ORBITAL TO GEOCENTRIC EQUATORIAL COORDINATE SYSTEM TRANSFORMATION. x y z. x y z GEOCENTRIC EQUTORIAL TO ROTATING COORDINATE SYSTEM TRANSFORMATION

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1 ORITL TO GEOCENTRIC EQUTORIL COORDINTE SYSTEM TRNSFORMTION z i i i = (coωcoω in Ωcoiinω) (in Ωcoω + coωcoiinω) iniinω ( coωinω in Ωcoi coω) ( in Ωinω + coωcoicoω) in icoω in Ωini coωini coi z o o o GEOCENTRIC EQUTORIL TO ROTTING COORDINTE SYSTEM TRNSFORMTION Th quatoial plan coincid with th plan of th pap. Th ath otat anti-clockwi with angula vlocit Ω. and a a attachd to th ath and otat with it. z i and z a coincid. z i z Ω i i Satllit Obit (2) D. M. M. Dawoud

2 z = co( Ω T ) in( Ω ) T in( Ω co( Ω T T ) ) 1 z i i i ` T i th tim lapd inc th ai coincidd with th i ai. Th valu of Ω T at an tim t, pd in minut aft midnight UT i givn b: ΩT = α g, t dg. Wh α g, i th ight acnion of th Gnwich midian at h UT at Julian da JD and i givn b: 2 α g, = T c Tc dg wh Tc i th lapd tim in Julian cntui btwn h UT on Julian da JD and noon UT on Janua 1, 19. T c = ( JD 24152) / dd.5 to th JD valu ud in thi quation bfo ubtituting in th pviou quation ( inc it i calculatd at h UT). JULIN DYS ND JULIN DTES Standad tim i Unival tim UT (man ola tim at Gnwich obvato na London). tonom u Julian da and Julian dat. Julian da tat at noon. Julian dat tim fnc i 12 noon UT on Janua 1, 4713 C Satllit Obit (21) D. M. M. Dawoud

3 Eampl: Noon on Dcmb 31, 1899 wa th bginning of Julian da 2,415,2 Noon UT on Dcmb 31, 1984 wa th tat of Julian da 2,446,66 :: hou UT on Janua 1, 1985 wa Julian dat 2,446,66.5 JULIN DTES T THE EGINNING OF ECH YER FOR (1986-2) Ya Julian dat Ya Julian dat Dat DY NUMER FOR NOON ON THE LST DY OF ECH MONTH Da No. Lap a Dat Da No. Lap a Jan Jul Fb 28/ ug Mach Spt p Oct Ma Nov Jun Dc Satllit Obit (22) D. M. M. Dawoud

4 Eampl of Julian dat calculation: 1. Find th Julian dat JD coponding to 3 h UT on Oct 11,1986. Oct 11 i da numb = Stat of Oct 11 (h UT) i 284 t 3:: UT i (3/24) =.125 da Da and tim will b dd thi to th Julian dat fo Jan 1, 1986 W gt: 2,4, + 46, = 2,446, Find th Julian dat JD coponding to 15:: h UT on Mach 1, Mach 1 i da numb = 69.5 t 15:: UT i.125 da aft noon Da and tim will b = dd thi to th Julian dat fo Jan 1, 1999 W gt: 2,4, + 51, = 2,451, Satllit Obit (23) D. M. M. Dawoud

5 LOOK NGLE DETERMINTION Dfinition: Look angl a th coodinat to which an ath tation antnna mut b pointd to communicat with th atllit. Local vtical Noth El z Eat zimuth (z) Th angl maud atwad fom gogaphic noth to th pojction of th atllit path on a locall hoizontal plan at th ath tation. Elvation (El) Th angl maud upwad fom th hoizontal plan to th atllit path. Satllit Obit (24) D. M. M. Dawoud

6 Satllit Obit (25) D. M. M. Dawoud THE SUSTELLITE POINT Th point wh a lin dawn fom th cnt of th ath to th atllit pa though th ath ufac. L Th noth latitud of th ubatllit point. l Th wt longitud of th ubatllit point. ] [ co z z L + + = + + = fouth quadant thid quadant ond quadant quadant fit l tan tan 9 c tan 18 ) ( tan L l Subatllit point

