ is: r () t r () t r () t (6) S_ rl _ S (5) At any givn tim, th satllit is accssibl from th ground sgmnt if Eq. 7 is satisfid: ( t) 9 cos 1 r () t r () t S_ rl _ r () t min (7) S_ rl _ In Eq. 7, r () t and r S_ rl _ ar magnituds of r () t S_ rl _ and r (), t rspctivly. ε accounts for minimum min ground lvation constraint, typically 5-1 dgrs for r LAG MINIMUM TIME INTERVAL TO STUDY? In LEO missions, chronological distribution of th ground sgmnt accss to th satllit varis as th tim intrval of study is incrasd. This brings up an immdiat drawback sinc, in this mannr, LAG will b a tim-dpndnt mtric. Yt, aftr a crtain simulation tim, it is obsrvd that distribution of accss vnts rpats idntically. This tim intrval is calld rpatability cycl and is takn as th minimum tim intrval to obtain tim-indpndnt LAG mtric. For a satllit mission with givn orbit, on may obtain rpatability cycl, i.. D, from Eq. 8: D = R v *( w - W ) n + n + w Whr Rv is intgr numbr of full rvolution in D days, and 7. 951 5 rad/sc is Earth s rotation rat. For sun-synchronous orbits, w hav 1. 99651 7 rad/sc. Also, Δn and ar: n 4( 1 ) nj nj 41 ( ) R a R a cos i 1 5cos i 1 In Eq. 8, only intgr valus of D giv admissibl scnarios. Chronological distribution of accss vnts is idntical aftr ach D days and, conscutivly, LAG mtric is dtrmind in a tim-indpndnt mannr. Thus, rpatability cycl obtaind from Eq. 8 is takn as th tim intrval to study LAG mtric. SITE LOCATION OF GROUND SEGMENT As it was discussd in th sction Numrical mthod of LAG dtrmination, for a mission with givn orbit, LAG mtric dpnds on th ground sgmnt location. In this sction, slction of ground sgmnt location is mployd as a mchanism to improv LAG mtric. Sit location of singl ground sgmnt Location of a ground sgmnt on th trrstrial surfac is givn by thr paramtrs, namly longitud, latitud and (8) J. Arosp.Tchnol. Manag., São José dos Campos, Vol., No.1, pp. 5-58, Jan. - Apr., 11 55
Khamsh, H.B., Navabi, M. altitud rlativ to th man surfac lvl. In this papr, ffct of longitud and latitud of th ground sgmnt on LAG mtric is studid and zro altitud is assumd for all ground sgmnt locations. Effct of ground sgmnt longitud Through xtnsiv simulations for givn rpatability cycls, it was obsrvd that pattrn of accss to LEO sun-synchronous satllit rmains constant as th location of ground sgmnt is altrd in th longitud dirction. In Li and Liu (), it was analytically shown that th Probability Dnsity Function (PDF) of lvation angls for a givn ground sgmnt dos not dpnd on its longitud. Also, th sam rsults wr vrifid by xtnsiv simulations in Modiri and Mohammady (8). Consquntly, slction of ground sgmnt location to rduc LAG mtric must b don in th latitud dirction, only. in Fig.. In accss typ (a), th ground sgmnts accss to th satllit do not ovrlap at all. In accss typs (b) and (c), th ground sgmnts accss to th satllit partially ovrlap ach othr. Finally, in accss typs (d) and (), a ground sgmnt accss to th satllit initiats bfor and xtnds aftr th othr ground sgmnt accss to th satllit. Rgarding ths fiv accss typs, singl ground sgmnt accss vnts must b mrgd accordingly to obtain th ntwork accss pattrn. In th nxt sction, a cas study is discussd to valuat th ffct of ground sgmnt(s) location on LAG mtric. SIMULATION AND RESULTS To valuat th ffct of ground sgmnt sit location on LAG mtric in a givn LEO sun-synchronous mission, a cas study is considrd. Orbital paramtrs of our cas study calld RS-Sat hraftr ar shown in Tabl 1. Effct of ground sgmnt latitud Basd on th rsults obtaind in Li and Liu (), th PDF of lvation angls is symmtrical for both northrn and southrn hmisphrs. Thus, for two ground sgmnts at latitud of ± lat, idntical accss pattrns and LAG mtrics ar obtaind. Du to th fact that most of th lands at th trrstrial surfac rsid in th northrn hmisphr, on may assum that th ground sgmnt rsids in northrn hmisphr. Latitud of th ground sgmnt is changd from Equator to 9 N i.. North Pol. Stp siz for latitud variation may b chosn according to th rquird