A-B-Cs of Sun-Synchronous Orbit Mission Design

Transcription

1 A-B-Cs of Sun-Synhronous Orbi Mission Design Ronald J. Boain Je Propulsion aboraory California nsiue of Tehnology AAS/AAA Spae Fligh Mehanis Conferene Maui, Hawaii 8-12 February 24 9 February 24

2 1 W S F -*.. *.- a.- v & % - n a 1 - $ z > ).- a x * W s 1 ".s! n iu Y r" E E e.- E io 2 e s F d- v e e e e e

3 Earh-Sun Geoery Sheai Earh s orbial MT = Mean oal Tie of Asending Node 9 February 24 MT

4 n n v) n Y x n - F rr v) W > h u v) a r n *, 2 S.- v) W Q n b E & - r E Z b % W 1-2 n W u> h v) W u 6) n = : n S - % n +-J F a 6) 6).. F n N n z (/> <i, a = u> r E h Y- r d ) E CD y) W y) 1 & ) S S, -,, - n n n n +, * w.)lr n - v) v) v) h Y- 8 v. 6 w b r

5 Sun-Synhronous Condiion: nlinaion vs. Aliude (e = ) 1 12? a February 24 h Aliude, k

6 Rekoning Tie ndersanding how ie is rekoned is a oplex subje - Sidereal ie - Apparen solar ie - Mean solar ie Sidereal ie is based on he earh s roaion rae relaive o he sarshernal equinox and is no useful for rekoning ie sine i loses approxiaely 4 inues per day easured in ean solar ie Apparen solar ie is inonvenien sine he sun s oion is no regular wih respe o he bakground sars and an vary >6 in per day - Obliquiy of he elipi, i.e., sun s hange in delinaion - Ellipi earh orbi, i.e., The Equaion of Tie Only ean solar ie based on he ean sun rossing he ean solar eridian is onsisen wih 864 seonds per day The MT for SS-Os is also based on he ean solar eridian 9 February 24

7 Syse Engineering he Mission Design Saed Siene Requireens1 Desires iiaion on he range o a arge; viewing angle onsrains Nuber and disribuion of arges o be observed (for disree arges) Area overage o be provided (for oninuous arges) ~~~ Frequeny wih whih argedareas are o be sapled Sun-lighing ondiions o be provided (for opial easureens) Seasonal onsideraions of observaions Overall duraiodperiod of ie neessary o easure soe Moivaing Objeive or insruen Charaerisi nsruen sensiiviy, resoluion, field of viewkwah-widh, allowable elongaion/ disorion over a fooprin, e. nique geographi arges o be easured Perenage of earh's surfae o be aessible for observaion Allowable ie inerval before a repea observaion is possible Consisen sun shadows for arges Visual aess o Anaria (for exaple) during Anari suer ife expeany for insruens, syse, ission life Traeable Orbi C haraerisilparaeer Orbi aliude Orbi aliude, inlinaion; groundrak grid densiy; groundrak ied poin o ahieve over-fligh of speifi lallon Orbi inlinaion, aliude Orbi aliude Orbi nodal posiion and/or nodal Mean oal Tie; orbi inlinaion Orbi nodal posiion and/or nodal Mean oal Tie; orbi inlinaion Orbi aliude 9 February 24

8 Dela EV Perforane o SS- Aliude NASA EV Perforane Esiaion Curve(s) EO Cirular wih inlinaion Sun- Sy nhronous Please noe ground rules and assupions below.,8,6,4,2,.--. 2,8 2,6 $ 2,4 = 2,2 2, 1,8 1,6 1,4 1,2 9 February , 1,2 1,4 1,6 1,8 2, Aliude &)