7 ELEVTION EVLUTION Satllit Local hoizontal d El Subatllit point (L, l ) Eath tation (L, l ) Cnt of ath co( γ ) = co( L )co( L )co( l l ) + in( L )in( L ) d 2 = co( γ ) Satllit Obit (26) D. M. M. Dawoud

8 El = ψ 9 Uing th law of in : d = in( ψ ) in( γ ) co( El ) = in( γ ) = d 1+ in( γ ) 2 2 co( γ ) Th quation pmit th valuation of th lvation angl fom a knowldg of th ubatllit point and ath tation coodinat. ZIMUTH CLCULTION Th atllit, ub-atllit point and th ath tation li on th am vtical plan. Thfo th azimuth angl can b maud fom th noth diction going atwad towad th ub-atllit point. Th gomt ud fo th calculation dpnd on whth th ub-atllit point i at o wt of th ath tation and which hmiph contain th ub-atllit point and th ath tation. Thi calculation i implifid fo th idal gotationa obit. Satllit Obit (27) D. M. M. Dawoud

9 Pol C Y Pol C Y X X Nothn hmoph, wt of Nothn hmoph, wt of X C Y Pol Y C Pol X Southn hmoph, wt of Southn hmoph, wt of Eith point o point can b th ath tation; th oth mut b th ub-atllit point. i clo to th pol that i na to both point. Point,, and th pol fom a phical tiangl with pola angl C and angl X and Y at th vtic and. Satllit Obit (28) D. M. M. Dawoud

10 C = l l o C = 36 l l Whichv mak C 18 dg Ca 1: t lat on point in th nothn hmiph. L >L i chon to b clo to th noth pol. Th baing X and Y ma b found fom: tan[.5( Y cot(.5c)in[.5( L X )] = co[.5( L + L L )] )] tan[.5( Y + cot(.5c)co[.5( L X )] = in[.5( L + L )] L )] X =.5( Y + X ) +.5( Y X ) Y =.5( Y + X ).5( Y X ) Th lationhip btwn X, Y, and th azimuth z dpnd on th idntit of point and and on Satllit Obit (29) D. M. M. Dawoud

11 thi gogaphical lationhip. Th a givn in th following tabl. Fomula fo calculating th azimuth. t lat on point in th nothn hmiph Sub-atllit point Eath Station Rlation zimuth wt of 36 - Y wt of X wt of Y wt of 36 - X oth point in th outhn hmiph Sub-atllit point Eath Station Rlation zimuth wt of 18 + Y wt of 18 - X wt of 18 - Y wt of 18 + X Satllit Obit (3) D. M. M. Dawoud

12 CLCULTION OF LOOK NGLES FOR GEO-STTIONRY STELLITES Sub-atllit point i at th quato. thfo L =. Th go-nchonou adiu = Km Th ath' adiu = 637 Km Th cntal angl γ i givn b: co( γ ) = co( L )co( l l ) Th ditanc d fom th ath tation to th atllit i givn b: d = 42242[ co( γ )] 1/ 2 Km Th lvation angl i thn givn b: in( γ ) co( El ) = [ co( γ )] 1/ 2 Satllit Obit (31) D. M. M. Dawoud

13 zimuth calculation i impl than th gnal ca, bcau th ub-atllit point li on th quato. W f to th following figu fo thi calculation. χ α E a = l l c c = L L S a G Coniding th half pimt of th tiangl = =.5( a + c + γ ) Th angl a at th vt ma b obtaind fom: in( )in( ) tan 2 α γ c ( ) = 2 in( )in( a) and α = 2 tan 1 in( γ )in( L in( )in( l l Satllit Obit (32) D. M. M. Dawoud

14 γ α E E α γ c c S a G G a S SSP outh-wt of ES SSP outh-at of ES S a γ G c α E G c α E a γ GS SSP noth-wt of ES SSP noth-at of ES Equation fo calculating azimuth fom phical tiangl angl α SSP Sub-atllit point ES Eath Station Situation Equation 1. SSP South-wt of ES z = 18 o + α 2. SSP South-at of ES z = 18 o - α 3. SSP Noth-wt of ES z = 36 o - α 4. SSP Noth-at of ES z = α Satllit Obit (33) D. M. M. Dawoud