Sun Synchronous Orbits for the Earth Solar Power Satellite System

Size: px

Start display at page:

Download "Sun Synchronous Orbits for the Earth Solar Power Satellite System"

Frank Nicholson
10 years ago
Views:

1 Sun Synchrnus Orbts fr th Earth Sar Pwr Satt Systm Sm f th mst prmsng rbts fr th Earth Sar Pwr Systm ar crcuar Sun synchrnus rbts whch nvr ntr Earth's shaw. In ths rbts, gravty grant stabz "pwr twrs" w rbt n pans whch ar wthn abut 30 f prpncuar t th EarthSun n an th sar arrays can b st fr nar ptmum pwr captur. Th sar synchrncty f th rbts s caus by th Earth's batnss (.., th J 2 trm n Earth's gptnta). Thr ar a numbr f quantts whch must b cnsr tgthr whn chsng rbts fr th Earth Sar Pwr Systm. Hwvr, th anayss s qut smp. If w chs crcuar Sunsynchrnus rbts as ur basn cnfguratn, th chc f th ncnatn f th rbt trmns th rbta attu ( raus & pr) as w as th spacmnt n ngtu btwn succssv ascnng r scnng ns ( an hnc th stanc btwn succssv ascnng r scnng ns at th quatr). Th chc f ncnatn as trmns th maxmum attu xcursns away frm th ps ma by th gruntrack f satts n th rbt. Pts 1 thrugh 5 hav bn vp wth rspct t crcuar Sun synchrnus Earth rbts. Fgurs 1 an 2 shw th varatn n rbta raus an rbta attu vrsus rbta ncnatn, rspctvy, fr crcuar Sun synchrnus rbts. Fgurs 3 an 4 shw th anguar an nar stancs, rspctvy, btwn succssv ascnng (scnng) ns masur ang th quatr f th Earth vrsus rbta ncnatn fr crcuar Sun synchrnus rbts. Fgur 5 s a pt f th rbta prs f crcuar Sun synchrnus rbts vrsus rbta ncnatn. In rr fr an rbt t b Sun synchrnus, th n n must mv astwar at a rat f n rvutn pr yar. Ths mtn, caus by th batnss f th Earth, s scrb by th quatn J 2 = 3 2 *(R q / p)2 n J 2 *cs() whr p = a( 1 2 ), = 0, J 2 = , R q = km, an s th ncnatn f th rbt. Th rtatn rat f th Earth s gvn by = ra / s. arth

Th sar synchrncty f th rbts s caus by th Earth's batnss (.., th J 2 trm n Earth's gptnta). Thr ar a numbr f quantts whch must b cnsr tgthr whn chsng rbts fr th Earth Sar Pwr Systm.

2 13000 Orbt Raus (km) vs O r12000 b t11000 R a u s 8000 k m Fgur 1. Orbta Raus vrsus Orbta Incnatn fr Crcuar Sun Synchrnus Earth Orbts 6000 Attu (km) vs A t t u k m Fgur 2. Orbta Attu vrsus Orbta Incnatn fr Crcuar Sun Synchrnus Earth Orbts

3 20 Lngtu Chang pr Rv (g) vs D 25 t30 a 35 L 40 n g g Fgur 3. Anguar Dspacmnt pr Rvutn ( Masur Ang th Equatr Ratv t a Rtatng Earth) vrsus Orbta Incnatn fr Crcuar Sun Synchrnus Earth Orbts 2000 A N Dst Wst Ang Equatr pr AN (km) vs Inc (g) t A N k m 6500 Fgur 4. Lnar Dspacmnt pr rvutn Masur Ang th Equatr vrsus Orbta Incnatn fr Crcuar Sun Synchrnus Earth Orbts

Sun Synchrnus Earth Orbts 2000 A N 2500 3000 Dst Wst Ang Equatr pr AN (km) vs Inc (g) t3500 4000 A