9 Orbi Paraeers for SS-Os wih an neger Nuber of Revs in One-Day Five soluions, orresponding o 12, 1, 14, 1, & 16 revs per day, exis over a range of aliudes desired for low earh SS-Os The equaorial aliude for hese soluions ranges beween 2 and 168 k These soluions have oarse GT grids, e., >2 k beween adjaen groundraks - q is he angle subended fro he nadir direion o he adjaen groundrak Alhough ineresing orbis, hey provide only loalized overage Revs per Day, ## 12 Orbial Period, se 72. Equaor Aliude, k Dis bew/ Adj GTs, k (q=1.") (q=6.1") (q=61") 76.OO (y66.7") 4.oo (qz72.7") 9 February 24

10 SS-Os wih Finer GT Grids Nex onsider SS-Os whih repea heir GT in wo-days: - f soluions exis for all inegers beween 12 and 16 for he oneday repea, hen soluions exis for inegers beween 24 and 2 for he wo-day repea: 24, 2, 26, 27, 28, 29,,1, 2 - Apparenly 9 possible soluions A quik alulaion shows ha soluions for 24, 26, 28,, and 2 are degenerae wih 12, for one-day repeas, e., hey have idenially he sae periods, wih he ineger soluions for he oneday repea - Therefore, here are only four new soluions for he wo-day repea, bu hese have 2,27,29, and 1 revs, hereby dereasing he spaing beween nodes a he expense of inreasing he re-visi ie ("aess'l) 9 February 24

11 Noaion for Soluions wih R Revs in D Days Exending he previous reasoning, repea GT orbis an be found for,4,,6,7,... and so forh days Exaple: Thee-day repea orbis 6, 7, 8, 9,4,41,42,4,44,4,46,47,48 Reoving he degenerae soluions yields 8 unique soluions whih repea heir GT in hree-days: 7, 8,4,41,4,44,46,47 A onvenien noaion for one of hese soluions is: D4R = -day repea in exaly 4 revs or D47R = -day repea in exaly 47 revs and so forh Anoher exaple: Seven-day repea orbi soluions => 7D8R, 7D86R, 7D87R,... 7D19R, 7D111 R 9 February 24

12 S % n S a, n..._....._ z? r--- -e# - -' ? 4 _> $* z? E-*

13 Earh-Cenered Coordinae Frae 17 Pole Y Equaor X Sz = MT 9 February 24

14 Analea in Delinaion - Equaion of Tie Spae Annelea o Nov 17-No\ Feb 1 -Feb an Equaion of Tie 9 February 24 Mean Sun a Coordinaes = (,O)

15 a E G s N2 a s 8 W X \ 8 v

16 Aqua Solar Bea-Angle Prediion AQA Predied -- Solar Bea Angle Pos NC# 1 1/7/. No ore NC odeled Bea low M 4 2. G d f 6 r i i i O Jan 24 Jul OC Jan 2 * 2 EOSPM 1. EpohTex () 9 February 24 C : Jan 26

17 Given Spherial Triangle A-B-C, he aw of Cosines gives: Orbi Plane Geoery for Copuing he Tie Spen in Shadow os( 9/2)=os(q)los( p) rr 1."ngular Moenu Y Orbi Plane A X./ 4 9 February 24 Earh Earh's figure

18 Suary SS-Os are defined as low earh orbis whih have a nodal preession rae equal o he earh s Mean Moion - There is a unique oupling beween orbi aliude and inlinaion o ahieve his preession rae as iplied by Eq. 1 - This preession has he effe of aking he posiion of he nodes wih respe o he ean sun reain fixed (o firs order) SS- aliudes an be seleed o provide a repea groundraks in an ineger nuber of revs in an ineger nuber of days Sun-lighing ondiions on he orbi and for observaions ade fro he orbi an be deerined by seleing he MT The paper provides several siple algorihs ha enable he alulaion of aliude (hene inlinaion) and MT o saisfy oon ission requireens 9 February 24

19 n v), 2 Y- O v),,.- - E r 6) 6) F r j - 6) 7 r j 6 -,, 2 8, Y- O Q) v),, -.( ) a E s v