accuracy. Hr w will adopt 1 dg stps, in northward dirction. Sit location of two ground sgmnts To achiv furthr improvmnt in LAG mtric, twoground-sgmnt mission architcturs ar discussd in this sction. W will assum co-latitud ground sgmnts. From prvious subsctions, longitud of ithr ground sgmnts has ngligibl ffct on LAG mtric. Thus, at constant latitud, only th rlativ longitud distanc btwn th two ground sgmnts must b slctd. In two-ground-sgmnt mission architcturs, car must b takn to mrg accss pattrns of two ground sgmnts in ordr to obtain th combind ntwork accss pattrn. In gnral, squntial accss pattrn of a two-ground-sgmnt ntwork to a satllit may tak any of th fiv typs shown Figur : Possibl squntial typs of two ground sgmnts accss to a satllit. Tabl 1: Orbital charactristics of RS-Sat Paramtr Valu Orbit altitud 655 km Eccntricity Inclination 98.1 dg (sun-synchronous) Local tim of ascnding nod 1: a.m. 56 J. Arosp.Tchnol. Manag., São José dos Campos, Vol., No.1, pp. 5-58, Jan. - Apr., 11
On rduction of longst accssibility gap in LEO sun-synchronous satllit missions Orbital altitud of 655 km has bn slctd to rflct th popularity of th 6-1, km rang for rmot snsing applications (Stphns, ; Sandau, 1). Similarly, local tim of ascnding nod of 1: a.m. has bn purposfully adoptd to rflct th popularity of such architctur for imagry purposs (Stphns, ). From Eq. 8, rpatability cycl of RS-Sat is 1 days. Thus, simulation was carrid out for a 1-day priod from 1 Jan 1 :: to 1 Jan 1 4::. Just as in th cas of prcding paramtrs, a 1-day priod rflcts th uppr-bound of rvisit-tim rquirmnts for various rmot snsing applications (Stphns, ). Singl ground sgmnt scnarios In th first scnario, th ground sgmnt rsids at th Equator and th arbitrary longitud of N. In subsqunt scnarios, latitud of ground sgmnt is incrasd in 1 dg stps. By this rasoning, location of th ground sgmnt in th tnth scnario will b in E 9 N, i.. in th cntr of th arctic rgion. For th 1-day simulation priod, LAG mtric in ach scnario was obtaind and illustratd in Fig. 4, in which it can b radily sn that vry littl improvmnt in LAG mtric is obtaind as th ground sgmnt movs from th Equator to th latitud of 5 N. At th latitud intrval of 6 N 7 N, LAG mtric xprincs additional improvmnt. Significant improvmnt in LAG mtric is achivd only in th 7 N - 9 N latitud intrval, spcially in th uppr-bound limits, i.. th arctic rgion. Howvr, du to advrs nvironmntal conditions and poor accss to rquird oprational rsourcs (.g. lctricity) at affordabl cost, Polar Rgions ar highly disadvantagous for ground sgmnt dploymnt. As a rsult, ffctivnss of singl-ground-sgmnt architctur is qustionabl. Longst accssibility gap (Hours) 14 1 1 8 6 4 1 4 5 6 7 8 9 Latitud of ground sgmnt (Dg) Figur 4: Longst accssibility gap mtric for RS-Sat in singl ground sgmnt scnarios. Two-ground-sgmnt scnarios To achiv furthr improvmnt in LAG mtric, twoground-sgmnt mission architcturs ar xplord in this sction. To avoid difficultis ncountrd in Polar Rgions, w will assum 6 N as th uppr latitud limit for ground sgmnts location. Co-latitud ground sgmnts at 6 N ar considrd. From prvious subsctions, longitud of ithr ground sgmnts has ngligibl ffct on LAG mtric. In th first scnario, location of th first and scond ground sgmnt will b considrd at E 6 N and 4 E 6º N, rspctivly i.. a 1º diffrnc in longitud dirction. In th subsqunt scnarios, longitud diffrnc will b incrasd in 1 stps in th astward dirction. Thus, th longitud distanc btwn th two ground sgmnts in j th scnario i.. ΔL j is (Eq. 9): whr j is th squntial numbr of th scnario. Th 1 incrmnt in longitud diffrnc btwn th two ground sgmnts will rsult in 5 scnarios. Du to circular cross sction of th Earth, only 18 uniqu two-ground-sgmnt scnarios ar takn into account. For th 1-day rpatability cycl, simulations wr carrid out for th 18 dscribd scnarios and pattrn of two-ground-sgmnt ntwork accss to RS-Sat was obtaind for ach scnario. Rsults for LAG mtric for ach scnario ar givn in Fig. 5. As it can b sn from