4 240 O r 220 b t200 Orbt Pr (mn) vs P180 r m 100 n 80 Fgur 5. Orbta Pr vrsus Orbta Incnatn fr Crcuar Sun Synchrnus Earth Orbts Th fwng facts, whch hav bn vp frm ntrprtatn f ths pts, ar nt. 1. A Sun synchrnus rbts ar rtrgra (.., thy hav ncnatns n th rang Th attu rang cvr by th gruntrack f a Sun synchrnus rbt s ± δ whr δ = (180 ). Ths mans, fr xamp, that n rr fr th grun track t g 60 nrth an suth f th quatr, th ncnatn f th Sun synchrnus rbt wu b 120, r f th gruntrack wr t g 70 nrth an suth f th quatr, th ncnatn f th rbt wu b Assumng that th rbta attus wr that 1000 km wu pruc t much rag, th mnmum ncnatn avaab fr Sun sy;nchrnus rbts w b abut 100. Lwr ncnatns, whch ar csr t par rbts, wu a t Sun synchrnus rbts at attus bw 1000 km. Sun synchrnus rbts havng ncnatns btwn 90 an 96 ar mpssb bcaus th rqur rbta attus ar ss than th raus f th Earth. 4. Sun synchrnus rbts wth ncnatns n th rang ar unaccptab bcaus thr grun tracks nt g far nugh nrth r suth. Fr δ = 30. A rang such that δ 50 s mr rastc frm th pnt f vw f ggraphc cvrag fr pwr transmssn t th surfac f th Earth. As a pnt f rfrnc, Anchrag, Aaska s cat at a attu f abut 60 Nrth.

Ths mans, fr xamp, that n rr fr th grun track t g 60 nrth an suth f th quatr, th ncnatn f th Sun synchrnus rbt wu b 120, r f th gruntrack wr t g 70 nrth an suth f th quatr, th ncnatn f th rbt wu b

5 5. Th csr a crcuar Sun synchrnus rbt s t par, th wr th rbt attu. 6. Sun synchrnus rbts wth grun tracks whch rach frm 50 t 80 nrth an suth (ncnatns btwn 100 an 130 ) w hav attus yng n th rang btwn 1000 km an 4500 km. 7. Sun synchrnus rbts wth ncnatns btwn 100 an 130 hav prs n th rang f 108 mnuts t just vr 188 mnuts. 8. Sun synchrnus rbts wth ncnatns btwn 100 an 130 hav ascnng ns (ratv t th Earth) whch ar 27 t 47 apart, Th crrspnng stancs btwn ascnng ns (masur ang th Earth's quatr) ar btwn 3000 km an 5240km. Atna Gmtrc Cnsratns Th ang btwn th rbt pan f a Sun synchrnus rbt an th EarthSun n w nt rman cnstant. Cnsr th cas f an rbt fr whch, n th at f th wntr sstc (apprxmaty Dc 21st), th ang btwn th rbta pan an th EarthSun n, β, ca th Sun ang, s 90. On ths at, th rbta anguar mmntum vctr f th rbt pnts rcty away frm th Sun. Ths rbt w hav an ncnatn f apprxmaty Th satt's ascnng n w b aha f th Earth ang th Earth's vcty vctr arun th Sun. Th n f ns s n th pan prpncuar t th EarthSun n. Thr mnths atr, at th tm f th vrna qunx (abut March 21st), th ncnatn f th rbt w rman th sam an th n n w hav prcss 90. Th ascnng n w st b "aha" f th Earth but w nt b n th vcty vctr snc th Earth's vcty vctr w nt, at ths tm, n th quatra pan. Th satt's rbta anguar mmntum vctr w hav prcss such that th n f ns st s n th pan prpncuar t th EarthSun n, but th nrthrn part f th rbt pan s ncn twar th Sun. Th ang btwn th rbta pan an th EarthSun n s nw ( ~ 66.5 ). Nt that th ncnatn f th rbt wth rspct t Earth's quatr has nt chang, but th n f ns has prcss 90 urng ths thr mnths. At th tm f th summr sstc, th rbt w agan b n a pan such that th n f ns s n th pan prpncuar t th EarthSun n. Hwvr, th ang btwn th rbta pan an th EarthSun n w nw b abut 43 ( 90 2*23.5 ). Agan, th nrthrn haf f th rbt w b ncn twar th Sun. Earth Shaw Effcts Fgur 6 s a pt f th raus f th shaw f th Earth, masur prpncuar t th EarthSun n an Rsmast, th mnmum cmpnnt f a

Sun synchrnus rbts wth ncnatns btwn 100 an 130 hav prs n th rang f 108 mnuts t just vr 188 mnuts. 8.