Fig. 5, minimum LAG is xprincd in th 1 th scnario, in which th ground sgmnts rsid at E 6 N and 15 E 6 N, i.. 1 apart in th longitud dirction. In this scnario, LAG mtric is 11549 sconds, i.. hours 1 minuts and 9 sconds. At this point, it must b vrifid that lands 1 apart in th longitud dirction actually xist at th latitud of 6 N ovr th Earth s surfac (for practical applications, th two ground sgmnts must rsid on land not in th sas!). If th prfrrd two-groundsgmnt architctur did not fit into th land distribution ovr th trrstrial surfac, th scnario with scond-bst LAG mtric would b xamind, and so on. It is rcalld that if it was dsird to achiv th sam LAG mtric i.. 11549 sconds by singl ground sgmnt architctur, latitud of th ground sgmnt would b 77.5 N somwhr in th arctic rgions. This vrifis th ffctivnss of th two-ground-sgmnt architctur to improv LAG mtric whil avoiding oprational difficultis of ground sgmnts in vry-high latituds and th arctic rgion. CONCLUSION LAG is an important mtric which is rlatd to minimum rquirmnt of in-orbit autonomy. An analytical approach was adoptd to dtrmin th prscribd mtric. Sit slction of singl and two ground sgmnts to improv LAG mtric (9) J. Arosp.Tchnol. Manag., São José dos Campos, Vol., No.1, pp. 5-58, Jan. - Apr., 11 57
Khamsh, H.B., Navabi, M. Figur 5: Longst accssibility gap mtric for RS-Sat in two-ground-sgmnt scnarios. in LEO sun-synchronous missions was discussd. Our rsults showd that, for singl ground sgmnt, LAG mtric improvs as th ground sgmnt movs to high latituds and Polar Rgions. Also, for two-ground-sgmnt mission architcturs, th rlativ distanc to achiv improvd LAG mtric was obtaind. It was obsrvd that two-groundsgmnt mission architcturs ar ffctiv in that thy offr improvd LAG mtric whil avoiding oprational difficultis of polar ground sgmnts. By mploying th procdurs discussd in this papr, on may dtrmin singl and twoground-sgmnt architcturs to provid accptabl LAG mtric in a givn mission. REFERENCES Anilkumar, A.K., Sudhr Rddy, D., 9, Statistical Conjunction Analysis and Modling of Low-Earth-Orbit Catalogud Objcts, Journal of Spaccraft and Rockts, Vol. 46, No. 1, pp. 16-167. doi: 1.514/1.6976. Bonyan Khamsh, H., Navabi, M., 1a, Dvlopmnt of Mtrics for Ground Sgmnt Sit Location Basd on Satllit Accssibility Pattrn from Ground Sgmnt, Procdings of th 4 th Asia-Pacific Confrnc on Systms Enginring, Klung, Taiwan. Bonyan Khamsh, H., Navabi, M., 1b, Dvlopmnt of Accss-basd Mtrics for Sit Location of Ground Sgmnt in LEO Missions, Journal of Arospac Tchnology and Managmnt, Vol., No., pp. 79-86. doi: 1.58/jatm.1.81. Capdrou, M., 5, Satllits Orbits and Missions, Springr-Vrlag, Brlin, Grmany, 64 p. Chstr, E., 9, Down to Earth systms nginring: Th forgottn ground sgmnt, Acta Astronautica, Vol. 65, No 1-, pp. 6-1. Dittbrnr, G., McKnight, D., 199, Collision Risk in Sunsynchronous Low Earth Orbit, Advancs in Spac Rsarch, Vol. 1, No. 8, pp. 187-19. doi: 1.116/7-1177(9)9589-4. Li, S.Y., Liu, C.H.,, An analytical modl to prdict th probability dnsity function of lvation angls for LEO satllits, IEEE Communications Lttrs, Vol. 6, No. 4, pp. 18-14. Modiri, A., Mohammady, L., 8, Mathmatical Prdiction of Sun-synchronous Polar LEO Satllit Visions for Earth Stations, Procdings of 1 th Intrnational Confrnc on Advancd Communication Tchnology, Kora, pp. 1559-156. Ptrsn, J.L., 1994, Th Road to 15: Profils of th Futur, Wait Group Prss, Cort Madra, CA, USA. Sandau, R., 1, Status and Trnds of Small Satllit Missions for Earth Obsrvation, Acta Astronautica, Vol. 66, No. 1-, pp. 1-1. Stphns, J.P.,, A Novl Intrnational Partnrship: Th Disastr Monitoring Constllation of Small Low Cost Satllits, Procdings of th Unitd Nations Rgional Workshop on th Us of Spac Tchnology for Disastr Managmnt in Asia and th Pacific, Bangkok, Thailand. Wrtz, J.R., Larson, W.J., 1999, Spac Mission Analysis and Dsign, rd Ed., Microcosm Prss, Bloomington, IN, USA, 969 p. 58 J. Arosp.Tchnol. Manag., São José dos Campos, Vol., No.1, pp. 5-58, Jan. - Apr., 11