6 crcuar Sun synchrnus rbt nrma t th EarthSun n vrsus rbta ncnatn S m a R Rshaw & Rsmast (km) vs p 6400 r 6300 p n6200 c6100 u Fgur 6. Rshaw (th raus f Earth's Shaw) an Rsmast (th Mnmum Crcuar Sun Synchrnus Orbt Cmpnnt Nrma t th EarthSun Ln) vrsus Orbta Incnatn. Th Earth / Sun / rbt gmtry fr Sun Synchrnus rbts wth anguar mmntum vctrs that prjct nt th Earth Sun n (±) s such that rbts wth ncnatns gratr than g nt th Earth's shaw at ast nc pr yar. Sun synchrnus rbts wth anguar mmntum vctrs whch prjct nt th cptc pan at a an ang ø away frm th Earth Sun n g nt th Earth's shaw at ncnatns vn narr t par. Thus, th ncnatns fr Sun synchrnus rbts whch nt g nt th shaw f th Earth must b ss than (ra 9694 km r attus 3316 km). Th prs f ths rbts ar ss than 9500 scns (158 1/3 mnuts). Th anguar spacmnt pr rvutn ratv t th rtatng Earth fr such rbts s 39.6, masur n th quatr ( 39.6 s quvant t 4407 km btwn succssv nrthbun quatr crssngs). As, nt frm Fgur 6 that fr crcuar Sun synchrnus rbts wth ncnatns ss than abut ( s csr), th satt agan gs nt th shaw f th Earth, vn wth th n f ns ang th 6AM 6PM n. Thus, f w ny us rbts that rman n cnstant sunght, ur rbts ar rstrct t

Th Earth / Sun / rbt gmtry fr Sun Synchrnus rbts wth anguar mmntum vctrs that prjct nt th Earth Sun n (±) s such that rbts wth ncnatns gratr than 115.36 g nt th Earth's shaw at ast nc pr yar.

7 < Incnatn < km < Raus < 9694 km 1403 km < Attu < 3316 km mn < Pr < mn 28.5 < Na Dspacmnt * pr rv < km < Na Dspacmnt * pr rv < 4407 km * Na spacmnts ar masur ratv t th surfac f th Earth. Thy ar mnat by th ffct f th rtatn f th Earth (abut 15 pr hur), but as ncu th prcssn u t J2 (n rvutn pr yar). Ths tw ffcts ar n ppst rctns fr Sun synchrnus rbts.

6 3170 km < Na Dspacmnt * pr rv < 4407 km * Na spacmnts ar masur ratv t th surfac f th Earth.

8 Sun Synchrnus Orbt Pwr Transmssn Gmtry Lt us assum that a satt s n a crcuar Sun synchrnus rbt wth attu h an that th raus f th Earth s Rq. Assum that th mnmum vatn (ang abv th hrzn) frm whch a grun statn can rcv pwr s EL. W n t fn th wth f th swath nt whch th satt cu pssby bam pwr, gvn th attu h an th mnmum vatn, EL. W w xprss th wth f th swath bth n anguar masur (g) an n nar masur (km). EL θ h R R Usng th aws f sns, th angs θ, φ, an EL can b fun as functns f th rbta attu, h. If th graphs ar rawn fr th vatn ang takng n th vaus EL = 20 an fr EL = 30, w gt th pts f swath wth n grs an n km shwn bw.

W n t fn th wth f th swath nt whch th satt cu pssby bam pwr, gvn th attu h an th mnmum vatn, EL.

9 70 Swath Ang fr EL = 20 & 30 vs S 65 w a 60 t h55 a50 n g45 40 ( g 25 ) Swath Wth fr EL = 20 & 30 vs S7500 w 7000 a t6500 h 6000 W t h k m

Swath Wth fr EL = 20 & 30 vs S7500 w 7000 a t6500 h 6000 W 5500 5000

tis, cis cunc - cunc - tis, cis tis, cis cunc - tis, func - def - def - tis, U func - def - func - tis, pa - tri pa - tri pa - tri tu - per - tu -

tis, cis cunc - cunc - tis, cis tis, cis cunc - tis, func - def - def - tis, U func - def - func - tis, pa - tri pa - tri pa - tri tu - per - tu - 1 B Ihsu dulcs cuncts [Supr 1] [Supr 2] Tnr B B B B - B - B - Ih - Ih - Ih - su su su cs cs cs cunc - cunc - cunc - Amns, Bblthèqu Cntl L Agn, ms 162 D, ff 2v-10 ts, ts, ts, E-tr - E-tr - E-tr - n p n